Finite Group DatabasebetaFinite Group Databasebeta| order | 9216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×#72230852 |
| Fitting | C2×C3×#62817 ⋊ D3 |
| derived | C3×#11710730 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊#87588 |
| commutator, cosocle, hypocenter | C3×#11710730 | C22 |
| Frattini | C22 | C2×C3⋊#87588 |
| Fitting | C2×C3×#62817 | D3 |
| socle | C23×C3 | #87588 |
| LCS | G ▷ C3×#11710730 | |
| UCS | C1 ◁ C23 | |
42482 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 42482 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#72209641 |
| maximal normal subgroup of | C2×D3×#72209641 |
Past the SmallGroups library coverage — no SmallGroups id.