Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13680 |
378 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 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)(54,57,61,75)(55,63,66,77)(56,68,71,84)(58,62,59,74)(60,80,81,67)(64,72,76,70)(65,69,85,83)(73,79,82,78);(54,56)(55,62)(57,68)(58,77)(59,63)(60,70)(61,71)(64,80)(65,82)(66,74)(67,76)(69,78)(72,81)(73,85)(75,84)(79,83);(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)(54,55,61,66)(56,67,71,80)(57,72,75,70)(58,76,59,64)(60,65,81,85)(62,77,74,63)(68,78,84,79)(69,82,83,73)Polycyclic presentation:
2^8,53|a^2=h,c^2=h,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fg,i^a=i^52,d^b=dh,e^b=efgh,g^b=gh,d^c=df,f^c=fh,g^c=gh,e^d=egh,f^d=fh,f^e=fh698 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90321);