Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#430 ⋊ C2 |
| Sylow | C53 ⋊ #20867 |
1312 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)(55,63)(61,76)(62,78)(64,74)(65,77)(70,79)(75,81)(80,85);(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)(58,71)(59,72)(60,73)(61,75)(63,78)(64,79)(65,80)(67,82)(68,84)(69,83)(70,74)(76,81)(77,85);(54,56,59,67,60,69,58,68)(55,61,64,77,63,76,74,65)(57,66,72,82,73,83,71,84)(62,75,79,85,78,81,70,80);(54,55,59,64,60,63,58,74)(56,65,67,61,69,77,68,76)(57,70,72,62,73,79,71,78)(66,81,82,80,83,75,84,85)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,f^a=fh,e^b=eh,f^c=fh,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, 170470);