Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C28×C42 |
| direct product | C2×#123482 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | #386 |
| commutator | C2×C4 | C2×C43 |
| Frattini, cosocle | C24×C4 | C24 |
| prime radical | C26 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C2 ▷ C1 | |
14077 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72219669, #72317064, C2×#72239567, … |
| maximal normal subgroup of | C2×#72219669, #72317064, C2×#72239567, … |
Past the SmallGroups library coverage — no SmallGroups id.