Finite Group DatabasebetaFinite Group Databasebeta| order | 22066 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11033 |
| unambiguous semidirect product | C11⋊D1003 |
| unambiguous semidirect product | C17⋊D649 |
| unambiguous semidirect product | C59⋊D187 |
| Fitting, socle, derived, Hall | C11×C17×C59 ⋊ C2 |
| Hall | C17×C59 ⋊ D11 |
| Hall | C11×C59 ⋊ D17 |
| Hall | C11×C17 ⋊ D59 |
| Sylow | C59 ⋊ D187 |
| Sylow | C17 ⋊ D649 |
| Sylow | C11 ⋊ D1003 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C17×C59 | C2 |
| LCS | G ▷ C11×C17×C59 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 11033 |
A minimal faithful permutation representation — 2 generators on 87 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(2,11)(3,10)(4,9)(5,8)(6,7)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(30,87)(31,86)(32,85)(33,84)(34,83)(35,82)(36,81)(37,80)(38,79)(39,78)(40,77)(41,76)(42,75)(43,74)(44,73)(45,72)(46,71)(47,70)(48,69)(49,68)(50,67)(51,66)(52,65)(53,64)(54,63)(55,62)(56,61)(57,60)(58,59)Polycyclic presentation:
2,11,17,59|b^a=b^10,c^a=c^16,d^a=d^585518 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22066, 8);