Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D53×#2189 |
| Fitting | C53×#2189 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2189 |
1146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(2,4)(5,8,11,10)(6,13,15,25)(7,17,19,26)(9,20,24,23)(12,28,30,29)(14,21,32,35)(16,33,34,31)(18,22,27,36)(37,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39);(5,7)(6,12)(8,17)(9,22)(10,26)(11,19)(13,28)(14,31)(15,30)(16,21)(18,23)(20,27)(24,36)(25,29)(32,33)(34,35);(1,2)(3,4)(5,6,11,15)(7,16,19,34)(8,13,10,25)(9,21,24,35)(12,27,30,18)(14,20,32,23)(17,33,26,31)(22,28,36,29);(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)(88,89)812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323333);