Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C210 |
| direct product | C2×#146479 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #1781 |
| commutator | C22×C4 | C22×C42 |
| Frattini, cosocle | C23×D4 | C24 |
| prime radical | C25×D4 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25 ◁ C25×D4 ◁ G | |
| LECS | G ▷ C23×D4 ▷ C22 ▷ C2 ▷ C1 | |
21953 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72218521, C2×#72219159, D3×#146479, … |
| maximal normal subgroup of | C2×#72218521, C2×#72219159, #72314478 |
| maximal quotient of | D3×#146479, C2×#72238685 |
Past the SmallGroups library coverage — no SmallGroups id.