Finite Group DatabasebetaFinite Group Databasebeta| order | 1260 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic15 |
| unambiguous semidirect product | C3⋊(Dic5×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×Dic15)⋊C3 |
| derived | C3×C5×C7 ⋊ C3×C4 |
| Hall | C3×C5×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C3×ΓL(1,𝔽8) ⋊ Dic5 |
| Hall | C5×C7 ⋊ C3×Dic3 |
| Sylow | C7 ⋊ C3×Dic15 |
| Sylow | C5 ⋊ Dic3×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)×D15 |
| commutator, hypocenter | C3×C5×C7 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C5×C7 | C2×C3 |
| prime radical | C2×C3×C5×ΓL(1,𝔽8) | C2 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 420 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1260, 46);