Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #33371 |
1208 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1208 conjugacy classes of subgroups — too many to draw. Only its 311 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)(54,58,61,60)(55,64,66,65)(56,69,70,75)(57,71,59,72)(62,78,80,79)(63,81,73,82)(67,83,77,85)(68,84,74,76);(54,57,61,59)(55,63,66,73)(56,68,70,74)(58,72,60,71)(62,77,80,67)(64,82,65,81)(69,76,75,84)(78,83,79,85);(54,56)(55,62)(57,68)(58,69)(59,74)(60,75)(61,70)(63,77)(64,78)(65,79)(66,80)(67,73)(71,84)(72,76)(81,85)(82,83);(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)(54,55,60,65,61,66,58,64)(56,67,69,83,70,77,75,85)(57,63,71,81,59,73,72,82)(62,76,79,74,80,84,78,68)Polycyclic presentation:
2^8,53|a^2=f,c^2=h,d^2=h,e^2=h,f^2=h,b^a=be,e^a=eg,g^a=gh,i^a=i^52,e^b=eh,f^b=fgh,d^c=dh,f^e=fh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322427);