Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #12850 |
430 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 135 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) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 points:
(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)(55,57)(59,66,67,68)(60,71)(62,77)(65,79,70,81)(69,84,83,82)(72,74)(75,78)(80,89,85,88);(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)(58,60)(59,65)(61,72)(62,76)(63,74)(64,71)(66,81)(67,70)(68,79)(69,85)(73,77)(75,87)(78,86)(80,83)(82,88)(84,89);(54,55)(56,57)(58,59,62,69,63,66,78,82,64,67,77,83,61,68,75,84)(60,70,73,85,74,79,87,88,71,65,76,80,72,81,86,89)Polycyclic presentation:
2^8,53|a^2=f,c^2=d,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=ch,f^b=fh,f^c=fh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85797);