Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C3 · Schur multiplier (H2) = C215 |
| direct product | C2×C3×#60399 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C22×#120 |
| commutator, Frattini, cosocle | C23 | C26×C3 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C23×C3×D4 ◁ G | |
46784 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
348 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | C2×D3×#60399 |
| maximal subgroup of | C2×D3×#60399, C2×C3×#11715839, C2×C3×#6499874, … |
| maximal normal subgroup of | C2×D3×#60399, C2×C3×#6499874, C2×C3×#133839 |
Past the SmallGroups library coverage — no SmallGroups id.