Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C211 |
| direct product | C2×C8×B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | #120 |
| commutator | C23 | C24×C8 |
| Frattini, cosocle | C23×C4 | C25 |
| socle | C23 | C4×#120 |
| prime radical | C22×B(4,𝔽2) | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8 ◁ C24×C8 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
9881 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #106×B(4,𝔽2), #102×B(4,𝔽2), #97×B(4,𝔽2), … |
| maximal normal subgroup of | #106×B(4,𝔽2), #102×B(4,𝔽2), #97×B(4,𝔽2), … |
Past the SmallGroups library coverage — no SmallGroups id.