Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C7 |
| direct product | C13×#10596885 |
| Fitting, socle, Hall | C72×C13 ⋊ Dic3 |
| derived, Hall | #3862 ⋊ C4×C13 |
| Hall | C13×#3862 ⋊ C4 |
| Sylow | C72 ⋊ Dic3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #10596885 |
| commutator, hypocenter | #3862 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C72×C13 | Dic3 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C13 | |
36 conjugacy classes of subgroups.
130 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#10596885⋊C3, #37524856, #37524857, … |
| maximal normal subgroup of | C13×#10596885⋊C3, #37524856, #37524857, … |
| maximal quotient of | C13×#13183544, C3×C13×#10596885, C13×C3⋊#10596885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 243);