Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C53×#413 ⋊ C2 |
| Sylow | C53 ⋊ #21017 |
1692 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)(54,58,60,59)(55,63,64,65)(56,67,68,72)(57,70,71,73)(61,75,76,78)(62,77,69,79)(66,80,81,82)(74,84,83,85);(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)(54,57)(55,62)(56,66)(58,70)(59,73)(60,71)(61,74)(63,77)(64,69)(65,79)(67,80)(68,81)(72,82)(75,84)(76,83)(78,85);(54,56,59,72,60,68,58,67)(55,61,63,75,64,76,65,78)(57,66,73,82,71,81,70,80)(62,74,77,84,69,83,79,85);(54,55,59,65,60,64,58,63)(56,61,67,75,68,76,72,78)(57,69,70,79,71,62,73,77)(66,74,82,85,81,83,80,84)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,d^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,e^b=eh,f^b=fh,g^b=gh,e^c=eh,g^c=gh,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, 171600);