Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C218 |
| direct product | C2×C4×#32898 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×#120 |
| commutator | C24 | C25×C4 |
| Frattini, cosocle | C25 | C26 |
| socle | C24 | C22×#120 |
| prime radical | C22×#32898 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C26×C4 ◁ G | |
| LECS | G ▷ C25 ▷ C2 ▷ C1 | |
505002 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
392 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×#11715850, C2×C4×#245225 |
| maximal normal subgroup of | C2×C4×#245225 |
| maximal quotient of | C2×#72317393 |
Past the SmallGroups library coverage — no SmallGroups id.