Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D53×#2264 |
| Fitting | C53×#2264 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2264 |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 117 points:
(2,9)(8,30)(10,33)(11,34)(12,28)(13,40)(18,39)(24,58)(31,60)(32,38)(35,61)(36,49)(37,62)(41,48)(45,64)(50,56)(65,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67);(1,3,7,17)(2,8,9,30)(4,19,23,53)(5,25,27,59)(6,29,26,16)(10,35,33,61)(11,37,34,62)(12,38,28,32)(13,39,40,18)(14,42,44,21)(15,46,47,20)(22,57,55,52)(24,31,58,60)(36,64,49,45)(41,50,48,56)(43,54,51,63);(1,2)(3,13)(4,18)(5,24)(6,28)(7,9)(8,14)(10,21)(11,20)(12,26)(15,45)(16,48)(17,40)(19,37)(22,56)(23,39)(25,35)(27,58)(29,41)(30,44)(31,52)(32,51)(33,42)(34,46)(36,63)(38,43)(47,64)(49,54)(50,55)(53,62)(57,60)(59,61);(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117)728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 327704);