Finite Group DatabasebetaFinite Group Databasebeta| order | 13530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#17985242 |
| 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:
(2,3,5,9,16)(4,7,13,12,22)(6,11,20,31,28)(8,14,25,37,32)(10,18,29,17,24)(15,26,38,30,40)(19,27,39,23,34)(21,33,35,41,36)(43,47,48,46,51,44,45,52,49,50)(54,55);(1,2,4,8,15,27,20,32,39,34,9,17,29,14,11,21,16,28,3,6,12,23,35,40,33,38,31,41,18,25,37,26,22,13,24,36,7,5,10,19,30)(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,d^c=d^4,e^c=e^18162 conjugacy classes — view the full character table.
| maximal subgroup of | #17985236⋊D3, #17985248⋊D3, D3×#17985242, … |
| maximal normal subgroup of | #17985236⋊D3, #17985248⋊D3, D3×#17985242, … |
| maximal quotient of | C3⋊#22583153, C2×C3⋊#17985242 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13530, 56);