Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#14274262 |
| Fitting, socle, derived, Hall | C22×C72×C13 ⋊ C3 |
| Hall | C72×C13 ⋊ A4 |
| Hall | C22×C72 ⋊ C13⋊C3 |
| Hall | C22×C13 ⋊ #3861 |
| Sylow | C72 ⋊ C22⋊(C13⋊C3) |
| Sylow | C13 ⋊ C22⋊#3861 |
| Sylow | C22 ⋊ #14274262 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C72×C13 | C3 |
| LCS | G ▷ C22×C72×C13 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
Polycyclic presentation:
3,2^2,7^2,13|b^a=c,c^a=bc,d^a=d^4,e^a=e^4,f^a=f^3852 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 353);