Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#20275001 |
| Sylow | C53 ⋊ C2×#1868 |
1342 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)(57,63)(58,66)(60,70)(61,69)(62,72)(64,76)(65,75)(67,79)(68,80)(71,82)(73,78)(74,84)(77,86)(81,83)(85,87);(56,58,60,68,61,67,71,81)(57,62,64,74,65,73,77,85)(59,66,70,80,69,79,82,83)(63,72,76,84,75,78,86,87);(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)(56,57,60,64,61,65,71,77)(58,62,68,74,67,73,81,85)(59,63,70,76,69,75,82,86)(66,78,80,87,79,72,83,84);(54,55)1832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 170673);