Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×#101×C53 ⋊ C2 |
| Sylow | C53 ⋊ #25142 |
986 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)(55,57);(58,61,63,74)(59,65,67,81)(60,68,70,72)(62,75,76,73)(64,77,79,80)(66,82,83,71)(69,86,87,85)(78,88,89,84);(55,57)(58,60,62,69,63,70,76,87)(59,64,66,78,67,79,83,89)(61,72,73,86,74,68,75,85)(65,80,71,88,81,77,82,84);(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)(56,57)(58,59,62,66,63,67,76,83)(60,64,69,78,70,79,87,89)(61,71,73,81,74,82,75,65)(68,84,85,80,72,88,86,77)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,c^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^52,c^b=cg,g^b=gh,f^c=fh1187 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 216851);