Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #33360 |
1188 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1188 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)(54,57,59,70)(55,62,64,79)(56,65,67,68)(58,69,71,83)(60,73,63,78)(61,74,76,77)(66,80,81,82)(72,84,75,85);(54,56,59,67)(55,61,64,76)(57,68,70,65)(58,66,71,81)(60,72,63,75)(62,77,79,74)(69,82,83,80)(73,85,78,84);(55,60)(58,71)(61,72)(62,73)(63,64)(66,81)(69,83)(74,84)(75,76)(77,85)(78,79)(80,82);(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)(56,61)(57,62)(58,63,71,60)(59,64)(65,74)(66,75,81,72)(67,76)(68,77)(69,78,83,73)(70,79)(80,85,82,84)Polycyclic presentation:
2^8,53|a^2=f,c^2=h,d^2=h,e^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, 322377);