Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#92280⋊C2 |
| Fitting, Sylow | C3×#6908 ⋊ C22 |
| derived | #6908 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92280⋊C2 |
| commutator, cosocle, hypocenter | #6908 | C22×C3 |
| Frattini | C32 | C3×D3×C3⋊D3 |
| Fitting | C3×#6908 | C22 |
| socle | C32 | ((C3⋊D3)⋊C3)⋊D3 |
| LCS | G ▷ #6908 | |
| UCS | C1 ◁ C3 | |
569 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 569 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | #72243786, C3×#72221983, #72243868, … |
| maximal normal subgroup of | C3×#72221983, D3×#92280⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.