Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#152049 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #12693 |
| commutator | C2×C42 | C23×C4 |
| Frattini, cosocle | C2×#127 | C24 |
| prime radical | C2×#60644 | C2 |
| LCS | G ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C24×C4 ◁ C22×#535 ◁ G | |
| LECS | G ▷ C2×#127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
7391 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
82 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213428, #72250924, #72250928, … |
| maximal normal subgroup of | C2×#72213428, #72250924, #72250928, … |
| maximal quotient of | #72282793, C2×#72231262, C22×#152049, … |
Past the SmallGroups library coverage — no SmallGroups id.