Finite Group DatabasebetaFinite Group Databasebeta| order | 12168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C13⋊C3×(C22⋊D13)⋊C3 |
| Fitting | C22×C132 ⋊ C2×C32 |
| Hall | C13⋊C32 ⋊ D4 |
| Hall | C13×C22⋊D13 ⋊ C32 |
| Sylow | C132 ⋊ C32×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C13⋊C3×D13⋊C3 |
| commutator, socle, cosocle | C2×C132 | C22×C32 |
| Fitting | C22×C132 | C2×C32 |
| hypercenter | C22 | C13⋊C3×D13⋊C3 |
| hypocenter | C132 | C32×D4 |
| LCS | G ▷ C2×C132 ▷ C132 | |
| UCS | C1 ◁ C2 ◁ C22 | |
212 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 156 |
161 conjugacy classes — view the full character table.
| maximal subgroup of | #72242022 |
| maximal normal subgroup of | #72242022 |
Past the SmallGroups library coverage — no SmallGroups id.