Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #12461 |
188 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 67 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)(54,56,58,64)(55,59,61,68)(57,66,67,63)(60,69,65,62)(72,82)(76,90)(80,94)(83,89)(84,98)(91,95)(96,99)(97,101);(70,72,81,97,74,84,87,89,75,82,92,101,86,98,73,83)(71,76,85,96,78,91,93,94,79,90,100,99,88,95,77,80);(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)(56,62,64,69)(57,65,67,60)(59,66,68,63)(70,71,75,79)(72,80,82,94)(73,85,87,100)(74,88,86,78)(76,89,90,83)(77,92,93,81)(84,99,98,96)(91,97,95,101)Polycyclic presentation:
2^8,53|a^2=gh,b^2=df,c^2=g,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,i^a=i^52,c^b=ch,e^c=eg,i^c=i^521181 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83950);