Order = 4080 = 24.3.5.17.
Mult = 1.
Out = 4.

Porting notes

Porting incomplete.

Standard generators

Standard generators of L2(16) are a, b where a has order 2, b has order 3 and ab has order 15.

Standard generators of L2(16):2 are c, d where c is in class 2B, d has order 4 and cd has order 15.

Standard generators of L2(16):4 are e, f where e is in class 2A, f is in class 4B/B', ef has order 8, eff has order 6 and efeffefff has order 4.

Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File
L2(16) 〈〈 a, b | some conditions 〉〉 Download

Presentations

L2(16) a, b | a2 = b3 = (ab)15 = ((ab)5(ab−1)3)2 = 1 〉 Details
L2(16):2 c, d | c2 = d4 = [c, dcd]2 = cd(cdcd2)2(cd2cd)2cdcd−1 = 1 〉 Details
L2(16):4 e, f | e2 = f4 = (ef)8 = (ef2)6 = (ef)3(ef−1)3(ef)2(ef−1)2(ef)2ef2 = 1 〉 Details

Conjugacy classes

Conjugacy classes of L2(16)

Conjugacy class Centraliser order Power up Class rep(s)
1A4 080 aa
2A16 a
3A15 (ab)5
5A15 (abab)3
5B15 (ab)3
15A15 ab
15B15 abababab
15C15 abab
15D15 abababababababab
17A17 ababb
17B17 ababbababbababbababb
17C17 ababbababb
17D17 ababbababbababbababbababbababbababbababb
17E17 (ababbababb)3
17F17 (ababbababbababbababbababbababbababbababb)3
17G17 (ababbababbababbababb)3
17H17 (ababb)3

Conjugacy classes of L2(16):2

Conjugacy class Centraliser order Power up Class rep(s)
1A8 160 cdcdcddcdcdcddcdcdcddcdcdcdd
2A32 cdcdcddcdcdcdd
3A30 cdcddcdcdd
5A30 cddcddcddcdd
5B30 cddcdd
15A15 cd
15C15 cdcd
17A17 (cdcdcdddcdcdcddd)3
17C17 (cdcdcddd)3
17E17 cdcdcdddcdcdcddd
17G17 cdcdcddd
2B120 (cdcdd)3
4A8 cdcdcdd
6A6 cdcdd
10A10 cdd
10B10 (cdd)3

Conjugacy classes of L2(16):4

Conjugacy class Centraliser order Power up Class rep(s)
1A16 320 (ef)8
2A64 (ef)4
3A60 (efeff)4
5A30 (efefeffeff)2
15A15 efefeff
17A17 (efefff)3
17E17 efefff
2B240 (efeff)6
4A16 (ef)2
6A12 (efeff)2
10A10 efefeffeff
4B24 (efeff)3
4B'24 (efeff)9
8A8 ef
8A'8 (ef)3
12A12 (efeff)7
12A'12 efeff