Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #33065 |
746 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)(63,72)(64,76)(65,79)(67,81)(68,82)(69,83)(70,84)(71,87)(73,80)(74,88)(75,89)(77,91)(78,92)(85,93)(86,90);(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)(62,65,67,78,69,77,68,64)(63,71,73,86,75,85,74,70)(66,79,81,92,83,91,82,76)(72,87,80,90,89,93,88,84);(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)(54,56,57,60)(55,58,59,61)(62,64,67,65,69,78,68,77)(63,70,73,71,75,86,74,85)(66,76,81,79,83,92,82,91)(72,84,80,87,89,90,88,93);(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)(56,58)(57,59)(60,61)(62,63,69,75)(64,71,78,85)(65,70,77,86)(66,80,83,88)(67,74,68,73)(72,82,89,81)(76,90,92,84)(79,87,91,93)Polycyclic presentation:
2^8,53|a^2=h,b^2=fh,c^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,f^a=fh,g^a=gh,i^a=i^52,c^b=ch,i^b=i^52,i^c=i^52,g^d=gh878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 319905);