Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | M32×D113 |
| Fitting | M32×C113 ⋊ C2 |
| Sylow | C113 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D113 |
| commutator, socle | C2×C113 | C22×C8 |
| Fitting | M32×C113 | C2 |
| hypercenter | M32 | D113 |
| hypocenter | C113 | C2×M32 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C8 ◁ M32 | |
90 conjugacy classes of subgroups.
1160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #347×D113, #28392177, #349×D113, … |
| maximal normal subgroup of | #347×D113, #28392177, #349×D113, … |
| maximal quotient of | #346×D113, M32×Dic113, #28392167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 962);