Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13456 |
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 99 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)(54,57,58,56)(55,59,60,61)(63,69)(64,75)(66,81)(67,80)(68,82)(70,85)(71,73)(72,86)(74,89)(76,78)(77,91)(79,87)(83,92)(84,88);(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)(54,56,58,57)(55,59,60,61)(62,64,65,76)(63,68,70,74)(66,77,79,91)(67,75,80,78)(69,84,85,92)(71,82,86,89)(72,88,73,83)(81,90,87,93);(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)(54,55,58,60)(56,61,57,59)(62,63,65,70)(64,74,76,68)(66,69,79,85)(67,72,80,73)(71,87,86,81)(75,83,78,88)(77,92,91,84)(82,90,89,93)Polycyclic presentation:
2^8,53|a^2=d,b^2=d,c^2=dh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^a=i^52,c^b=cf,f^b=fh,i^b=i^52,e^c=eg,f^c=fh,g^c=gh1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89211);