Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×#72225017 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C23×D8 |
| commutator, Frattini, cosocle | C22×C8 | C26 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C22×C4×#41 ◁ C22×C8×#41 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
60756 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72225133 |
| maximal normal subgroup of | C2×#72225133 |
| maximal quotient of | C2×#72225018 |
Past the SmallGroups library coverage — no SmallGroups id.