Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #33701 |
590 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)(62,66,69,85)(63,72,76,75)(64,78,80,82)(65,81,83,79)(67,84,87,68)(70,89,92,91)(71,93,77,90)(73,74,88,86);(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)(55,59)(58,61)(62,65,67,82,85,79,68,80,69,83,87,78,66,81,84,64)(63,71,73,91,72,93,74,70,76,77,88,89,75,90,86,92);(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)(54,56,57,60)(55,58,59,61)(62,64,68,79,66,78,67,65,69,80,84,81,85,82,87,83)(63,70,74,90,75,91,73,77,76,92,86,93,72,89,88,71);(54,55)(56,58)(57,59)(60,61)(62,63)(64,77)(65,70)(66,72)(67,86)(68,88)(69,76)(71,80)(73,84)(74,87)(75,85)(78,90)(79,91)(81,89)(82,93)(83,92)Polycyclic presentation:
2^8,53|b^2=f,c^2=e,d^2=h,e^2=gh,f^2=g,g^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fgh,g^a=gh,c^b=ch,i^b=i^52,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, 324891);