Finite Group DatabasebetaFinite Group Databasebeta| order | 7432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D929 |
| unambiguous semidirect product | C929⋊C23 |
| unambiguous semidirect product | (C2×C929)⋊C22 |
| Fitting, socle | C22×C929 ⋊ C2 |
| derived, Sylow | C929 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D929 |
| commutator, hypocenter | C929 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C929 | C2 |
| LCS | G ▷ C929 | |
| UCS | C1 ◁ C22 | |
32 conjugacy classes of subgroups.
1864 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28415427, C2×C4×D929, D4×D929, … |
| maximal normal subgroup of | #28415427, C2×C4×D929, D4×D929, … |
| maximal quotient of | C2×C4×D929, C22×Dic929, D4×D929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7432, 12);