Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C3×C7×C22⋊D7 |
| Fitting | C22×C3×C72 ⋊ C2 |
| Hall | C3×C72 ⋊ D4 |
| Sylow | C72 ⋊ C3×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
357 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#11924207, C3×#11716115, D3×C7×C22⋊D7, … |
| maximal normal subgroup of | C3×#11924207, C3×#11716115, D3×C7×C22⋊D7, … |
| maximal quotient of | C3×C7×#4268, C2×C3×C7×C22⋊D7, C3×C7×#1142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 188);