Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C23 ⋊ #107 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^5,23|a^2=d,b^2=c,d^2=e,b^a=bd,f^a=f^22,d^b=de124 conjugacy classes — view the full character table.
| maximal subgroup of | #107×D23, C2×#10624989, #13092452, … |
| maximal normal subgroup of | #107×D23, C2×#10624989, #13092452, … |
| maximal quotient of | #13092169, #13092179, #13092242, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 13);