Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #13288 |
354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(54,56,57,61)(55,58,59,60)(62,65,81,83,68,75,67,66)(63,70,84,71,73,88,72,80)(64,76,92,77,79,91,78,82)(69,85,93,89,87,90,86,74);(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)(62,64,75,91,81,92,66,82,68,79,65,76,67,78,83,77)(63,69,70,85,84,93,71,89,73,87,88,90,72,86,80,74);(54,55,57,59)(56,60,61,58)(62,63)(64,74,79,89)(65,80)(66,70)(67,84)(68,73)(69,77,87,82)(71,75)(72,81)(76,86,91,93)(78,85,92,90)(83,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=def,c^2=eh,d^2=g,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,d^b=dh,f^b=fh,i^b=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88192);