Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11744762 |
| commutator, socle | C2×C113 | C22×C8 |
| Fitting | Q8×C113 | C8 |
| hypercenter | Q8 | #11744762 |
| hypocenter | C113 | #504 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,d^2=e,e^2=f,g^a=g^18,c^b=cf,g^b=g^112,g^c=g^112,g^d=g^98,g^e=g^112110 conjugacy classes — view the full character table.
| maximal subgroup of | #28407792, #28407793, #28407794, … |
| maximal normal subgroup of | #28407792, #28407793, #28407794, … |
| maximal quotient of | #28407736, #28407746, #28407766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1671);