Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C215×C4 |
| direct product | C2×C42×#120 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C42 | C23 |
| commutator | C22 | C24×C42 |
| Frattini, cosocle | C24 | C26 |
| prime radical | C23×#120 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
96813 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72280386, C2×C4×D4×#120, C2×#120×#127, … |
| maximal normal subgroup of | C2×#72280386, C2×C4×D4×#120, C2×#120×#127, … |
| maximal quotient of | C2×#95×#120, C22×C42×#120, C2×C4×#14694 |
Past the SmallGroups library coverage — no SmallGroups id.