Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C23 ⋊ #103 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^5,23|a^2=c,b^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^22,d^b=de124 conjugacy classes — view the full character table.
| maximal subgroup of | #103×D23, C2×#10625017, #13092412, … |
| maximal normal subgroup of | #103×D23, C2×#10625017, #13092412, … |
| maximal quotient of | Q8⋊(C23⋊C8), #13092154, #13092163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 41);