Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1846 ⋊ C2 |
| Sylow | C53 ⋊ #25050 |
720 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
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)(62,65,66,79,67,80,68,81)(63,71,72,78,73,87,82,92)(64,75,76,90,77,91,83,93)(69,84,74,88,85,89,70,86);(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)(62,64)(63,70)(65,75)(66,76)(67,77)(68,83)(69,72)(71,86)(73,74)(78,84)(79,90)(80,91)(81,93)(82,85)(87,88)(89,92);(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)(62,64,68,83,67,77,66,76)(63,69,82,70,73,85,72,74)(65,75,81,93,80,91,79,90)(71,84,92,86,87,89,78,88);(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)(64,74)(65,78)(66,82)(67,73)(68,72)(69,76)(70,77)(71,79)(75,89)(80,92)(81,87)(83,85)(84,91)(86,93)(88,90)Polycyclic presentation:
2^8,53|b^2=ef,d^2=e,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^52,c^b=cg,g^b=gh,i^b=i^52,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 215522);