Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | D3×#92262 |
| Fitting, Sylow | C3×C9⋊H(3,𝔽3) ⋊ C22 |
592 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #72254049, #72254050, #72254051, … |
| maximal normal subgroup of | D3×3−1+2×(C3⋊D3)⋊C3, D3×D9⋊((C3⋊D3)⋊C3) |
| maximal quotient of | #72254049, #72254050, #72254051, … |
Past the SmallGroups library coverage — no SmallGroups id.