Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#3291 ⋊ C2 |
| Sylow | C53 ⋊ #13674 |
454 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 848 |
A minimal faithful permutation representation — 3 generators on 69 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)(54,56)(55,59)(57,62)(58,64)(60,66)(61,68)(63,65)(67,69);(54,55,58,61)(56,59,64,68)(57,60,65,69)(62,66,63,67);(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)(57,65)(59,66)(67,68)Polycyclic presentation:
2^8,53|b^2=h,f^2=h,b^a=bd,c^a=ce,f^a=fg,i^a=i^52,e^b=efgh,g^b=gh,d^c=df,f^c=fh,g^c=gh,e^d=egh,f^d=fh,f^e=fh779 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90284);