Finite Group DatabasebetaFinite Group Databasebeta| order | 5880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×D5×ΓL(1,𝔽8)⋊D7 |
| Fitting, socle | C2×C5×C72 ⋊ C22×C3 |
| derived, Hall | C5×C72 ⋊ C23×C3 |
| Hall | C2×D5×C7⋊D7 ⋊ C3 |
| Hall | C5×C7×ΓL(1,𝔽8) ⋊ C23 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C22×D5 |
| Sylow | C72 ⋊ C22×C3×D5 |
| Sylow | C5 ⋊ C22×ΓL(1,𝔽8)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×ΓL(1,𝔽8)⋊D7 |
| commutator, cosocle, hypocenter | C5×C72 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72 | C22×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C2 | |
320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 210 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×ΓL(1,𝔽8)⋊D7, C2×D5×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×ΓL(1,𝔽8)⋊D7, C2×D5×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.