Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ C22⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#11744762 |
| commutator | C2×C113 | C2×C16 |
| Fitting | C2×C4×C113 | C8 |
| socle | C22×C113 | C2×C8 |
| hypercenter | C2×C4 | #11744762 |
| hypocenter | C113 | C22⋊C16 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^18,g^b=g^112,g^d=g^98,g^e=g^112152 conjugacy classes — view the full character table.
| maximal subgroup of | #28407597, #28407598, #28407609, … |
| maximal normal subgroup of | #28407597, #28407598, #28407609, … |
| maximal quotient of | #28407596, #28407608, #28407617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1646);