Finite Group DatabasebetaFinite Group Databasebeta| order | 630 |
| isoclinism | isoclinic class of D5×ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D5×ΓL(1,𝔽8) |
| unambiguous semidirect product | C5⋊(C2×C3×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×D5)⋊C32 |
| unambiguous semidirect product | (C3×C7×D5)⋊C3 |
| Fitting, socle | C3×C5×C7 ⋊ C2×C3 |
| derived, Hall | C5×C7 ⋊ C2×C32 |
| Hall | C3×C5×ΓL(1,𝔽8) ⋊ C2 |
| Hall | C7×D5 ⋊ C32 |
| Sylow | C7 ⋊ C32×D5 |
| Sylow | C5 ⋊ C2×C3×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C5×C7 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7 | C2×C3 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 105 |
60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(630, 14);