Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4 |
| direct product | C2×#356069 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | D42 |
| commutator | C2×C4 | C23×C42 |
| Frattini, cosocle | C23×C4 | C25 |
| socle | C23 | #2358 |
| prime radical | C22×#585 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
19171 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | #72340605, #72340669, C2×#72226293, … |
| maximal normal subgroup of | #72340605, #72340669, C2×#72226293, … |
Past the SmallGroups library coverage — no SmallGroups id.