Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic43⋊C7 |
| unambiguous semidirect product | (ΓL(1,𝔽8)×Dic43)⋊C7 |
| derived | C7×C43 ⋊ C3×C4×C7 |
| Hall | C7×Dic43⋊C7 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C43⋊C7 ⋊ C4 |
| Hall | C7×C43⋊C7 ⋊ C3×C4 |
| Hall | Dic43 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C43 ⋊ C4×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)×D43⋊C7 |
| commutator, hypocenter | C7×C43 | C3×C4×C7 |
| Fitting, socle, cosocle | C2×C7×C43 | C2×C3×C7 |
| prime radical | C2×ΓL(1,𝔽8)×C43⋊C7 | C2 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1204 |
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 90);