Order = 25015379558400 = 220.36.52.7.11.17.
Mult = 1.
Out = 2.


Porting notes

Fully copied from version 2. 30/7/06.

Standard generators

Standard generators of O10(2) are a, b where a is in class 2A, b is in class 5B, ab has order 33 and abababb has order 18. Alternatively: a is in class 2A, b is in class 5B, ab has order 33 and abab4 has order 3.

Standard generators of O10(2):2 are c, d where c is in class 2E, d has order 11 and cd has order 36.


Representations

Representations of O10(2)

Representations of O10(2):2


Maximal subgroups

Maximal subgroups of O10(2)

Subgroup Order Index Programs/reps
28:O8(2)
S8(2)
21+12:(U4(2) S3)
(3 O8+(2)):2
26+8:(3 A8)
23+12:(L3(2) A5)
A12
3 U5(2)
(A5 A8):2
(S3 S3 U4(2)):2

Maximal subgroups of O10(2):2

Subgroup Order Index Programs/reps
O10-(2)
28:O8-(2):2
S8(2) × 2
21+12:(U4(2):2 × S3)
S3 × O8+(2):2
26+8:(S3 × A8)
23+12:(L3(2) × S5)
S12
M12:2
(3 × U5(2)):2
S5 × S8
(S3 × S3):2 × U4(2):2