Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216×C4 |
| direct product | C2×#607558 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C24 |
| commutator | C23 | C25×C4 |
| Frattini, cosocle | C24 | C26 |
| prime radical | C28 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
424709 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72268550, C2×#72268558, C2×#72235090, … |
| maximal normal subgroup of | C2×#72268550, C2×#72268558, C2×#72235090, … |
| maximal quotient of | C2×#72296142, C2×C4×#14679, #72303065, … |
Past the SmallGroups library coverage — no SmallGroups id.