Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #13734 |
150 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 150 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) = 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)(62,63,70,80,65,71,85,88,76,84,90,93,89,91,75,78,67,69,82,92,77,83,74,81,66,72,86,87,73,79,64,68);(54,56,57,61)(55,58,59,60)(63,69)(68,78)(71,83)(72,84)(79,91)(80,92)(81,88)(87,93);(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)(56,60,61,58)(63,68)(64,70)(65,73)(66,76)(69,78)(71,87)(72,88)(74,90)(75,82)(77,89)(79,80)(81,84)(83,93)(85,86)(91,92)Polycyclic presentation:
2^8,53|a^2=d,b^2=d,c^2=ef,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^a=i^52,c^b=ch2126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90599);