Finite Group DatabasebetaFinite Group Databasebeta| order | 1260 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| direct product | ΓL(1,𝔽8)×A5 |
| unambiguous semidirect product | C7⋊(C3×A5) |
| unambiguous semidirect product | (C7×A5)⋊C3 |
| Fitting, Sylow | C7 ⋊ C3×A5 |
| socle, derived | C7×A5 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C7×A5 | C3 |
| Fitting, cosocle | C7 | C3×A5 |
| LCS | G ▷ C7×A5 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 35 |
25 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1260, 61);