Order = 174182400 = 212.35.52.7.
Mult = 2 × 2.
Out = S3.

Porting notes

Porting incomplete. Needs attention. Standard generators have many comments.

Standard generators

Standard generators of O8+(2) are a, b where a is in class 2E, b is in class 5A, ab is in class 12F/G and ababababbababbabb has order 8. Alternatively: a has order 2, b has order 5, ab has order 12, abb has order 15 and ababababbababbabb has order 8.

Standard generators of 2.O8+(2) are preimages A, B where B has order 5, ABB has order 15 and B is in class +5A. Alternatively: B has order 5, ABB has order 15 and ABABB has order 15.

Standard generators of 22.O8+(2) are preimages A, B where B has order 5 and ABB has order 15.

Standard generators of O8+(2):2 are c, d where c is in class 2F, d is in class 10BC and cd has order 18. Alternatively: c is in class 2F, d has order 10, cd has order 18 and cdd has order 30.

Standard generators of 2.O8+(2).2 are preimages C, D where CD(CD4)3 has order 3.

Presentations

Group Presentation Link
O8+(2):2 〈 c, d | c2 = d10 = (cd)18 = [c,d]2 = [c,d2]2 = [c,d5]4 = [c,d3]3 = [c,d4]3 = (cd2)2(cd4)2cd2(cd−4)2cd4 = (cd3cd4)7 = 1 〉 Details

Representations

Representations of O8+(2)