Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C215 |
| direct product | C2×#72236754 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | #2403 |
| commutator | C25 | C24×C4 |
| Frattini, cosocle | C26 | C25 |
| prime radical | C22×#35346 | C2 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C27 ◁ G | |
| LECS | G ▷ C26 ▷ C22 ▷ C1 | |
249876 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72246416, C2×C4×#245225 |
| maximal normal subgroup of | C2×C4×#245225 |
Past the SmallGroups library coverage — no SmallGroups id.