Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #13265 |
338 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
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);(62,64,75,92,65,79,82,77,68,78,81,83,67,76,66,80)(63,69,84,91,70,87,90,85,73,86,89,93,72,74,71,88);(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)(54,55,57,59)(56,60,61,58)(62,63,66,71,67,72,81,89,68,73,82,90,65,70,75,84)(64,74,77,91,76,86,92,88,78,87,80,93,79,69,83,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=def,c^2=e,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^52,d^b=dh,f^b=fh2156 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88095);