Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| isoclinism | isoclinic class of #3862 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C7 |
| direct product | C4×C13×#3862 |
| Fitting, Hall | C4×C72×C13 ⋊ C3 |
| derived, Sylow | C72 ⋊ C3×C4×C13 |
| Hall | C72×C13 ⋊ C3×C4 |
| Hall | C4×C72 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C13 | #3862 |
| commutator, hypocenter | C72 | C3×C4×C13 |
| Frattini | C2 | C2×C13×#3862 |
| Fitting | C4×C72×C13 | C3 |
| socle | C2×C72×C13 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C4×C13 | |
60 conjugacy classes of subgroups.
988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 140);