Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C212 |
| direct product | C2×#354188 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C4 | C24 |
| commutator | C23 | C23×C42 |
| Frattini, cosocle | C23×C4 | C25 |
| socle | C25 | C23×C4 |
| prime radical | C24×D4 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
20437 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72237135, C2×#72237131, C2×#72237122 |
| maximal normal subgroup of | C2×#72237135, C2×#72237131, C2×#72237122 |
| maximal quotient of | C2×#72239256, #72320654, #72322207 |
Past the SmallGroups library coverage — no SmallGroups id.