Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C29 |
| direct product | C2×#146392 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×C42 |
| commutator | C2×C4 | C22×C4×C8 |
| Frattini, cosocle | C23×C8 | C24 |
| socle | C24 | C2×#97 |
| prime radical | C26 | M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C23×C8 ▷ C4 ▷ C2 ▷ C1 | |
7017 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72249948, C2×#72250246, C2×#72256837, … |
| maximal normal subgroup of | C2×#72249948, C2×#72250246, C2×#72256837, … |
Past the SmallGroups library coverage — no SmallGroups id.