Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×#14274263 |
| Fitting, socle, Hall | C22×C72×C13 ⋊ C3 |
| derived, Hall | C72×C13 ⋊ C22×C3 |
| Hall | C22×C72 ⋊ C13⋊C3 |
| Hall | C22×C13 ⋊ #3861 |
| Sylow | C72 ⋊ C22×C13⋊C3 |
| Sylow | C13 ⋊ C22×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #14274263 |
| commutator, hypocenter | C72×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C13 | C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C22 | |
200 conjugacy classes of subgroups.
860 conjugacy classes — view the full character table.
| maximal subgroup of | #37525405, #37525407, A4×#14274263, … |
| maximal normal subgroup of | #37525405, #37525407, A4×#14274263, … |
| maximal quotient of | C22×#19153200, C2×D3×#14274263, C22×C3×#14274263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 364);