Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | #261⋊#3862 |
| Fitting, socle, derived, Hall | C72×C13 ⋊ C3×C4 |
| Hall | C72×#261 ⋊ C3 |
| Hall | C13⋊#3862 ⋊ C4 |
| Hall | #261 ⋊ #3862 |
| Sylow | C72 ⋊ AGL(1,𝔽13) |
| Sylow | C13 ⋊ C4×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C13 | C3×C4 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,7^2,13|a^2=c,f^a=f^5,d^b=d^2,e^b=e^4,f^b=f^3,f^c=f^12125 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 225);