Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C28 |
| direct product | C3×#394321 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C2×#392 |
| commutator, Frattini, cosocle | C23×C4 | C24×C3 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C24×C3×C4 ◁ G | |
6524 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
204 conjugacy classes — view the full character table.
| Fitting subgroup of | D3×#394321, #72255066 |
| maximal subgroup of | D3×#394321, #72255066, C3×#72214076 |
| maximal normal subgroup of | D3×#394321, #72255066, C3×#72214076 |
Past the SmallGroups library coverage — no SmallGroups id.