Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1341 ⋊ C2 |
| Sylow | C53 ⋊ #11688 |
432 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 79 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)(54,57,60,59)(55,62,64,75)(56,66,69,68)(58,70,74,73)(61,76,78,77)(63,71,81,80)(65,82,83,79)(67,72,85,84);(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)(55,61)(57,66)(58,72)(59,68)(60,69)(62,76)(63,79)(64,78)(65,71)(67,73)(70,85)(74,84)(75,77)(80,83)(81,82);(54,55,57,62,60,64,59,75)(56,65,68,79,69,83,66,82)(58,71,73,63,74,80,70,81)(61,72,76,85,78,84,77,67)Polycyclic presentation:
2^8,53|a^2=e,c^2=h,d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,d^a=df,g^a=gh,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,i^c=i^52,e^d=eh560 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79728);