Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #12843 |
366 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
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)(59,64)(60,71)(62,76)(63,67)(65,74)(66,79)(68,75)(69,84)(70,77)(72,87)(73,82)(78,81)(80,85)(83,89)(86,88);(58,60,70,88,63,73,62,72,64,74,78,80,75,89,79,84)(59,65,81,85,68,83,66,69,61,71,77,86,67,82,76,87);(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)(58,59,63,67,64,61,75,68)(60,69,73,85,74,87,89,86)(62,77,78,66,79,81,70,76)(65,80,82,84,71,88,83,72)Polycyclic presentation:
2^8,53|a^2=f,b^2=dgh,d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,e^c=eh,f^c=fh2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85775);