Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C43 · Schur multiplier (H2) = C27×C42 |
| direct product | C2×#180797 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C42 | C24 |
| commutator | C22 | C22×C43 |
| Frattini, cosocle | C2×C42 | C25 |
| socle | C24 | C22×C42 |
| prime radical | C25 | C2×C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
7229 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72318410, C2×#72318392, #72323091 |
| maximal normal subgroup of | C2×#72318410, C2×#72318392, #72323091 |
Past the SmallGroups library coverage — no SmallGroups id.