Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #11336 |
694 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)(58,61)(59,66)(60,71,73,88)(62,77)(63,76)(64,78)(65,79,80,89)(67,84)(68,83)(69,85)(70,86,81,82)(72,75,74,87);(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)(58,60,62,72,64,73,63,74)(59,65,67,70,69,80,68,81)(61,75,76,71,78,87,77,88)(66,82,83,89,85,86,84,79);(54,55,56,57)(58,59,63,67,64,69,62,68)(60,70,74,80,73,81,72,65)(61,66,76,84,78,85,77,83)(71,82,87,79,88,86,75,89)Polycyclic presentation:
2^8,53|a^2=g,b^2=d,c^2=e,d^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=cf,e^b=eh,i^b=i^52,d^c=dh1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78245);