Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #11345 |
698 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)(54,55,56,57)(58,61)(59,65)(60,68)(62,73)(63,72)(64,75)(66,78)(67,79)(69,71)(70,81)(74,85)(76,86)(77,83)(80,88)(82,84)(87,89);(58,60)(59,64)(61,71,72,68)(62,70)(63,69)(65,75,78,83)(66,77)(67,76)(73,84,85,81)(74,82)(79,86,88,89)(80,87);(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)(55,57)(58,59,62,67,63,66,74,80)(60,64,70,76,69,77,82,87)(61,65,73,79,72,78,85,88)(68,75,81,86,71,83,84,89)Polycyclic presentation:
2^8,53|a^2=g,b^2=d,c^2=e,g^2=h,b^a=bd,c^a=ce,f^a=fh,i^a=i^52,c^b=cf,f^b=fh,d^c=dh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78294);