Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C3⋊(#4175⋊C3) |
| Fitting | C2×C3×#6909 ⋊ C2 |
| derived | C34 ⋊ C22×C32 |
| Sylow | C3×#6909 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(#4175⋊C3) |
| commutator, cosocle, hypocenter | C34 | C22×C32 |
| Frattini | C32 | C2×C32×C3⋊D3 |
| Fitting | C2×C3×#6909 | C2 |
| socle | C2×C32 | C3×(C3⋊D3)⋊C3 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
1102 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221887, C2×#72221889, C2×#72221892, … |
| maximal normal subgroup of | C2×#72221892, C2×#72221895 |
| maximal quotient of | C2×#72221889 |
Past the SmallGroups library coverage — no SmallGroups id.