Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7832 |
322 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 101 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)(54,57)(55,60)(56,62)(58,64)(59,65)(61,67)(63,69)(66,68)(70,73,75,74)(71,77,78,82)(72,80,81,83)(76,84,85,79)(87,92)(89,97)(91,98)(93,94)(95,101)(99,100);(54,56)(55,59)(57,62)(58,63)(60,65)(61,66)(64,69)(67,68)(70,72,75,81)(71,76,78,85)(73,80,74,83)(77,84,82,79)(86,88,90,96)(87,91,94,100)(89,95,97,101)(92,98,93,99);(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)(54,55,58,61)(56,59,63,66)(57,60,64,67)(62,68,69,65)(70,71,75,78)(72,79,81,84)(73,77,74,82)(76,83,85,80)(86,87,90,94)(88,91,96,100)(89,92,97,93)(95,98,101,99)Polycyclic presentation:
2^8,53|a^2=fgh,b^2=fh,c^2=f,d^2=f,e^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,i^a=i^52,d^b=df,e^b=eg,d^c=dg,e^c=eh,i^c=i^521025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 58883);