Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1846 ⋊ C2 |
| Sylow | C53 ⋊ #13534 |
330 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 97 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)(55,57)(58,61)(59,68)(60,66)(62,76)(63,77)(64,80)(65,75)(67,82)(69,85)(70,84)(71,83)(72,87)(73,74)(78,81)(79,89)(86,88);(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)(58,60,73,76,65,77,64,81)(59,67,71,89,72,85,88,84)(61,66,74,62,75,63,80,78)(68,82,83,79,87,69,86,70);(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)(58,59,66,70,73,88,62,69,65,72,63,79,64,71,78,82)(60,68,75,85,81,83,74,84,77,87,61,67,76,86,80,89)Polycyclic presentation:
2^8,53|a^2=dg,b^2=degh,d^2=g,e^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^52,c^b=cf,d^b=dg,e^b=eg,g^b=gh,i^b=i^52,d^c=dg,e^c=eg,g^c=gh,i^c=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89674);