Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C212 |
| direct product | C22×A4×#120 |
| Fitting, Sylow | C24×#120 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×A4 |
| commutator, cosocle | C24 | C25×C3 |
| Frattini | C22 | C25×A4 |
| Fitting | C24×#120 | C3 |
| socle | C26 | C23×C3 |
| hypercenter | C22×#120 | A4 |
| hypocenter | C22 | C22×C3×#120 |
| LCS | G ▷ C24 ▷ C22 | |
| UCS | C1 ◁ C24 ◁ C22×#120 | |
101510 conjugacy classes of subgroups; only the 1668 normal subgroups are shown.
This group has 101510 conjugacy classes of subgroups — too many to draw. Only its 1668 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #120×GL(2,ℤ/4), A42×#120 |
| maximal normal subgroup of | #120×GL(2,ℤ/4), A42×#120 |
Past the SmallGroups library coverage — no SmallGroups id.