Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C28 |
| direct product | C2×C3×#144364 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | #10336 |
| commutator, Frattini, cosocle | C23×D4 | C24×C3 |
| LCS | G ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C24×C3 ◁ C24×C3×D4 ◁ G | |
13582 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×B(5,𝔽2) |
| maximal normal subgroup of | C2×C3×B(5,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.