Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D53×#1830 |
| Fitting | C53×#1830 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1830 |
1218 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
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)(54,57)(55,61,62,68)(56,65)(58,70)(59,69)(60,73,64,79)(63,76,77,82)(66,81)(67,80)(71,83)(72,75)(74,84,78,85);(54,56,59,67)(55,60,62,64)(57,65,69,80)(58,71,72,66)(61,73,68,79)(63,78,77,74)(70,83,75,81)(76,85,82,84);(54,55,58,63,59,62,72,77)(56,64,66,78,67,60,71,74)(57,68,70,82,69,61,75,76)(65,73,81,84,80,79,83,85);(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)812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 169432);