Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C2×#6383891 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C8 | C24 |
| commutator | C23 | C25×C4 |
| Frattini, cosocle | C22×C4 | C26 |
| socle | C24 | C24×C4 |
| prime radical | C2×#34681 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C8 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
23537 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4×#2929, C2×#72318330, #72321510, … |
| maximal normal subgroup of | C2×D4×#2929, C2×#72318330, #72321510, … |
| maximal quotient of | C2×#72318317 |
Past the SmallGroups library coverage — no SmallGroups id.