Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | C2×#10585859 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D8 |
| commutator, Frattini, cosocle | C8 | C27 |
| socle | C22 | C24×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×#41 ◁ C23×#131 ◁ G | |
| LECS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
82881 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72286071, C2×#72307105 |
| maximal normal subgroup of | C2×#72286071, C2×#72307105 |
Past the SmallGroups library coverage — no SmallGroups id.