Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211×C4 |
| direct product | C2×#493512 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C22×D8 |
| commutator | C2×C8 | C24×C4 |
| Frattini, cosocle | C22×C8 | C25 |
| prime radical | C25×D8 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C25×C4 ◁ C25×C8 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
43701 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216453, C2×#72231308, C2×#72231322, … |
| maximal normal subgroup of | C2×#72216453, C2×#72231308, C2×#72231322, … |
| maximal quotient of | C2×#72280536, #72318443 |
Past the SmallGroups library coverage — no SmallGroups id.