Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C23×#2121 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C2×#99 |
| commutator | C23 | C25×C4 |
| Frattini, cosocle | C2×D4 | C26 |
| prime radical | C23×#534 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C26 ◁ C25×D4 ◁ G | |
| LECS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
52101 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#147567, C22×#147819, C23×#33551, … |
| maximal normal subgroup of | C22×#147567, C22×#147819, C23×#33551, … |
| maximal quotient of | #72240299 |
Past the SmallGroups library coverage — no SmallGroups id.