Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C42 · Schur multiplier (H2) = C223 |
| direct product | C25×#95 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C28 | C22 |
| commutator | C2 | C25×C42 |
| Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C28 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
1060245 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1024 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×#392, C23×#14757, C23×D4×#95, … |
| maximal normal subgroup of | C25×#392, C23×#14757, C23×D4×#95, … |
| maximal quotient of | C23×D4×#95, C26×#95 |
Past the SmallGroups library coverage — no SmallGroups id.