Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #10804 |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(58,61,62,73,63,74,75,88)(59,65,66,78,67,72,79,87)(60,69,70,83,71,84,85,89)(64,76,68,80,77,86,81,82);(54,55,56,57)(58,60)(59,64,67,77)(61,69)(62,70)(63,71)(65,76,72,86)(66,68,79,81)(73,83)(74,84)(75,85)(78,80,87,82)(88,89);(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)(58,59)(60,68,71,81)(61,72,74,65)(62,66)(63,67)(64,70,77,85)(69,82)(73,87,88,78)(75,79)(76,83)(80,84)(86,89)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=d,d^2=h,b^a=bd,c^a=ce,e^a=eh,g^a=gh,i^a=i^52,f^b=fh,f^c=fh2144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 75214);