Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C224 |
| direct product | C23×#2846 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C26 | C24 |
| commutator, Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C26 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
4304845 conjugacy classes of subgroups; only the 60245 normal subgroups are shown.
This group has 4304845 conjugacy classes of subgroups — too many to draw. Only its 60245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
352 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.