Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #21556 |
874 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)(54,56,57,55)(60,72)(65,80)(70,81)(71,86)(73,74)(79,85)(84,89)(87,88);(58,61)(59,66)(60,71)(62,76)(63,78)(64,77)(65,79)(67,75)(68,83)(69,82)(70,84)(72,86)(73,87)(74,88)(80,85)(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)(58,60,62,73,64,72,63,74)(59,65,67,70,69,80,68,81)(61,71,76,87,77,86,78,88)(66,79,75,84,82,85,83,89);(54,55,57,56)(58,59,64,69)(60,70,72,81)(61,75,77,83)(62,68,63,67)(65,74,80,73)(66,78,82,76)(71,85,86,79)(84,88,89,87)Polycyclic presentation:
2^8,53|a^2=g,b^2=e,d^2=gh,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,d^b=dh,i^b=i^52,f^c=fh1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 176477);