Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9671 |
434 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 123 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)(54,57,58,59)(55,60,56,61)(62,65,66,76,67,77,79,90)(63,69,71,75,70,83,78,89)(64,72,74,86,73,85,87,91)(68,80,81,84,82,92,88,93);(54,56,59,61,58,55,57,60)(62,64,67,73)(63,68)(65,72,77,85)(66,74,79,87)(69,80)(70,82)(71,81)(75,84)(76,86,90,91)(78,88)(83,92)(89,93);(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)(54,55,59,60,58,56,57,61)(62,63)(64,68,73,82)(65,75)(66,78)(67,70)(69,76)(71,79)(72,84,85,93)(74,88,87,81)(77,89)(80,91,92,86)(83,90)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,c^2=e,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^52,c^b=ch,d^b=dg,f^b=fg1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 68509);