Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #10428 |
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 89 points:
(1,2)(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)(54,56,57,55)(59,64)(61,70)(63,71)(65,66)(67,69)(72,73)(76,82)(77,86)(79,87)(80,85)(83,84)(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)(54,55)(56,57)(58,60,62,68)(59,63,66,73)(61,69,70,67)(64,72,65,71)(74,76)(75,79)(77,82)(78,83)(80,87)(81,88)(84,86)(85,89);(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)(55,56)(58,59,62,66)(60,63,68,73)(61,64,70,65)(67,71,69,72)(74,75,78,81)(76,79,83,88)(77,85,86,80)(82,89,84,87)Polycyclic presentation:
2^8,53|a^2=h,b^2=g,c^2=d,e^2=g,f^2=gh,b^a=bd,c^a=ce,e^a=eg,f^a=fh,i^a=i^52,c^b=cf,e^b=eh,f^b=fgh,i^b=i^52,e^c=eg,f^c=fgh,i^c=i^521022 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 73063);