Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×#204555 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C22×D4 |
| commutator | C22×C4 | C24×C4 |
| Frattini, cosocle | C2×C42 | C25 |
| socle | C24 | C22×C22⋊C4 |
| prime radical | C2×#34936 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C2×C4×#117 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
11505 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72318402, C2×#72318352, C2×#72318415 |
| maximal normal subgroup of | C2×#72318402, C2×#72318352, C2×#72318415 |
Past the SmallGroups library coverage — no SmallGroups id.