Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C92 · Schur multiplier (H2) = C2×C9 |
| direct product | D32×C92 |
| Fitting, Sylow | C32×C92 ⋊ C22 |
| derived | C32 ⋊ C22×C92 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C92 | D32 |
| commutator, hypocenter | C32 | C22×C92 |
| Frattini | C32 | C32×D32 |
| Fitting | C32×C92 | C22 |
| socle, cosocle | C34 | C22×C32 |
| prime radical | C32×D32 | C32 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C92 | |
978 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 978 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
729 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D32×#6900, D32×C9⋊D9, D32×C9×D9 |
| maximal normal subgroup of | D32×#6900, D32×C9⋊D9, D32×C9×D9 |
Past the SmallGroups library coverage — no SmallGroups id.