Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C22×#33657 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#481 |
| commutator, Frattini, cosocle | C2×C8 | C26 |
| prime radical | C22×#3058 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ C23×#131 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
12773 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#500349, C22×#7623148, C22×#500164 |
| maximal normal subgroup of | C22×#500349, C22×#7623148, C22×#500164 |
Past the SmallGroups library coverage — no SmallGroups id.