Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C53×#344 ⋊ C2 |
| Sylow | C53 ⋊ #10961 |
926 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)(58,61,62,74,63,71,75,72)(59,65,79,80,66,81,67,83)(60,68,73,85,69,86,70,87)(64,76,77,89,78,84,82,88);(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)(58,60)(59,64,66,78)(61,68)(62,73)(63,69)(65,76,81,84)(67,82,79,77)(70,75)(71,86)(72,87)(74,85)(80,89,83,88);(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)(58,59,62,67,63,66,75,79)(60,64,70,77,69,78,73,82)(61,65,72,80,71,81,74,83)(68,84,85,89,86,76,87,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=ef,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,i^a=i^52,d^b=dh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh,e^c=eh,f^c=fh1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 76042);