Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D53×#2020 |
| Fitting | C53×#2020 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2020 |
1902 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(5,8,11,26)(6,13,16,32)(7,18,21,35)(9,25,10,24)(12,27,29,33)(14,31,15,22)(17,30,28,36)(19,23,20,34)(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);(2,4)(5,7)(6,12)(8,23)(9,20)(10,19)(11,21)(13,30)(14,28)(15,17)(16,29)(18,25)(22,33)(24,35)(26,34)(27,31)(32,36);(1,2)(3,4)(5,6,11,16)(7,17,21,28)(8,22,26,31)(9,15,10,14)(12,20,29,19)(13,25,32,24)(18,33,35,27)(23,30,34,36);(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)728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 196764);