Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#486341 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #18194 |
| commutator, Frattini, cosocle | C2×M16 | C25 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×#131 ◁ G | |
| LECS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
6218 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
94 conjugacy classes — view the full character table.
| maximal subgroup of | #72280512, C2×#72231620, C2×#72231715, … |
| maximal normal subgroup of | #72280512, C2×#72231620, C2×#72231715, … |
Past the SmallGroups library coverage — no SmallGroups id.