Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D53×#1915 |
| Fitting | C53×#1915 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1915 |
1670 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)(56,65)(58,72)(59,69)(60,73)(62,68)(63,79)(64,70)(66,80)(67,82)(71,81)(74,85)(75,83)(76,77)(78,84);(54,56,64,67,59,66,58,71)(55,60,63,78,62,75,77,74)(57,65,70,82,69,80,72,81)(61,73,79,84,68,83,76,85);(54,55,58,63,59,62,64,77)(56,60,67,74,66,75,71,78)(57,68,70,79,69,61,72,76)(65,73,81,84,80,83,82,85);(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, 171593);