Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C53×#430 ⋊ C2 |
| Sylow | C53 ⋊ #33656 |
556 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)(54,57,60,59)(55,62,64,74)(56,66,67,75)(58,69,71,73)(61,76,77,78)(63,70,79,85)(65,80,81,82)(68,83,84,72);(54,56,59,75,60,67,57,66)(55,61,62,76,64,77,74,78)(58,72,73,84,71,83,69,68)(63,80,70,81,79,82,85,65);(58,71)(63,79)(65,81)(68,84)(69,73)(70,85)(72,83)(80,82);(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)(56,65)(57,62)(58,70)(59,74)(60,64)(61,68)(63,73)(66,80)(67,81)(69,79)(71,85)(72,78)(75,82)(76,83)(77,84)Polycyclic presentation:
2^8,53|c^2=eg,d^2=h,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,i^a=i^52,f^b=fh,e^c=eh,f^c=fgh,g^c=gh1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324464);