Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #11059 |
842 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)(58,61,64,77)(59,66,67,73)(60,70,72,87)(62,76,63,75)(65,79,80,86)(68,84,69,83)(71,88,78,74)(81,89,85,82);(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)(58,60)(59,65)(61,74)(62,78)(63,71)(64,72)(66,82)(67,80)(68,85)(69,81)(70,75)(73,89)(76,87)(77,88)(79,83)(84,86);(55,57)(58,59,63,69,64,67,62,68)(60,65,71,81,72,80,78,85)(61,73,76,83,77,66,75,84)(70,86,74,89,87,79,88,82)Polycyclic presentation:
2^8,53|a^2=g,b^2=d,c^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eh,c^b=cf,f^b=fh,i^b=i^52,f^c=fh,g^c=gh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 76574);