Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C29 · Schur multiplier (H2) = C235 |
| direct product | C24×#585 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C24 |
| commutator, Frattini, cosocle | C2 | C29 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C2 ▷ C1 | |
8373525 conjugacy classes of subgroups; only the 8283765 normal subgroups are shown.
This group has 8373525 conjugacy classes of subgroups — too many to draw. Only its 8283765 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 256 |
544 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.