Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #11259 |
590 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)(55,57)(58,61)(59,65,66,78)(60,69)(62,73)(63,74)(64,76,68,80)(67,72,79,87)(70,83)(71,84)(75,88)(77,86,81,82)(85,89);(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)(58,60,62,70,63,71,75,85)(59,64,67,77,66,68,79,81)(61,69,73,83,74,84,88,89)(65,76,72,86,78,80,87,82);(58,59)(60,68,71,64)(61,72,74,87)(62,67)(63,66)(65,73,78,88)(69,82)(70,81,85,77)(75,79)(76,83)(80,89)(84,86)Polycyclic presentation:
2^8,53|a^2=g,b^2=e,c^2=d,e^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=cf,g^b=gh,g^c=gh,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 77769);