Finite Group DatabasebetaFinite Group Databasebeta| order | 2646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C7 |
| direct product | C3×C3⋊#64425 |
| Fitting, socle | C32×C72 ⋊ C2×C3 |
| derived | C3×C72 ⋊ C2×C32 |
| Hall | C32×#3862 ⋊ C2 |
| Sylow | C72 ⋊ C32×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#64425 |
| commutator, cosocle, hypocenter | C3×C72 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72 | C2×C3 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C3 | |
146 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 126 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72222210, C3×D3×#64425, D3×C3⋊#64425, … |
| maximal normal subgroup of | C3×#72222210, C3×D3×#64425, D3×C3⋊#64425, … |
Past the SmallGroups library coverage — no SmallGroups id.