Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12615 |
418 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(58,60,62,72,63,73,75,86,64,70,76,84,61,71,74,85)(59,66,68,80,67,79,82,88,69,81,83,89,65,77,78,87);(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)(54,55,56,57)(59,65,69,67)(60,70)(66,79,81,77)(68,78,83,82)(71,73)(72,84)(80,88,89,87)(85,86);(58,59,62,68,63,67,75,82,64,69,76,83,61,65,74,78)(60,66,72,80,73,79,86,88,70,81,84,89,71,77,85,87)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,d^2=h,e^2=g,g^2=h,b^a=bd,d^a=dh,f^a=fh,c^b=ch,i^b=i^522168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84676);