Finite Group DatabasebetaFinite Group Databasebeta| order | 4320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C22×C3 |
| direct product | C5×#11724027 |
| derived | (C22⋊A4)⋊C9 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #11724027 |
| commutator, cosocle, hypocenter | (C22⋊A4)⋊C9 | C2×C5 |
| Frattini | C3 | C5×A4⋊S4 |
| Fitting, socle | C24×C3×C5 | C3⋊D3 |
| LCS | G ▷ (C22⋊A4)⋊C9 | |
| UCS | C1 ◁ C5 | |
328 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#72213207, D5×#11724027 |
| maximal normal subgroup of | C5×#72213207, D5×#11724027 |
Past the SmallGroups library coverage — no SmallGroups id.