Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×#3862 ⋊ C4 |
| Hall | C72×C13 ⋊ Dic3 |
| Hall | #3862 ⋊ Dic13 |
| Sylow | C72 ⋊ Dic39 |
| Sylow | C13 ⋊ #10596868 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C13⋊#64418 |
| commutator, hypocenter | C13×#3862 | C4 |
| Fitting, socle | C2×C72×C13 | D3 |
| LCS | G ▷ C13×#3862 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,7^2,2|a^2=f,b^a=b^2,c^a=c^12,d^a=d^2e^3,e^a=d^6e^5,d^b=d^4e^4,e^b=e^2268 conjugacy classes — view the full character table.
| maximal subgroup of | #37524679, #37524680, #37524683, … |
| maximal normal subgroup of | #37524679, #37524680, #37524683, … |
| maximal quotient of | #37524378, C3×#21439563, C3⋊#21439563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 132);