Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#196858 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C22×C22⋊C4 |
| commutator | C22×C4 | C24×C4 |
| Frattini, cosocle | C23×C4 | C25 |
| prime radical | C2×#36614 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C26×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
43339 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #72260355, C2×#72231199, C2×#72234285, … |
| maximal normal subgroup of | #72260355, C2×#72234285, #72261538, … |
| maximal quotient of | #72261036 |
Past the SmallGroups library coverage — no SmallGroups id.