Finite Group DatabasebetaFinite Group Databasebeta| order | 23328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | D3×#72210295 |
| Fitting, socle | C35 ⋊ C22×SL(2,𝔽3) |
| derived | C3×#10620211 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#10620211 | C22×C3 |
| Fitting, socle | C35 | C22×SL(2,𝔽3) |
| LCS | G ▷ C3×#10620211 | |
| UCS | C1 | |
1746 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 1746 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72210382 |
| maximal normal subgroup of | D3×#72210382 |
Past the SmallGroups library coverage — no SmallGroups id.