Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | AGL(1,ℤ/8)×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C25×D4 |
| commutator, Frattini, cosocle | C2×C4 | C27 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C4×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Only the 32031 normal subgroups are shown; non-normal subgroups are omitted.
187 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×B(4,𝔽2), #72316255, #72316283, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×B(4,𝔽2), #72316255, #72316283, … |
| maximal quotient of | #72283791, H(5,𝔽2)×#442 |
Past the SmallGroups library coverage — no SmallGroups id.