Finite Group DatabasebetaFinite Group Databasebeta| order | 14520 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×#72213666 |
| Hall | C3×#11757246 ⋊ C5 |
| Hall | C3×#10597243 ⋊ D4 |
| Hall | #11757246 ⋊ C3×C5 |
| Hall | #10597243 ⋊ C3×D4 |
| Hall | C3×C112 ⋊ C5×D4 |
| Sylow | C112 ⋊ C3×C5×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #11925892⋊C2 |
| commutator, cosocle | C2×C112 | C22×C3×C5 |
| Frattini | C2 | C3×#11925892⋊C2 |
| Fitting, socle | C2×C3×C112 | C22×C5 |
| hypocenter | C112 | C3×C5×D4 |
| LCS | G ▷ C2×C112 ▷ C112 | |
| UCS | C1 ◁ C2×C3 | |
228 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
129 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72213693, D3×#72213666, #72247328 |
| maximal normal subgroup of | C3×#72213693, D3×#72213666, #72247328 |
Past the SmallGroups library coverage — no SmallGroups id.