Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #20857 |
1330 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)(59,66)(64,79)(65,80)(67,74)(68,82)(78,89)(81,83)(84,85);(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)(58,61,63,73)(59,65,66,80)(60,69,71,87)(62,76,77,72)(64,78,79,89)(67,83,74,81)(68,84,82,85)(70,88,75,86);(54,56,57,55)(58,60)(59,64)(61,69)(62,75)(63,71)(65,78)(66,79)(67,82)(68,74)(70,77)(72,88)(73,87)(76,86)(80,89)(81,84)(83,85);(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)(54,55,57,56)(58,59)(60,68)(61,65)(62,74)(63,66)(64,70)(67,77)(69,85)(71,82)(72,83)(73,80)(75,79)(76,81)(78,86)(84,87)(88,89)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,c^2=h,e^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^52,e^b=eh,f^b=fh,e^c=eh,i^c=i^521202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 170397);