Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C53×#421 ⋊ C2 |
| Sylow | C53 ⋊ #23403 |
1942 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 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)(58,62,64,63)(59,67,68,76)(60,71,72,77)(61,73,75,74)(65,79,80,69)(66,82,83,84)(70,86,87,88)(78,85,81,89);(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)(55,57)(58,61,64,75)(59,66,68,83)(60,70,72,87)(62,74,63,73)(65,78,80,81)(67,84,76,82)(69,85,79,89)(71,88,77,86);(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)(58,60)(59,65)(61,70)(62,71)(63,77)(64,72)(66,81)(67,79)(68,80)(69,76)(73,86)(74,88)(75,87)(78,83)(82,89)(84,85);(54,55)(56,57)(58,59)(60,69)(61,66)(62,67)(63,76)(64,68)(65,71)(70,85)(72,79)(73,82)(74,84)(75,83)(77,80)(78,88)(81,86)(87,89)Polycyclic presentation:
2^8,53|c^2=h,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,g^a=gh,c^b=cg,e^b=eh,i^b=i^52,d^c=dh,e^c=eh,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, 196514);