Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#3255 ⋊ C2 |
| Sylow | C53 ⋊ #12174 |
340 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 59 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:
(2,9,12,11)(8,23,25,24)(10,27,28,18)(13,26,30,29)(33,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35);(1,3,7,17)(2,8,12,25)(4,19,21,32)(5,16,6,15)(9,23,11,24)(10,26,28,29)(13,27,30,18)(14,22,31,20);(1,2)(3,13)(4,18)(5,9)(6,11)(7,12)(8,14)(10,20)(15,26)(16,29)(17,30)(19,23)(21,27)(22,28)(24,32)(25,31)(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)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)Polycyclic presentation:
2^8,53|b^2=h,c^2=g,d^2=fh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fh,g^a=gh,i^a=i^52,d^b=df,e^b=egh,f^b=fh,d^c=dg,e^d=eh701 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 82099);