Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#130786 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #8375 |
| commutator | C22×C8 | C23×C4 |
| Frattini, cosocle | C2×#131 | C24 |
| prime radical | C2×#61089 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×#131 ◁ G | |
| LECS | G ▷ C2×#131 ▷ C2×C4 ▷ C2 ▷ C1 | |
6245 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
94 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72231719, C2×#72231714, #72313675, … |
| maximal normal subgroup of | C2×#72231719, C2×#72231714, #72313675, … |
Past the SmallGroups library coverage — no SmallGroups id.