Finite Group DatabasebetaFinite Group Databasebeta| order | 2178 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3 |
| direct product | C32×C11×D11 |
| unambiguous semidirect product | C11⋊(C2×C32×C11) |
| Fitting, socle, Hall | C32×C112 ⋊ C2 |
| derived | C11 ⋊ C2×C32×C11 |
| Sylow | C112 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C11 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C32×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C112 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C32×C11 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
693 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D112, C3×D3×C11×D11, C3×D11×D33, … |
| maximal normal subgroup of | C32×D112, C3×D3×C11×D11, C3×D11×D33, … |
| maximal quotient of | C32×C11×Dic11, C2×C32×C11×D11, C32×C11×D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2178, 27);