Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C53×#338 ⋊ C2 |
| Sylow | C53 ⋊ #23723 |
972 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 271 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(57,70)(61,69)(66,81)(71,76)(74,77)(78,83)(80,85)(82,84);(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)(54,57)(55,61)(56,66)(58,71)(59,70)(60,74)(62,78)(63,69)(64,80)(65,76)(67,82)(68,81)(72,84)(73,83)(75,77)(79,85);(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)(54,56,65,67,59,68,58,72)(55,60,73,64,63,75,62,79)(57,66,76,82,70,81,71,84)(61,77,83,85,69,74,78,80);(54,55,58,62,59,63,65,73)(56,64,67,75,68,79,72,60)(57,69,71,83,70,61,76,78)(66,80,82,77,81,85,84,74)Polycyclic presentation:
2^8,53|a^2=e,b^2=ef,e^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,e^b=eh,f^b=fh,i^b=i^52,d^c=dh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 199320);