Finite Group DatabasebetaFinite Group Databasebeta| order | 7440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | D4×AGL(1,𝔽31) |
| Fitting | D4×C31 ⋊ C2×C3×C5 |
| Hall | D4×D31⋊C5 ⋊ C3 |
| Hall | D4×D31⋊C3 ⋊ C5 |
| Hall | D4×D31 ⋊ C3×C5 |
| Hall | (C31⋊C3)⋊C5 ⋊ C2×D4 |
| Hall | ΓL(1,𝔽32) ⋊ C2×C3×D4 |
| Hall | C31⋊C3 ⋊ C2×C5×D4 |
| Sylow | C31 ⋊ C2×C3×C5×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×AGL(1,𝔽31) |
| commutator, socle, cosocle | C2×C31 | C23×C3×C5 |
| Fitting | D4×C31 | C2×C3×C5 |
| hypercenter | D4 | AGL(1,𝔽31) |
| hypocenter | C31 | C2×C3×C5×D4 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ D4 | |
216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 124 |
155 conjugacy classes — view the full character table.
| maximal subgroup of | S4×AGL(1,𝔽31), C2×D4×AGL(1,𝔽31) |
| maximal normal subgroup of | C2×D4×AGL(1,𝔽31) |
| maximal quotient of | C2×D4×AGL(1,𝔽31), #72277886 |
| automorphism group of | Dic62, D124, C2×Dic31 |
| holomorph of | C4×C31 |
Past the SmallGroups library coverage — no SmallGroups id.