Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | C3×#14579330 |
| Fitting, socle, Hall | C3×C72×C13 ⋊ C4 |
| derived, Hall | C72×C13 ⋊ C3×C4 |
| Hall | C3×C72 ⋊ #261 |
| Sylow | C72 ⋊ C3×#261 |
| Hall | C3×C13 ⋊ #5997 |
| Sylow | C13 ⋊ C3×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14579330 |
| commutator, hypocenter | C72×C13 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C4 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
489 conjugacy classes — view the full character table.
| maximal subgroup of | #37524493, #37524494, #37524497, … |
| maximal normal subgroup of | #37524493, #37524494, #37524497, … |
| maximal quotient of | C9×#14579330, C32×#14579330, C3×C3⋊#14579330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 322);