Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1415 ⋊ C2 |
| Sylow | C53 ⋊ #13712 |
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56,57,60)(55,59,58,61)(63,69)(65,76)(66,77)(67,75)(68,81)(70,71)(72,87)(73,88)(74,89)(78,93)(79,84)(80,85)(82,83)(86,91)(90,92);(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)(55,58)(59,61)(63,68)(69,81)(70,82)(71,83)(72,80)(79,91)(84,86)(85,87);(54,55)(56,59)(57,58)(60,61)(62,63)(64,68)(65,69)(66,79)(67,80)(70,76)(71,77)(72,75)(73,81)(74,91)(78,87)(82,88)(83,89)(84,92)(85,90)(86,93)Polycyclic presentation:
2^8,53|c^2=dh,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^b=i^52,e^c=ef,f^c=fg,g^c=gh1037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90497);