Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1338 ⋊ C2 |
| Sylow | C53 ⋊ #11618 |
324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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) = 6784 |
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)(54,56,57,61)(55,58,60,59)(62,65,67,68)(63,70,71,73)(64,75,77,78)(66,79,81,82)(69,83,74,85)(72,86,87,89)(76,90,80,91)(84,92,88,93);(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)(56,58)(57,60)(59,61)(62,64)(63,69)(65,78)(66,80)(67,77)(68,75)(70,85)(71,74)(72,88)(73,83)(76,81)(79,90)(82,91)(84,87)(86,92)(89,93);(54,55,56,58,57,60,61,59)(62,63,66,72,68,73,82,89,67,71,81,87,65,70,79,86)(64,74,76,88,75,85,90,93,77,69,80,84,78,83,91,92)Polycyclic presentation:
2^8,53|a^2=e,c^2=f,d^2=fh,e^2=g,g^2=h,b^a=bd,d^a=df,c^b=ch,d^b=dfh,e^b=eh,i^b=i^52,i^c=i^521064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79424);