Finite Group DatabasebetaFinite Group Databasebeta| order | 1014 |
| isoclinism | isoclinic class of D169⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D169⋊C3 |
| unambiguous semidirect product | (C169⋊C3)⋊C2 |
| Fitting, derived, Sylow | C169 ⋊ C2×C3 |
| Hall | C169⋊C3 ⋊ C2 |
| Hall | D169 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C169 | C2×C3 |
| Frattini, socle | C13 | D13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 169 |
Polycyclic presentation:
2,3,13^2|c^13=d,c^a=c^12d^12,d^a=d^12,c^b=c^9d,d^b=d^934 conjugacy classes — view the full character table.
| maximal subgroup of | #10621721⋊C3, C2×D169⋊C3, C3×D169⋊C3, … |
| maximal normal subgroup of | #10621721⋊C3, C2×D169⋊C3, C3×D169⋊C3, … |
| maximal quotient of | Dic169⋊C3, C2×D169⋊C3, D169⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1014, 1);