Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#2138 ⋊ C2 |
| Sylow | C53 ⋊ #33697 |
598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 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)(62,66,69,83)(63,72,76,75)(64,77,79,80)(65,78,81,93)(67,68,82,84)(70,85,88,87)(71,89,90,86)(73,91,92,74);(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)(55,59)(58,61)(62,65,67,80,83,93,84,79,69,81,82,77,66,78,68,64)(63,71,73,85,72,89,91,88,76,90,92,87,75,86,74,70);(54,56,57,60)(55,58,59,61)(62,64,68,78,66,77,82,81,69,79,84,93,83,80,67,65)(63,70,74,86,75,87,92,90,76,88,91,89,72,85,73,71);(54,55)(56,58)(57,59)(60,61)(62,63)(64,71)(65,70)(66,72)(67,74)(68,73)(69,76)(75,83)(77,89)(78,85)(79,90)(80,86)(81,88)(82,91)(84,92)(87,93)Polycyclic presentation:
2^8,53|b^2=f,c^2=e,d^2=h,e^2=gh,f^2=g,g^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fgh,g^a=gh,i^c=i^521220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324866);