Finite Group DatabasebetaFinite Group Databasebeta| order | 13530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#17985249 |
| 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:
(2,6,7,23,17,3,4,12,14,29)(5,18,19,32,33,9,10,31,20,35)(8,24,25,26,30,16,13,36,37,38)(11,34,27,28,41,21,22,15,40,39)(43,47,48,46,51,44,45,52,49,50)(54,55);(1,2,5,11,23,35,25,22,32,18,7,15,28,41,37,24,4,8,17,30,19,31,38,29,16,6,13,26,39,40,27,12,10,20,34,36,33,14,21,9,3)(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^16150 conjugacy classes — view the full character table.
| maximal subgroup of | #17985237⋊D3, #17985243⋊D3, D3×#17985249, … |
| maximal normal subgroup of | #17985237⋊D3, #17985243⋊D3, D3×#17985249, … |
| maximal quotient of | C3⋊#22583160, C2×C3⋊#17985249 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13530, 63);