Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#419 ⋊ C2 |
| Sylow | C53 ⋊ #11031 |
1262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 points:
(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)(58,61)(59,66)(60,70)(62,76)(63,79)(64,77)(65,80)(67,83)(68,74)(69,86)(71,75)(72,88)(73,87)(78,84)(81,89)(82,85);(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)(58,60,64,73)(59,65,68,81)(61,75,77,88)(62,72,63,71)(66,82,74,86)(67,85,78,69)(70,79,87,76)(80,83,89,84);(54,55,56,57)(58,59)(60,69)(61,74,77,66)(62,78)(63,67)(64,68)(65,71)(70,82,87,86)(72,81)(73,85)(75,89,88,80)(76,83,79,84)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,c^b=cf,d^b=dh,f^b=fh,f^c=fh,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 76415);