Finite Group DatabasebetaFinite Group Databasebeta| order | 12168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#14523144⋊C3 |
| Fitting, socle | C2×C132 ⋊ C32×C4 |
| derived, Sylow | C132 ⋊ C2×C32×C4 |
| Hall | C13⋊C32 ⋊ C2×C4 |
| Hall | C2×#10621728 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #14523144⋊C3 |
| commutator, hypocenter | C132 | C2×C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132 | C32×C4 |
| prime radical | C2×(C13⋊C3)⋊(D13⋊C3) | C2 |
| cosocle | C13⋊D13 | C22×C32 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2 | |
256 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
92 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.