Finite Group DatabasebetaFinite Group Databasebeta| order | 7776 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C33 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | #127×#6900 |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C22×C32 | C23×C33 |
| prime radical | C33×#127 | C32 |
| LCS | G ▷ C22×C32 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ G | |
3780 conjugacy classes of subgroups; only the 1170 normal subgroups are shown.
This group has 3780 conjugacy classes of subgroups — too many to draw. Only its 1170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
714 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #127×#92314, #72220022 |
| maximal normal subgroup of | #127×#92314, #72220022 |
Past the SmallGroups library coverage — no SmallGroups id.