Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of Dic42 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D84 |
| unambiguous semidirect product | C4⋊(C7×D21) |
| Fitting | C3×C4×C72 ⋊ C2 |
| Hall | C3×C72 ⋊ D4 |
| Sylow | C72 ⋊ D12 |
| Sylow | C3 ⋊ C7×D28 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C7 | C2×D21 |
| commutator, cosocle | C2×C3×C7 | C22×C7 |
| Frattini | C2 | C2×C7×D21 |
| Fitting | C3×C4×C72 | C2 |
| socle | C2×C3×C72 | C22 |
| hypercenter | C4×C7 | D21 |
| hypocenter | C3×C7 | C7×D4 |
| LCS | G ▷ C2×C3×C7 ▷ C3×C7 | |
| UCS | C1 ◁ C2×C7 ◁ C4×C7 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
315 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72246460, D3×C7×D28, #72246465, … |
| maximal normal subgroup of | #72246460, D3×C7×D28, #72246465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 201);