Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×C7×D7 |
| unambiguous semidirect product | (D3×C7)⋊(C22×C7) |
| unambiguous semidirect product | (C3×D7)⋊(C22×C7) |
| unambiguous semidirect product | D21⋊(C22×C7) |
| Fitting, socle | C2×C3×C72 ⋊ C22 |
| derived | C3×C7 ⋊ C23×C7 |
| Hall | C3×C72 ⋊ C23 |
| Sylow | C72 ⋊ C22×D3 |
| Sylow | C3 ⋊ C22×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D3×D7 |
| commutator, cosocle, hypocenter | C3×C7 | C23×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C72 | C22 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C7 | |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#64423, D3×C7×C22⋊D7, D3×#87641, … |
| maximal normal subgroup of | C2×D3×#64423, D3×C7×C22⋊D7, D3×#87641, … |
| maximal quotient of | D3×C7×C22⋊D7, D32×C7×D7, C2×C7×(C3⋊D3)⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 263);