Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D43×ΓL(1,𝔽8)⋊D7 |
| unambiguous semidirect product | (ΓL(1,𝔽8)×D43)⋊D7 |
| Fitting, socle, derived, Hall | C72×C43 ⋊ C22×C3 |
| Hall | D43×C7⋊D7 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8)×C43 ⋊ C22 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×D43 |
| Sylow | C72 ⋊ C2×C3×D43 |
| Sylow | C43 ⋊ C2×ΓL(1,𝔽8)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C43 | C22×C3 |
| LCS | G ▷ C72×C43 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 903 |
506 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 239);