Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1958 ⋊ C2 |
| Sylow | C53 ⋊ #8528 |
728 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 107 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)(57,61)(58,60)(62,65)(63,69)(64,73)(66,80)(67,78)(68,82)(70,86)(71,76)(72,88)(74,91)(75,90)(77,81)(79,89)(83,92)(84,87)(85,93);(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)(56,61)(57,59)(58,60)(62,64)(63,68)(65,73)(66,79)(67,75)(69,82)(70,85)(71,83)(72,87)(74,81)(76,92)(77,91)(78,90)(80,89)(84,88)(86,93);(55,59)(56,57)(60,61)(62,63)(64,72,75,85)(65,76,78,69)(66,70)(67,71)(68,74,83,79)(73,88)(77,86,80,84)(81,87)(82,89)(90,93)(91,92)Polycyclic presentation:
2^8,53|a^2=f,d^2=h,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,e^b=egh,f^b=fgh,i^b=i^52,d^c=dgh,e^c=eg,f^c=fgh,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, 62112);