Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #10782 |
1178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(58,61)(59,66)(60,71)(62,76)(63,77)(64,78)(65,79)(67,75)(68,83)(69,82)(70,84)(72,85)(73,87)(74,86)(80,88)(81,89);(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)(58,60,63,72,64,74,62,73)(59,65,67,80,69,81,68,70)(61,71,77,85,78,86,76,87)(66,79,75,88,82,89,83,84);(54,55,56,57)(58,59,62,68,64,69,63,67)(60,70,73,81,74,80,72,65)(61,75,77,82,78,83,76,66)(71,79,85,88,86,89,87,84)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,d^2=h,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,d^b=dh,i^b=i^52,e^c=eh,f^c=fh1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 75090);