Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C53×#2873 ⋊ C2 |
| Sylow | C53 ⋊ #21220 |
1454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 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)(61,72)(65,78)(69,83)(73,82)(75,86)(79,88)(84,85)(87,89);(54,55,56,57)(58,61)(59,65)(60,69)(62,73)(63,72)(64,75)(66,78)(67,79)(68,82)(70,83)(71,84)(74,85)(76,87)(77,86)(80,88)(81,89);(58,60,68,71,63,70,62,74)(59,64,67,81,66,77,80,76)(61,69,82,84,72,83,73,85)(65,75,79,89,78,86,88,87);(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)(55,57)(58,59,62,67,63,66,68,80)(60,64,71,76,70,77,74,81)(61,65,73,79,72,78,82,88)(69,75,84,87,83,86,85,89)Polycyclic presentation:
2^8,53|a^2=g,b^2=egh,c^2=f,g^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^52,e^b=eh,g^b=gh,d^c=dh1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 173364);