Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211×C4 |
| direct product | C2×#186614 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C2×#120 |
| commutator | C42 | C24×C4 |
| Frattini, cosocle | C2×C42 | C25 |
| prime radical | C23×D42 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
56465 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72310284, C2×#72310286, C2×#72310287, … |
| maximal normal subgroup of | C2×#72310284, C2×#72310286, C2×#72310287, … |
Past the SmallGroups library coverage — no SmallGroups id.