Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #10817 |
642 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)(59,66,67,82)(60,71)(62,76)(63,78)(64,77)(65,79,70,84)(68,75,69,83)(72,86)(73,88)(74,87)(80,89,81,85);(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)(54,55,56,57)(58,60,63,74,64,73,62,72)(59,65,69,81,67,70,68,80)(61,71,78,87,77,88,76,86)(66,79,83,85,82,84,75,89);(58,59)(60,70,73,65)(61,75,77,83)(62,68)(63,69)(64,67)(66,76,82,78)(71,85)(72,81,74,80)(79,86)(84,87)(88,89)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=d,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,f^b=fh,f^c=fh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 75278);