Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#2252 ⋊ C2 |
| Sylow | C53 ⋊ #13719 |
202 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 75 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)(55,59)(58,61)(62,64,65,74,77,86,81,72,68,75,78,89,84,87,82,73,69,76,79,90,91,93,92,88,83,85,80,71,67,70,66,63);(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)(54,56,57,60)(55,58,59,61)(62,63,66,70,67,71,80,85,83,88,92,93,91,90,79,76,69,73,82,87,84,89,78,75,68,72,81,86,77,74,65,64);(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)(57,59)(60,61)(63,64)(65,66)(67,77)(68,83)(70,74)(71,86)(72,85)(73,76)(75,88)(78,92)(79,82)(80,81)(84,91)(87,90)(89,93)Polycyclic presentation:
2^8,53|b^2=e,c^2=d,d^2=fg,e^2=f,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,g^a=gh,i^a=i^52,i^b=i^52,i^c=i^521058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90538);