Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C49⋊#261 |
| Fitting, Hall | C3×C13×C49 ⋊ C4 |
| derived, Hall | C13×C49 ⋊ C3×C4 |
| Hall | C3×C49 ⋊ #261 |
| Sylow | C49 ⋊ C3×#261 |
| Hall | C3×C13 ⋊ Dic49 |
| Sylow | C13 ⋊ C3×Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C49⋊#261 |
| commutator, hypocenter | C13×C49 | C3×C4 |
| Frattini | C7 | C3×C7⋊#261 |
| Fitting | C3×C13×C49 | C4 |
| socle | C3×C7×C13 | Dic7 |
| LCS | G ▷ C13×C49 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
597 conjugacy classes — view the full character table.
| maximal subgroup of | #37524082, (C49⋊C9)⋊#261, #37524087, … |
| maximal normal subgroup of | #37524082, (C49⋊C9)⋊#261, #37524087, … |
| maximal quotient of | C9×C49⋊#261, C32×C49⋊#261, C3×C3⋊(C49⋊#261), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 51);