Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C29 · Schur multiplier (H2) = C237 |
| direct product | C26×#120 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C28 | C23 |
| commutator, Frattini, cosocle | C22 | C29 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C28 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
136608424 conjugacy classes of subgroups; only the 9782632 normal subgroups are shown.
This group has 136608424 conjugacy classes of subgroups — too many to draw. Only its 9782632 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 512 |
896 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.