Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #64422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×#64422 |
| Fitting | C4×C72 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C3×C4 |
| Hall | C4×C7×D7 ⋊ C3 |
| Hall | #3862 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #64422 |
| commutator, hypocenter | C72 | C2×C3×C4 |
| Frattini | C2 | C2×#64422 |
| Fitting | C4×C72 | C2×C3 |
| socle, cosocle | C2×C72 | C22×C3 |
| prime radical | C2×#64422 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C4 | |
67 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | #72245079, C4×#64422⋊C2, #72245084, … |
| maximal normal subgroup of | #72245079, C4×#64422⋊C2, #72245084, … |
| maximal quotient of | #72245968, AGL(1,𝔽5)×#64422 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 124);