Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D3×#5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C7 |
| direct product | D3×#5997 |
| Fitting, socle, derived, Hall | C3×C72 ⋊ C2×C4 |
| Sylow | C72 ⋊ C4×D3 |
| Sylow | C3 ⋊ C2×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72 | C2×C4 |
| prime radical | D3×C7⋊D7 | C2 |
| cosocle | C3×C7⋊D7 | C22 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 42 |
48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 231);