Finite Group DatabasebetaFinite Group Databasebeta| order | 5040 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| direct product | D5×SL(2,𝔽8) |
| Fitting, Sylow | C5 ⋊ C2×SL(2,𝔽8) |
| socle, derived | C5×SL(2,𝔽8) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C5×SL(2,𝔽8) | C2 |
| Fitting, cosocle | C5 | C2×SL(2,𝔽8) |
| LCS | G ▷ C5×SL(2,𝔽8) | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
36 conjugacy classes — view the full character table.
| maximal subgroup of | A5×SL(2,𝔽8) |
| maximal quotient of | Dic5×SL(2,𝔽8) |
Past the SmallGroups library coverage — no SmallGroups id.