Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C9 · Schur multiplier (H2) = C24×C3 |
| direct product | #120×C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, cosocle | C22×C32 | C23×C32 |
| commutator | C22×C3 | C23×C3×C9 |
| prime radical | C32×#120 | C32 |
| LCS | G ▷ C22×C3 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ G | |
1105 conjugacy classes of subgroups; only the 364 normal subgroups are shown.
This group has 1105 conjugacy classes of subgroups — too many to draw. Only its 364 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #120×#6900, #72220121 |
| maximal normal subgroup of | #120×#6900, #72220121 |
Past the SmallGroups library coverage — no SmallGroups id.