Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C113 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#90673 |
| commutator | C2×C113 | C2×C42 |
| Fitting | C22⋊C4×C113 | C4 |
| socle | C22×C113 | C22×C4 |
| hypercenter | C22⋊C4 | #90673 |
| hypocenter | C113 | #405 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,d^2=f,g^a=g^98,c^b=cf,g^d=g^112320 conjugacy classes — view the full character table.
| maximal subgroup of | #28406332, C2×#20299562, #28407134, … |
| maximal normal subgroup of | #28406332, C2×#20299562, #28407134, … |
| maximal quotient of | #28405775, #28405779, #28405785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1513);