Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #10952 |
890 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)(58,61,62,75,64,74,63,76)(59,66,68,73,67,82,69,81)(60,70,77,88,71,86,72,85)(65,78,83,87,80,89,79,84);(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)(58,60,63,72,64,71,62,77)(59,65,69,79,67,80,68,83)(61,70,76,85,74,86,75,88)(66,78,81,84,82,89,73,87);(58,59)(60,65,71,80)(61,73)(62,69)(63,68)(64,67)(66,75)(70,84,86,87)(72,83,77,79)(74,81)(76,82)(78,88,89,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=ef,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,d^b=dh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 75983);