Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×C3×#21776 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | #2308 |
| commutator | C23 | C24×C3×C4 |
| Frattini, cosocle | C24 | C25×C3 |
| prime radical | C2×C3×#3484 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C25×C3 ◁ G | |
10544 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#6499874, C2×C3×#139743, C2×C3×#139750 |
| maximal normal subgroup of | C2×C3×#6499874, C2×C3×#139743, C2×C3×#139750 |
Past the SmallGroups library coverage — no SmallGroups id.