Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C113 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#11744762 |
| commutator, socle | C2×C113 | C2×C16 |
| Fitting | C8×C113 | C8 |
| hypercenter | C8 | #11744762 |
| hypocenter | C113 | M64 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C4 ◁ C8 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^18,g^b=g^112,g^c=g^98,g^d=g^112152 conjugacy classes — view the full character table.
| maximal subgroup of | #28407664, #28407665, #28407805, … |
| maximal normal subgroup of | #28407664, #28407665, #28407805, … |
| maximal quotient of | #28407660, #28407667, #28407673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1658);