Finite Group DatabasebetaFinite Group Databasebeta| order | 2178 |
| isoclinism | isoclinic class of D3×C112⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C11 |
| direct product | D3×C112⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C112⋊C3) |
| unambiguous semidirect product | (D3×C112)⋊C3 |
| Fitting, socle, derived | C3×C112 ⋊ C2×C3 |
| Hall | C3×C112⋊C3 ⋊ C2 |
| Sylow | C112 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C112 | C2×C3 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 99 |
129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2178, 25);