Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14268661 |
| Fitting | C4×C113 ⋊ C16 |
| Sylow | C113 ⋊ C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14268661 |
| commutator, socle | C2×C113 | C2×C16 |
| Fitting | C4×C113 | C16 |
| hypercenter | C4 | #14268661 |
| hypocenter | C113 | C4⋊C16 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ C4 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^40,g^d=g^18,g^e=g^98,g^f=g^11268 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#14268661, Q8⋊#14268661, #28407838, … |
| maximal normal subgroup of | D4⋊#14268661, Q8⋊#14268661, #28407838, … |
| maximal quotient of | #28407838, #28407839, (C2×#14268661)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1676);