Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216 |
| direct product | C22×D4×#102 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C22×D4 |
| commutator | C2×C4 | C25×C4 |
| Frattini, cosocle | C22×C4 | C26 |
| prime radical | C23×D42 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ C23×C4×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
72229 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#6575490, C22×D4×#442, C22×#6575492, … |
| maximal normal subgroup of | C22×#6575490, C22×D4×#442, C22×#6575492, … |
| maximal quotient of | C22×D4×#360, C22×D4×#361, C2×#72318415, … |
Past the SmallGroups library coverage — no SmallGroups id.