Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C29 |
| direct product | A4×#2403 |
| Fitting, Sylow | C22×#2403 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×A4 |
| commutator, socle, cosocle | C25 | C24×C3 |
| Fitting | C22×#2403 | C3 |
| hypercenter | #2403 | A4 |
| hypocenter | C22 | C3×#2403 |
| LCS | G ▷ C25 ▷ C22 | |
| UCS | C1 ◁ C23 ◁ #2403 | |
21906 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | #72259267 |
| maximal normal subgroup of | #72259267 |
Past the SmallGroups library coverage — no SmallGroups id.