Finite Group DatabasebetaFinite Group Databasebeta| order | 14520 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×#20300008 |
| Fitting, socle | C2×C3×C112 ⋊ C22×C5 |
| derived, Hall | C3×C112 ⋊ C23×C5 |
| Hall | C2×D33⋊D11 ⋊ C5 |
| Hall | C3×#10597243 ⋊ C23 |
| Hall | #10597243 ⋊ C22×D3 |
| Sylow | C112 ⋊ C22×C5×D3 |
| Sylow | C3 ⋊ C2×#11925892⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #20300008 |
| commutator, cosocle, hypocenter | C3×C112 | C23×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C112 | C22×C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C2 | |
356 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#11925892⋊C2, #72247295, #72247308 |
| maximal normal subgroup of | C2×D3×#11925892⋊C2, #72247295, #72247308 |
| maximal quotient of | #72247308 |
Past the SmallGroups library coverage — no SmallGroups id.