Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | #41×#525 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C42 | C25 |
| commutator, Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
87077 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72304735, AGL(1,ℤ/8)×#525 |
| maximal normal subgroup of | #72304735, AGL(1,ℤ/8)×#525 |
| maximal quotient of | #72306267 |
Past the SmallGroups library coverage — no SmallGroups id.