Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13170 |
278 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,61,72,74,63,76,80,89,64,77,60,71,79,86,62,75)(59,66,78,88,69,84,65,81,70,85,82,87,68,83,67,73);(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)(55,57)(58,60,63,62,64,72,79,80)(59,65,68,78,70,67,69,82)(61,74,76,89,77,71,86,75)(66,73,83,87,85,81,84,88);(54,55)(56,57)(58,59,63,68,64,70,79,69)(60,65,62,78,72,67,80,82)(61,73,76,87,77,81,86,88)(66,74,83,89,85,71,84,75)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,c^2=eg,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,c^b=ch,i^b=i^52,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87622);