Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211×C4 |
| direct product | C2×#417790 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #15258 |
| commutator, Frattini, cosocle | C23×C4 | C25 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
23183 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
118 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216935, C2×#72215912, C2×#72215972, … |
| maximal normal subgroup of | C2×#72216935, C2×#72215912, C2×#72215972, … |
| maximal quotient of | C2×#72226729, C2×#72239627 |
Past the SmallGroups library coverage — no SmallGroups id.