Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | D3×#87520 |
| Fitting | C3×#585 ⋊ C2×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×#1020 |
| commutator, cosocle, hypocenter | C3×#997 | C23 |
| Frattini | C2 | C2×D3×#1020 |
| Fitting | C3×#585 | C2×D3 |
| socle | C2×C3 | C22×#1020 |
| LCS | G ▷ C3×#997 | |
| UCS | C1 ◁ C4 | |
3150 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 3150 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
78 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#11715828, D3×#11714184, D3×#11714162 |
| maximal normal subgroup of | D3×#11715828, D3×#11714184, D3×#11714162 |
| maximal quotient of | C4×D3×#5935 |
Past the SmallGroups library coverage — no SmallGroups id.