Finite Group DatabasebetaFinite Group Databasebeta| order | 11664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| direct product | C3×#72210299 |
| Fitting, socle | C35 ⋊ GL(2,𝔽3) |
| derived | #14519481 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #72210299 |
| commutator, cosocle, hypocenter | #14519481 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C35 | GL(2,𝔽3) |
| LCS | G ▷ #14519481 | |
| UCS | C1 ◁ C3 | |
972 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
63 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72210382, D3×#72210299, #72224537 |
| maximal normal subgroup of | C3×#72210382, D3×#72210299, #72224537 |
Past the SmallGroups library coverage — no SmallGroups id.