Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#20277895 |
| Sylow | C53 ⋊ C2×#2381 |
2326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 5 generators on 83 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(61,65)(64,66)(68,71,72,80)(69,75,74,82)(70,77,78,79)(73,81,76,83);(60,62,63,67)(61,64,65,66)(69,74)(73,76)(75,82)(81,83);(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)(62,67)(64,66)(68,70,72,78)(69,73,74,76)(71,79,80,77)(75,83,82,81);(56,57,58,59)(60,61)(62,66)(63,65)(64,67)(68,69)(70,76)(71,75)(72,74)(73,78)(77,83)(79,81)(80,82);(54,55)1532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 332202);