Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7650 |
384 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 119 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) = 13568 |
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)(54,56,58,57)(55,59,60,61)(62,65,66,74)(63,68,69,73)(64,71,72,77)(67,75,70,76)(79,84)(83,91)(85,92)(86,93);(62,64,66,72)(63,67,69,70)(65,71,74,77)(68,75,73,76)(78,80)(79,83)(81,89)(82,88)(84,91)(85,93)(86,92)(87,90);(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)(54,55,57,59,58,60,56,61)(62,63)(64,70,72,67)(65,73)(66,69)(68,74)(71,75,77,76)(78,79)(80,86,88,93)(81,85)(82,84)(83,87,91,89)(90,92)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=fh,d^2=g,e^2=h,b^a=bd,c^a=cfgh,d^a=df,i^a=i^52,d^b=dg,e^b=efg1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57886);