Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#200876 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#386 |
| commutator | C42 | C24×C4 |
| Frattini, cosocle | C2×C42 | C25 |
| prime radical | C2×#60798 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
11171 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72215564, C2×#72213685, #72240365, … |
| maximal normal subgroup of | C2×#72215564, C2×#72213685, #72240365, … |
Past the SmallGroups library coverage — no SmallGroups id.