Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C2×#10574839 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C27 |
| socle | C23 | C24×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
287185 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72310282, C2×#72251071, #72314842, … |
| maximal normal subgroup of | C2×#72310282, C2×#72251071, #72314842, … |
| maximal quotient of | C2×#72239231, C2×#72257831 |
Past the SmallGroups library coverage — no SmallGroups id.