Finite Group DatabasebetaFinite Group Databasebeta| order | 11664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C32 |
| direct product | C2×#72209952 |
| Fitting | C2×H(5,𝔽3) ⋊ SL(2,𝔽3) |
| derived | #14519166 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C3 | #14519481 |
| commutator, cosocle, hypocenter | #14519166 | C2×C3 |
| Frattini | C3 | C2×#14519481 |
| Fitting | C2×H(5,𝔽3) | SL(2,𝔽3) |
| LCS | G ▷ #14519166 | |
| UCS | C1 ◁ C2×C3 | |
751 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 751 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
70 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72210405, C2×#72221927 |
| maximal normal subgroup of | C2×#72210405, C2×#72221927 |
Past the SmallGroups library coverage — no SmallGroups id.