Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | D53×#1718 |
| Fitting | C53×#1718 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1718 |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 85 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)(56,63)(59,68)(62,69)(64,67)(70,72,74,80,73,79,81,85)(71,76,77,78,75,83,82,84);(54,56,57,64,58,63,66,67)(55,59,60,62,61,68,65,69)(71,75)(76,83)(77,82)(78,84);(54,55,58,61)(56,62,63,69)(57,65,66,60)(59,67,68,64)(70,71)(72,78)(73,75)(74,82)(76,80)(77,81)(79,84)(83,85);(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)728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 157312);