Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C53 ⋊ #20962 |
1742 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)(58,62,63,75)(59,66,67,74)(60,69,70,83)(61,72,73,86)(64,77,78,82)(65,79,71,85)(68,80,81,89)(76,87,84,88);(58,61)(59,65)(60,68)(62,72)(63,73)(64,76)(66,79)(67,71)(69,80)(70,81)(74,85)(75,86)(77,87)(78,84)(82,88)(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)(54,56,57,55)(58,60,63,70)(59,64,67,78)(61,68,73,81)(62,69,75,83)(65,76,71,84)(66,77,74,82)(72,80,86,89)(79,87,85,88);(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)(54,55,57,56)(58,59)(60,64)(61,71,73,65)(62,74)(63,67)(66,75)(68,76,81,84)(69,82)(70,78)(72,79,86,85)(77,83)(80,88,89,87)Polycyclic presentation:
2^8,53|a^2=g,b^2=egh,d^2=h,b^a=be,c^a=cf,d^a=dh,f^a=fh,i^a=i^52,f^b=fh,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, 171214);