Finite Group DatabasebetaFinite Group Databasebeta| order | 13530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C41⋊C5)⋊D11) |
| unambiguous semidirect product | (C41⋊C5)⋊D33 |
| 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:
(2,6,7,23,27,3,4,12,14,22)(5,19,20,25,26,9,10,34,13,36)(8,31,32,33,21,16,17,41,18,11)(15,38,39,24,37,29,30,40,28,35)(43,44)(45,46)(47,48)(49,50)(51,52)(54,55);(1,2,5,11,22,34,37,41,36,25,4,8,18,31,39,38,14,28,7,15,10,19,29,12,24,23,30,40,17,33,16,6,13,26,32,35,20,27,21,9,3)(42,43,45,47,49,51,52,50,48,46,44)(53,54,55)Polycyclic presentation:
2,3,5,11,41|b^a=b^2,d^a=d^10,e^a=e^40,e^c=e^10222 conjugacy classes — view the full character table.
| maximal subgroup of | D33×D41⋊C5, D11×C3⋊(D41⋊C5), D3×(C41⋊C5)⋊D11, … |
| maximal normal subgroup of | D33×D41⋊C5, D11×C3⋊(D41⋊C5), D3×(C41⋊C5)⋊D11, … |
| maximal quotient of | C3⋊#22583156, C2×C3⋊((C41⋊C5)⋊D11) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13530, 59);