Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×Dic21 |
| unambiguous semidirect product | (C2×C3)⋊(C7×Dic7) |
| unambiguous semidirect product | (C2×C7)⋊(C7×Dic3) |
| derived | C3×C7 ⋊ C2×C4×C7 |
| Hall | C3×C72 ⋊ C2×C4 |
| Sylow | C72 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ C2×C7×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C7 | D21 |
| commutator, hypocenter | C3×C7 | C2×C4×C7 |
| Frattini | C2 | C2×C7×D21 |
| Fitting, socle, prime radical | C22×C3×C72 | C2 |
| cosocle | C2×C3×C7 | C22×C7 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C22×C7 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#11924252, C2×D3×C7×Dic7, C2×#11924246, … |
| maximal normal subgroup of | C2×#11924252, C2×D3×C7×Dic7, C2×#11924246, … |
| maximal quotient of | C7×#66627 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 202);