Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C53 ⋊ #20954 |
1694 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)(59,67)(65,80)(66,75)(68,69)(70,81)(79,88)(82,83)(84,89);(58,61,64,78)(59,66,67,75)(60,71,73,86)(62,77,63,76)(65,79,80,88)(68,83,69,82)(70,84,81,89)(72,87,74,85);(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)(54,56,57,55)(58,60)(59,65)(61,71)(62,74)(63,72)(64,73)(66,79)(67,80)(68,81)(69,70)(75,88)(76,87)(77,85)(78,86)(82,84)(83,89);(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)(54,55,57,56)(58,59,63,69,64,67,62,68)(60,70,74,65,73,81,72,80)(61,75,77,82,78,66,76,83)(71,84,87,88,86,89,85,79)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,c^2=h,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,f^a=fh,i^a=i^52,e^b=eh,f^b=fh,g^b=gh,i^b=i^52,e^c=eh,g^c=gh1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 171162);