Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C42 · Schur multiplier (H2) = C218×C42 |
| direct product | C23×C4×#117 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C42 | C22 |
| commutator | C2 | C25×C42 |
| Frattini, cosocle | C23 | C27 |
| prime radical | C27 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
185461 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#514210, C23×C4×#525, C23×#35274, … |
| maximal normal subgroup of | C22×#514210, C23×C4×#525, C23×#35274, … |
Past the SmallGroups library coverage — no SmallGroups id.