Finite Group DatabasebetaFinite Group Databasebeta| order | 2178 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C11⋊D11)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C11 |
| unambiguous semidirect product | C3⋊(C3⋊(C11⋊D11)) |
| unambiguous semidirect product | C11⋊(C3⋊D33) |
| Fitting, socle, derived, Hall | C32×C112 ⋊ C2 |
| Sylow | C112 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C112 | C2 |
| LCS | G ▷ C32×C112 | |
| UCS | C1 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1089 |
Polycyclic presentation:
2,3^2,11^2|b^a=b^2,c^a=c^2,d^a=d^10,e^a=e^10546 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2178, 34);