Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C215×C4 |
| direct product | C2×C4×D4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C24 |
| commutator | C22 | C24×C42 |
| Frattini, cosocle | C24 | C26 |
| prime radical | C25×D4 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
88545 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72298087, C2×D4×#2433, C2×#72280492, … |
| maximal normal subgroup of | C2×#72298087, C2×D4×#2433, C2×#72280492, … |
| maximal quotient of | #72309058, C22×C4×D4×C22⋊C4, C2×D4×C22⋊#95, … |
Past the SmallGroups library coverage — no SmallGroups id.