Finite Group DatabasebetaFinite Group Databasebeta| order | 13530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#17985250 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C41 | C2×C5 |
| LCS | G ▷ C3×C11×C41 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1353 |
A minimal faithful permutation representation — 2 generators on 55 points:
(2,6,7,21,26,3,4,12,14,36)(5,17,18,13,39,9,10,31,23,24)(8,20,19,30,41,11,16,32,33,35)(15,38,22,40,25,28,29,37,27,34)(43,47,48,46,51,44,45,52,49,50)(54,55);(1,2,5,11,6,13,25,32,17,31,26,41,16,30,29,37,7,15,14,27,39,24,40,21,28,12,22,38,33,20,35,36,18,10,19,34,23,4,8,9,3)(42,43,46,51,45,48,52,47,50,49,44)(53,54,55)Polycyclic presentation:
2,3,5,11,41|b^a=b^2,d^a=d^10,e^a=e^40,d^c=d^4,e^c=e^37150 conjugacy classes — view the full character table.
| maximal subgroup of | #17985238⋊D3, #17985244⋊D3, D3×#17985250, … |
| maximal normal subgroup of | #17985238⋊D3, #17985244⋊D3, D3×#17985250, … |
| maximal quotient of | C3⋊#22583161, C2×C3⋊#17985250 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13530, 64);