Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C13⋊#64418 |
| unambiguous semidirect product | (C2×C13)⋊#64418 |
| Fitting, socle | C2×C72×C13 ⋊ D3 |
| derived, Hall | C13×#3862 ⋊ C22 |
| Hall | C72×C13 ⋊ C2×D3 |
| Hall | #3862 ⋊ C2×D13 |
| Sylow | C72 ⋊ C2×D39 |
| Sylow | C13 ⋊ C2×#64418 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C13⋊#64418 |
| commutator, hypocenter | C13×#3862 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C13 | D3 |
| LCS | G ▷ C13×#3862 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
268 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 312);