Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×ΓL(1,𝔽8)⋊Dic7 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(Dic7×C43) |
| derived, Sylow | C72 ⋊ C3×C4×C43 |
| Hall | C43×C7⋊Dic7 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8)×C43 ⋊ C4 |
| Hall | C72×C43 ⋊ C3×C4 |
| Hall | C7⋊Dic7 ⋊ C3×C43 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C4×C43 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3612 |
1892 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 139);