Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| isoclinism | isoclinic class of #5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C7 |
| direct product | C3×C13×#5997 |
| Fitting, socle, Hall | C3×C72×C13 ⋊ C4 |
| derived, Sylow | C72 ⋊ C3×C4×C13 |
| Hall | C72×C13 ⋊ C3×C4 |
| Hall | C3×C72 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | #5997 |
| commutator, hypocenter | C72 | C3×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C4 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C13 | |
56 conjugacy classes of subgroups.
624 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#5997⋊C9, #37524498, #37524499, … |
| maximal normal subgroup of | C13×#5997⋊C9, #37524498, #37524499, … |
| maximal quotient of | C9×C13×#5997, C32×C13×#5997, C3×C13×C3⋊#5997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 321);