Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C4×D3×C72 |
| Fitting | C3×C4×C72 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C4×C72 |
| Hall | C3×C72 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C72 | D3 |
| commutator, hypocenter | C3 | C2×C4×C72 |
| Frattini | C2 | C2×D3×C72 |
| Fitting | C3×C4×C72 | C2 |
| socle | C2×C3×C72 | C22 |
| prime radical | C2×D3×C72 | C2 |
| cosocle | C2×C3 | C22×C72 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C4×C72 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 588 |
588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D3×C7⋊D7, C2×C4×D3×C72, D3×C72×D4, … |
| maximal normal subgroup of | C4×D3×C7⋊D7, C2×C4×D3×C72, D3×C72×D4, … |
| maximal quotient of | C2×C4×D3×C72 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 195);