Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1843 ⋊ C2 |
| Sylow | C53 ⋊ #10666 |
354 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 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)(54,55)(56,59)(57,60)(58,61)(62,65)(63,69)(64,72)(66,78)(67,76)(68,80)(70,85)(71,84)(73,90)(74,88)(75,86)(77,79)(81,92)(82,83)(87,93)(89,91);(55,59)(56,57)(60,61)(62,64,66,73,67,74,79,91)(63,68,70,81,71,82,86,93)(65,72,78,90,76,88,77,89)(69,83,85,87,84,80,75,92);(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)(54,55,57,59,58,61,56,60)(62,63)(64,68)(65,75,76,85)(66,70)(67,71)(69,77,84,78)(72,87,88,92)(73,81)(74,82)(79,86)(80,89,83,90)(91,93)Polycyclic presentation:
2^8,53|a^2=dg,b^2=de,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,f^a=fgh,i^a=i^52,c^b=cf,d^b=dg,e^b=eg,f^b=fg,d^c=dh,e^c=eh,f^c=fg,i^c=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 74580);