Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C53×#504 ⋊ C2 |
| Sylow | C53 ⋊ #33611 |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
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)(58,60,63,69)(59,66,68,81)(61,70,74,83)(62,71,73,84)(64,75,78,86)(65,80,72,85)(67,82,76,87)(77,88,79,89);(55,57)(60,69)(66,81)(70,83)(71,84)(75,86)(80,85)(82,87)(88,89);(58,59,65,79,62,67,61,64,63,68,72,77,73,76,74,78)(60,66,80,89,71,82,70,75,69,81,85,88,84,87,83,86);(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)(54,55)(56,57)(59,64)(61,72)(62,73)(65,74)(66,75)(67,79)(68,78)(70,85)(71,84)(76,77)(80,83)(81,86)(82,89)(87,88)Polycyclic presentation:
2^8,53|b^2=egh,d^2=h,e^2=gh,g^2=h,b^a=be,c^a=cf,e^a=eg,g^a=gh,i^a=i^52,d^c=dh2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324096);