Finite Group DatabasebetaFinite Group Databasebeta| order | 2178 |
| isoclinism | isoclinic class of C3⋊(C11⋊D11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C11 |
| direct product | C3×C3⋊(C11⋊D11) |
| unambiguous semidirect product | C3⋊(C3×C11⋊D11) |
| unambiguous semidirect product | C11⋊(C3×D33) |
| Fitting, socle, Hall | C32×C112 ⋊ C2 |
| derived | C3×C112 ⋊ C2×C3 |
| Sylow | C112 ⋊ C3×D3 |
| Sylow | C32 ⋊ C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C11⋊D11) |
| commutator, cosocle, hypocenter | C3×C112 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C112 | C2 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C3 | |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 726 |
549 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2178, 31);