Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7451 |
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:
(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)(54,55,57,59)(56,61,60,58)(63,69)(64,76)(65,80)(67,77)(68,84)(70,73)(71,90)(72,85)(74,92)(75,89)(78,93)(79,82)(81,83)(86,88)(87,91);(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)(55,58)(56,60)(59,61)(62,63,65,71,81,90,93,69,68,74,64,75,67,73,82,87,66,72,79,86,77,88,76,85,84,91,78,70,83,89,80,92)Polycyclic presentation:
2^8,53|a^2=d,b^2=eh,c^2=fg,d^2=efg,f^2=gh,g^2=h,b^a=bc,c^a=ce,c^b=cf,d^b=def,f^b=fg,g^b=gh,i^b=i^522129 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57221);