Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| isoclinism | isoclinic class of #3862 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2×C7 |
| direct product | C22×C13×#3862 |
| Fitting, socle, Hall | C22×C72×C13 ⋊ C3 |
| derived, Sylow | C72 ⋊ C22×C3×C13 |
| Hall | C72×C13 ⋊ C22×C3 |
| Hall | C22×C72 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C13 | #3862 |
| commutator, hypocenter | C72 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C13 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22×C13 | |
100 conjugacy classes of subgroups.
988 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#3862⋊A4, #37525410, #37525411, … |
| maximal normal subgroup of | C13×#3862⋊A4, #37525410, #37525411, … |
| maximal quotient of | C22×C13×#89205, C2×D3×C13×#3862, C22×C3×C13×#3862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 359);