Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#64423⋊C2 |
| unambiguous semidirect product | #64423⋊(C2×C13) |
| unambiguous semidirect product | #64424⋊(C2×C13) |
| Fitting, socle, Hall | C72×C13 ⋊ C22×C3 |
| derived, Sylow | C72 ⋊ C22×C3×C13 |
| Hall | C13×D72 ⋊ C3 |
| Hall | C13×#3861 ⋊ C22 |
| Hall | D72 ⋊ C3×C13 |
| Hall | #3861 ⋊ C22×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #64423⋊C2 |
| commutator, hypocenter | C72 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C72×C13 | C22×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C13 | |
104 conjugacy classes of subgroups.
247 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 176);