Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C13×C49 ⋊ C3×C4 |
| Hall | C49⋊#261 ⋊ C3 |
| Hall | C13⋊C3×C49 ⋊ C4 |
| Sylow | C49 ⋊ AGL(1,𝔽13) |
| Hall | C13⋊C3 ⋊ Dic49 |
| Sylow | C13 ⋊ C3×Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C49 | C3×C4 |
| Frattini | C7 | #11763979 |
| socle | C7×C13 | C3×Dic7 |
| LCS | G ▷ C13×C49 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,7,13,7|a^2=c,d^7=f^6,d^a=d^6f,e^a=e^8,f^a=f^6,e^b=e^3,e^c=e^12205 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 27);