Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C22⋊Q8×AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C24×D4 |
| commutator, Frattini, cosocle | C22×C4 | C26 |
| prime radical | C23×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×C4×C22⋊Q8 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
17389 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
154 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 | #72306068 |
Past the SmallGroups library coverage — no SmallGroups id.