Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C3×C4×C7×D7 |
| Fitting | C3×C4×C72 ⋊ C2 |
| derived | C7 ⋊ C2×C3×C4×C7 |
| Hall | C3×C72 ⋊ C2×C4 |
| Sylow | C72 ⋊ C2×C3×C4 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C4×D72, C4×D3×C7×D7, C4×D7×D21, … |
| maximal normal subgroup of | C3×C4×D72, C4×D3×C7×D7, C4×D7×D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 185);