Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2975 ⋊ C2 |
| Sylow | C53 ⋊ #17623 |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,57,58,65)(55,61,60,67)(56,63,64,69)(59,66,62,68)(70,73,75,74)(71,78,77,82)(72,80,81,83)(76,85,84,79);(55,60)(57,65)(59,62)(63,69)(71,77)(76,84)(78,82)(79,85);(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)(55,59)(57,63)(58,64)(60,62)(61,66)(65,69)(67,68)(70,72)(71,76)(73,80)(74,83)(75,81)(77,84)(78,85)(79,82);(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)(56,62,64,59)(57,61)(58,60)(63,68,69,66)(65,67)(70,71)(72,79)(73,78)(74,82)(75,77)(76,80)(81,85)(83,84)Polycyclic presentation:
2^8,53|a^2=f,d^2=g,e^2=h,b^a=be,c^a=cg,e^a=eg,i^a=i^52,e^b=eh,f^b=fgh,i^b=i^52,d^c=dgh1193 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 137361);