Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C213×C4 |
| direct product | C2×C4×#1438 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C4 | C23 |
| commutator | C23 | C23×C42 |
| Frattini, cosocle | C25 | C25 |
| prime radical | C25×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C25 ▷ C1 | |
82117 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4×#1438, #72311816, #72312029, … |
| maximal normal subgroup of | C2×D4×#1438, #72311816, #72312029, … |
| maximal quotient of | C4×#154094 |
Past the SmallGroups library coverage — no SmallGroups id.