Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #12704 |
962 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 962 conjugacy classes of subgroups — too many to draw. Only its 139 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:
(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)(58,61,64,62)(59,66,68,75)(60,70,73,71)(63,74,78,76)(65,69,81,82)(67,83,85,84)(72,87,77,79)(80,86,89,88);(58,60,64,73)(59,65,68,81)(61,71,62,70)(63,77,78,72)(66,82,75,69)(67,80,85,89)(74,87,76,79)(83,88,84,86);(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)(58,59,63,67,64,68,78,85)(60,69,72,86,73,82,77,88)(61,66,74,83,62,75,76,84)(65,79,80,70,81,87,89,71)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=h,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,c^b=ch,d^b=dh,f^b=fgh,f^d=fh1178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85091);