Finite Group DatabasebetaFinite Group Databasebeta| order | 16182 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29×C31 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C29×C31 |
| unambiguous semidirect product | C3⋊(D3×C29×C31) |
| Fitting, socle, Hall | C32×C29×C31 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C29×C31 |
| Hall | C32×C31 ⋊ C2×C29 |
| Hall | C32×C29 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29×C31 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C2×C29×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C31 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C29×C31 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8091 |
5394 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C29×C31×#157, C29×C31⋊#157, C31×#11760330, … |
| maximal normal subgroup of | C29×C31×#157, C29×C31⋊#157, C31×#11760330, … |
| maximal quotient of | C29×C31×C3⋊Dic3, C2×C3⋊D3×C29×C31 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16182, 25);