Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C4×C23 ⋊ C2 |
| Sylow | C23 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D23 |
| commutator, socle, cosocle | C22×C23 | C23 |
| Fitting | C22×C4×C23 | C2 |
| prime radical | C2×C22⋊D23 | C2 |
| hypercenter | C22×C4 | D23 |
| hypocenter | C23 | #123 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 368 |
Polycyclic presentation:
2^5,23|c^2=e,b^a=be,c^a=cd,f^a=f^22190 conjugacy classes — view the full character table.
| maximal subgroup of | #13092606, #123×D23, C2×#10625100, … |
| maximal normal subgroup of | #13092606, #123×D23, C2×#10625100, … |
| maximal quotient of | #13092280, #13092290, #13092296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 124);