Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1320 ⋊ C2 |
| Sylow | C53 ⋊ #11484 |
368 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 83 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:
(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)(54,56,58,66,59,64,69,77)(55,61,63,74,60,70,72,81)(57,65,68,78,67,76,79,84)(62,73,75,83,71,80,82,85);(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)(55,60)(56,64)(63,72)(65,76)(66,77)(73,80)(78,84)(83,85);(54,55,57,62,58,63,68,75,59,60,67,71,69,72,79,82)(56,61,65,73,66,74,78,83,64,70,76,80,77,81,84,85)Polycyclic presentation:
2^8,53|a^2=e,c^2=g,e^2=g,g^2=h,b^a=bd,d^a=df,f^a=fh,c^b=ch,e^b=ef,i^c=i^52,e^d=eh722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78871);