Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #11029 |
1242 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 93 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)(62,65,68,83)(63,70,71,79)(64,75,78,92)(66,82,67,81)(69,84,74,90)(72,89,73,88)(76,91,77,80)(85,93,86,87);(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)(59,61)(62,64,68,78)(63,69,71,74)(65,80,83,91)(66,77,67,76)(70,87,79,93)(72,86,73,85)(75,82,92,81)(84,89,90,88);(54,55,56,57)(58,59)(60,61)(62,63,67,73,68,71,66,72)(64,74,77,85,78,69,76,86)(65,79,82,88,83,70,81,89)(75,84,91,93,92,90,80,87)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,c^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,c^b=cf,f^b=fh,g^b=gh,f^c=fh,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, 76403);