Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | SD16×#525 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D4 |
| commutator, Frattini, cosocle | C22×C4 | C26 |
| socle | C23 | C24×D4 |
| prime radical | D4×#525 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C4×#525 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
17765 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×#525 |
| maximal normal subgroup of | AGL(1,ℤ/8)×#525 |
| maximal quotient of | #72306155 |
Past the SmallGroups library coverage — no SmallGroups id.