Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | C22×#34670 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C24 |
| commutator, Frattini, cosocle | C23 | C27 |
| prime radical | C22×#2410 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
114821 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#7684390, C22×#7966357, C22×#7630336, … |
| maximal normal subgroup of | C22×#7684390, C22×#7966357, C22×#7630336, … |
| maximal quotient of | C22×C4×#2410, C22×#612700, C22×#607665, … |
Past the SmallGroups library coverage — no SmallGroups id.