Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#20274763 |
| Sylow | C53 ⋊ C2×#1813 |
1314 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 87 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)(56,59)(57,64)(58,68)(60,73)(61,76)(62,74)(63,77)(65,79)(66,72)(67,81)(69,84)(70,86)(71,85)(75,80)(78,87)(82,83);(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)(56,58,60,69,62,71,61,70)(57,63,65,67,66,78,75,82)(59,68,73,84,74,85,76,86)(64,77,79,81,72,87,80,83);(56,57,61,65,62,66,60,75)(58,67,70,78,71,82,69,63)(59,72,73,79,74,64,76,80)(68,83,84,87,85,81,86,77);(54,55)1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 169218);