Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13602 |
326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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 — 3 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)(54,57,60,58)(55,62,65,73)(56,67,71,68)(59,72,75,74)(61,76,78,83)(63,79,81,64)(66,82,80,77)(69,84,70,85);(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)(54,56,60,71)(55,61)(57,67,58,68)(59,69,75,70)(62,76)(63,80)(64,82)(65,78)(66,81)(72,84,74,85)(73,83)(77,79);(54,55)(56,66,69,76)(57,62)(58,73)(59,64,75,79)(60,65)(61,68,77,85)(63,74,81,72)(67,82,84,78)(70,83,71,80)Polycyclic presentation:
2^8,53|a^2=e,b^2=g,c^2=h,d^2=g,f^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,d^b=dgh,e^b=efgh,f^b=fh,i^b=i^52,e^d=egh,f^e=fh710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89940);