Finite Group DatabasebetaFinite Group Databasebeta| order | 5250 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×#6953 |
| Fitting, derived, Hall | C7×H(3,𝔽5) ⋊ C2×C3 |
| Hall | ΓL(1,𝔽8)×H(3,𝔽5) ⋊ C2 |
| Hall | C7×#6953 ⋊ C3 |
| Sylow | H(3,𝔽5) ⋊ C2×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×#6953 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | ΓL(1,𝔽8)×C5⋊D5 |
| commutator, Fitting, cosocle, hypocenter | C7×H(3,𝔽5) | C2×C3 |
| socle | C5×C7 | C3×C5⋊D5 |
| LCS | G ▷ C7×H(3,𝔽5) | |
| UCS | C1 ◁ C5 | |
120 conjugacy classes of subgroups.
110 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#6953, ΓL(1,𝔽8)×#92539, #72218985 |
| maximal normal subgroup of | AGL(1,𝔽7)×#6953, ΓL(1,𝔽8)×#92539, #72218985 |
Past the SmallGroups library coverage — no SmallGroups id.