Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212 |
| direct product | C22×#13348 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×D4 | C25 |
| prime radical | C23×B(4,𝔽2) | C2 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C25 ◁ C24×D4 ◁ G | |
| LECS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
24417 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#498927, C22×#498931, C22×#501097, … |
| maximal normal subgroup of | C22×#498927, C22×#498931, C22×#501097, … |
| maximal quotient of | #72263819, #72318608 |
Past the SmallGroups library coverage — no SmallGroups id.