Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#494758 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#1898 |
| commutator | C22×C4 | C24×C4 |
| Frattini, cosocle | C2×#41 | C25 |
| prime radical | C2×#60367 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ C23×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
17563 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72231746, #72281209, #72310502, … |
| maximal normal subgroup of | C2×#72231746, #72281209, #72310502, … |
| maximal quotient of | #72281209, #72282657, #72282838, … |
Past the SmallGroups library coverage — no SmallGroups id.