Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C212 |
| direct product | C2×#392954 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C4 | C24 |
| commutator | C24 | C24×C4 |
| Frattini, cosocle | C23×C4 | C25 |
| socle | C25 | C23×C4 |
| prime radical | C23×#121 | C4 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
19237 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72237137, C2×#72237132, C2×#72237122 |
| maximal normal subgroup of | C2×#72237137, C2×#72237132, C2×#72237122 |
Past the SmallGroups library coverage — no SmallGroups id.