Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | D53×#2249 |
| Fitting | C53×#2249 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2249 |
854 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2,3,4)(6,12)(11,24)(13,26)(14,23)(15,27)(20,35)(25,28)(29,34)(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);(5,7,16,30,10,19,22,33,9,18,31,36,21,32,8,17)(6,11,20,29,14,25,26,27,12,24,35,34,23,28,13,15);(2,4)(5,6)(7,15)(8,20)(9,12)(10,23)(11,17)(13,16)(14,21)(18,27)(19,34)(22,35)(24,33)(25,36)(26,31)(28,30)(29,32);(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)1064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324963);