Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C13 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C19 ⋊ C2×C3 |
| Hall | C19⋊#92789 ⋊ C2 |
| Hall | C13⋊D247 ⋊ C3 |
| Sylow | C132 ⋊ D19⋊C3 |
| Sylow | C19 ⋊ #11759816 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C19 | C2×C3 |
| LCS | G ▷ C132×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 741 |
A minimal faithful permutation representation — 2 generators on 45 points:
(2,6,7,3,4,8)(5,14,11,9,10,16)(12,17,19,18,15,13)(21,25,26,22,23,27)(24,31,30,28,29,32)(34,38,39,35,36,40)(37,43,44,41,42,45);(1,2,5,11,17,14,18,4,8,13,19,7,6,12,10,15,16,9,3)(20,21,24,23,27,30,29,31,32,26,25,28,22)(33,34,37,39,38,42,44,45,43,36,40,41,35)Polycyclic presentation:
2,3,13^2,19|c^a=c^12,d^a=d^12,e^a=e^18,c^b=c^3,d^b=d^9,e^b=e^7541 conjugacy classes — view the full character table.
| maximal subgroup of | #50310392, #50310393, D19⋊#11759816, … |
| maximal normal subgroup of | #50310392, #50310393, D19⋊#11759816, … |
| maximal quotient of | #50310215, C2×#34064210 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 45);