Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C211 |
| direct product | C2×#123531 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | #127 |
| commutator | C22×C4 | C22×C42 |
| Frattini, cosocle | C24×C4 | C24 |
| socle | C24 | #392 |
| prime radical | C27 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C2 ▷ C1 | |
28133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72239235, C2×#72236790, C2×#72237226, … |
| maximal normal subgroup of | C2×#72239235, C2×#72236790, C2×#72237226, … |
| maximal quotient of | C2×#72268042 |
Past the SmallGroups library coverage — no SmallGroups id.