Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7450 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 2 generators on 93 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)(54,55,57,59)(56,61,60,58)(63,68)(64,73)(65,74)(66,77)(69,70)(71,87)(72,81)(75,92)(76,90)(78,91)(79,82)(80,85)(83,93)(84,86)(88,89);(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)(55,58)(56,60)(59,61)(62,63,64,69,74,82,89,80,66,71,75,83,78,86,90,81,67,72,76,84,91,93,92,87,77,85,88,79,65,70,73,68)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fg,d^2=efg,f^2=gh,g^2=h,b^a=bc,c^a=ce,i^a=i^52,c^b=cf,d^b=def,f^b=fg,g^b=gh1037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57219);