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 | C7×#63271 ⋊ C4 |
| Sylow | C72 ⋊ AGL(1,𝔽13) |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C13 | C3×C4 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,7^2,13|a^2=c,e^a=e^6,f^a=f^5,d^b=d^2,f^b=f^9,f^c=f^1299 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊#11763981, #37524891, #37524894, … |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊#11763981, #37524891, #37524894, … |
| maximal quotient of | #37524474, C3×#21439659, C3⋊#21439659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 228);