Finite Group DatabasebetaFinite Group Databasebeta| order | 2178 |
| isoclinism | isoclinic class of C9⋊(C11⋊D11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C9⋊(C11⋊D11) |
| unambiguous semidirect product | C11⋊D99 |
| Fitting, derived, Hall | C9×C112 ⋊ C2 |
| Sylow | C112 ⋊ D9 |
| Sylow | C9 ⋊ C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C112 | C2 |
| Frattini | C3 | C3⋊(C11⋊D11) |
| socle | C3×C112 | D3 |
| LCS | G ▷ C9×C112 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1089 |
Polycyclic presentation:
2,3,11^2,3|b^3=e^2,b^a=b^2e,c^a=c^10,d^a=d^10,e^a=e^2546 conjugacy classes — view the full character table.
| maximal subgroup of | D9×C11⋊D11, D11×D99, C2×C9⋊(C11⋊D11), … |
| maximal normal subgroup of | D9×C11⋊D11, D11×D99, C2×C9⋊(C11⋊D11), … |
| maximal quotient of | C9⋊(C11⋊Dic11), C2×C9⋊(C11⋊D11), C5×C9⋊(C11⋊D11), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2178, 19);