Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | C2×#72249419 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C24×D4 |
| commutator, Frattini, cosocle | C22×C4 | C27 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C2×#36624 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
177580 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
296 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.