Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×#6438015 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#2410 |
| commutator, Frattini, cosocle | C22×C4 | C26 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
43045 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72236873, #72313048, #72313162, … |
| maximal normal subgroup of | C2×#72236873, #72313048, #72313162, … |
| maximal quotient of | #72310598, #72311499, C2×#72251071, … |
Past the SmallGroups library coverage — no SmallGroups id.