Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1376 ⋊ C2 |
| Sylow | C53 ⋊ #13333 |
546 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 105 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)(58,61,65,79)(59,67,70,71)(60,72,76,81)(62,74,82,75)(63,73,64,78)(66,68,84,87)(69,86,83,85)(77,89,88,80);(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)(55,57)(58,60,65,76)(59,66,70,84)(61,62,79,82)(63,75,64,74)(67,80,71,89)(68,86,87,85)(69,88,83,77)(72,73,81,78);(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)(56,57)(58,59)(60,71)(61,77)(62,80)(63,69)(64,83)(65,70)(66,73)(67,76)(68,72)(74,86)(75,85)(78,84)(79,88)(81,87)(82,89)Polycyclic presentation:
2^8,53|b^2=h,c^2=h,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,i^a=i^52,c^b=cf,d^b=dg,e^b=eg,f^b=fh,g^b=gh,i^b=i^52,d^c=dg,e^c=eg,f^c=fh,g^c=gh,i^c=i^521496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88447);