Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#500003 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #23960 |
| commutator, Frattini, cosocle | C22×C8 | C25 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ C2×#2929 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
6409 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213937, #72250326, #72250694, … |
| maximal normal subgroup of | C2×#72213937, #72250326, #72250694, … |
| maximal quotient of | #72252898, #72257121, #72307266, … |
Past the SmallGroups library coverage — no SmallGroups id.