Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #8306 |
810 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 89 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)(55,57)(58,61,62,69)(59,64,65,71)(60,67,68,73)(63,70,66,72)(76,82)(79,85)(83,88)(86,89);(58,60,62,68)(59,63,65,66)(61,67,69,73)(64,70,71,72)(74,76)(75,79)(77,83)(78,82)(80,86)(81,85)(84,88)(87,89);(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)(56,57)(58,59)(60,66,68,63)(61,64)(62,65)(67,72,73,70)(69,71)(74,75,77,80,78,81,84,87)(76,79,83,86,82,85,88,89)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^52,c^b=ch,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, 60922);