Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #4245 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#4245 |
| Hall | C3×C72 ⋊ D4 |
| Sylow | C72 ⋊ #67 |
| Sylow | C3 ⋊ C7×C22⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D3×D7 |
| commutator, cosocle | C2×C3×C7 | C22×C7 |
| Frattini | C2 | D3×C7×D7 |
| Fitting, socle | C2×C3×C72 | C22 |
| hypocenter | C3×C7 | C7×D4 |
| LCS | G ▷ C2×C3×C7 ▷ C3×C7 | |
| UCS | C1 ◁ C2×C7 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | #72222060, D3×C7×C22⋊D7, #72222109, … |
| maximal normal subgroup of | #72222060, D3×C7×C22⋊D7, #72222109, … |
| maximal quotient of | C7×#92694, C2×C7×#4245, C7×#66564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 148);