Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×ΓL(1,𝔽8)×D43⋊C7 |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8)×D43)⋊C7 |
| Fitting, socle | C2×C7×C43 ⋊ C2×C3×C7 |
| derived | C7×C43 ⋊ C22×C3×C7 |
| Hall | C2×C7×D43⋊C7 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C43⋊C7 ⋊ C22 |
| Hall | C7×C43⋊C7 ⋊ C22×C3 |
| Hall | C2×D43 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C43 ⋊ C22×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)×D43⋊C7 |
| commutator, cosocle, hypocenter | C7×C43 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C43 | C2×C3×C7 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C2 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 602 |
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 194);