Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#14268630 |
| Fitting | C4×C8×C113 ⋊ C2 |
| Sylow | C113 ⋊ C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D113 |
| commutator | C2×C113 | C2×C42 |
| Frattini | C2×C4 | C22×D113 |
| Fitting | C4×C8×C113 | C2 |
| socle | C22×C113 | C22×C4 |
| hypercenter | C4×C8 | D113 |
| hypocenter | C113 | C4×M16 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
142 conjugacy classes of subgroups.
1832 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14268630, #28388853, #28388860, … |
| maximal normal subgroup of | C8×#14268630, #28388853, #28388860, … |
| maximal quotient of | C8×#14268630, #28388860, #28388868, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 499);