Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #23542 |
1362 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 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)(65,81)(70,88)(75,92)(79,89)(80,93)(82,83)(84,91)(87,90);(55,57)(59,61)(62,65,66,82,68,81,67,83)(63,70,71,79,73,88,72,89)(64,75,76,93,78,92,77,80)(69,84,74,90,86,91,85,87);(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)(58,59)(60,61)(62,64,68,78)(63,69,73,86)(65,80,81,93)(66,77,67,76)(70,87,88,90)(71,85,72,74)(75,82,92,83)(79,91,89,84);(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)(62,63,68,73)(64,74,78,85)(65,79,81,89)(66,72,67,71)(69,77,86,76)(70,83,88,82)(75,91,92,84)(80,87,93,90)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,c^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,g^a=gh,i^a=i^52,c^b=cg,e^b=eh,f^b=fh,g^b=gh,i^b=i^52,d^c=dh1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 197539);