Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C53 ⋊ #12514 |
246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 101 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)(55,60)(59,67)(61,65)(62,68)(70,73,93,90,77,88,75,91,78,87,74,89,76,94,95,72)(71,80,99,98,84,96,82,92,85,86,81,97,83,100,101,79);(54,56,57,63,58,64,66,69)(55,59,61,62,60,67,65,68)(70,72,75,88,76,89,93,73,78,91,95,94,77,90,74,87)(71,79,82,96,83,97,99,80,85,92,101,100,84,98,81,86);(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)(56,62)(57,65)(58,60)(59,63)(61,66)(64,68)(67,69)(70,71,78,85)(72,86,91,80)(73,92,87,79)(74,82,93,101)(75,81,95,99)(76,84,77,83)(88,98,94,97)(89,100,90,96)Polycyclic presentation:
2^8,53|a^2=h,b^2=dgh,c^2=ef,d^2=fh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,g^a=gh,i^a=i^52,c^b=ch2126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84276);