Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D7×D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D7×Dic21 |
| unambiguous semidirect product | (C3×D7)⋊Dic7 |
| unambiguous semidirect product | (C7×D7)⋊Dic3 |
| derived, Hall | C3×C72 ⋊ C2×C4 |
| Sylow | C72 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ D7×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×D21 |
| commutator, hypocenter | C3×C72 | C2×C4 |
| Fitting, socle, cosocle | C2×C3×C72 | C22 |
| prime radical | C2×C3×C7×D7 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C2 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×D72, C4×D7×D21, D3×D7×Dic7, … |
| maximal normal subgroup of | Dic3×D72, C4×D7×D21, D3×D7×Dic7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 160);