Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1663 ⋊ C2 |
| Sylow | C53 ⋊ #19063 |
806 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 141 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) = 6784 |
A minimal faithful permutation representation — 4 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)(70,74,76,75)(71,79,80,88)(72,83,84,89)(73,85,87,86)(77,91,92,81)(78,93,94,95)(82,98,99,100)(90,96,101,97);(54,56)(55,59)(57,66)(58,63)(60,69)(61,68)(62,64)(65,67)(70,73,76,87)(71,78,80,94)(72,82,84,99)(74,86,75,85)(77,90,92,101)(79,95,88,93)(81,96,91,97)(83,100,89,98);(54,55,58,61)(56,59,63,68)(57,65,64,60)(62,69,66,67)(70,72,76,84)(71,77,80,92)(73,82,87,99)(74,83,75,89)(78,90,94,101)(79,91,88,81)(85,98,86,100)(93,96,95,97);(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)(56,62)(57,64)(59,67)(60,65)(63,66)(68,69)(70,71)(72,81)(73,78)(74,79)(75,88)(76,80)(77,83)(82,97)(84,91)(85,93)(86,95)(87,94)(89,92)(90,98)(96,99)(100,101)Polycyclic presentation:
2^8,53|b^2=h,c^2=g,d^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,e^a=eg,f^a=fgh,i^a=i^52,e^b=eg,f^b=fh,d^c=dg,e^c=eh,f^c=fgh,i^d=i^52554 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 151470);