Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C13 ⋊ C3×C4 |
| Hall | C7×C7⋊#261 ⋊ C3 |
| Hall | C13×#3861 ⋊ C4 |
| Hall | #3861 ⋊ #261 |
| Sylow | C72 ⋊ C3×#261 |
| Sylow | C13 ⋊ #10596873 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C13 | C3×C4 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,7^2,13|a^2=c,d^a=d^6,f^a=f^5,d^b=d^2,e^b=e^2,f^c=f^1291 conjugacy classes — view the full character table.
| maximal subgroup of | #37524863, #37524891, #37524892, … |
| maximal normal subgroup of | #37524891, #37524892, ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊#261, … |
| maximal quotient of | #37524442, C3×#21439627, C3⋊#21439627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 196);