Finite Group DatabasebetaFinite Group Databasebeta| order | 17082 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C73 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C13⋊C3×C73 |
| unambiguous semidirect product | (C2×C13)⋊(C32×C73) |
| unambiguous semidirect product | (C2×C3×C13)⋊(C3×C73) |
| Fitting, socle | C2×C3×C13×C73 ⋊ C3 |
| derived, Sylow | C13 ⋊ C2×C32×C73 |
| Hall | C2×C13×C73 ⋊ C32 |
| Hall | C13×C73 ⋊ C2×C32 |
| Hall | C2×C13 ⋊ C32×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C73 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C2×C32×C73 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13×C73 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C3×C73 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5694 |
3066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C73×Dic13⋊C3, C3×#26015654, C3×C13⋊C3×Dic73, … |
| maximal normal subgroup of | C3×C73×Dic13⋊C3, C3×#26015654, C3×C13⋊C3×Dic73, … |
| maximal quotient of | C3×C4×C13⋊C3×C73, C22×C3×C13⋊C3×C73 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17082, 72);