Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C53×#2896 ⋊ C2 |
| Sylow | C53 ⋊ #20952 |
1818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 73 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)(58,61,63,65)(59,60,68,72)(62,73,64,69)(66,70,67,71);(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)(62,64)(66,67)(69,73)(70,71);(54,56,57,55)(58,60)(59,65)(61,68)(62,71)(63,72)(64,70)(66,73)(67,69);(54,55,57,56)(58,59,64,67,63,68,62,66)(60,69,71,65,72,73,70,61)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,d^2=h,e^2=h,g^2=h,b^a=be,c^a=cf,f^a=fh,e^b=eh,f^b=fh,g^b=gh,e^c=eh,g^c=gh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 171141);