Finite Group DatabasebetaFinite Group Databasebeta| order | 13566 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊((C19⋊C3)⋊D7) |
| unambiguous semidirect product | (C19⋊C3)⋊D119 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C17×C19 | C2×C3 |
| LCS | G ▷ C7×C17×C19 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2261 |
A minimal faithful permutation representation — 2 generators on 43 points:
(2,6,7,3,4,8)(5,14,11,9,10,16)(12,17,19,18,15,13)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(38,39)(40,41)(42,43);(1,2,5,11,17,14,18,4,8,13,19,7,6,12,10,15,16,9,3)(20,21,23,25,27,29,31,33,35,36,34,32,30,28,26,24,22)(37,38,40,42,43,41,39)Polycyclic presentation:
2,3,7,17,19|c^a=c^6,d^a=d^16,e^a=e^18,e^b=e^7540 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D119, D17×(C19⋊C3)⋊D7, D7×C17⋊(D19⋊C3), … |
| maximal normal subgroup of | D19⋊C3×D119, D17×(C19⋊C3)⋊D7, D7×C17⋊(D19⋊C3), … |
| maximal quotient of | (C19⋊C3)⋊Dic119, C2×C17⋊((C19⋊C3)⋊D7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13566, 45);