Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1391 ⋊ C2 |
| Sylow | C53 ⋊ #7406 |
244 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 2 generators on 117 points:
(1,3)(2,8)(4,20)(5,16)(6,30)(7,18)(9,35)(10,32)(11,40)(12,34)(13,37)(14,23)(15,28)(17,21)(19,41)(22,47)(24,54)(25,53)(26,44)(27,50)(29,33)(31,39)(36,51)(38,64)(42,52)(43,61)(45,57)(46,55)(48,56)(49,60)(58,63)(59,62)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117);(1,2)(3,13,15,41)(4,19)(5,25,27,10)(6,29)(7,12)(8,14,31,44)(9,22,36,26)(11,21)(16,42,17,51)(18,43,48,64)(20,53,45,40)(23,58)(24,38)(28,39,56,59)(30,35,50,63)(32,49,33,54)(34,46,62,47)(37,60,61,57)(52,55)(65,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67)Polycyclic presentation:
2^8,53|a^2=d,c^2=fh,f^2=h,b^a=bc,c^a=ce,e^a=eg,f^a=fh,g^a=gh,c^b=cf,d^b=def,f^b=fh,g^b=gh,i^b=i^52,d^c=dg,e^c=eh,e^d=eh707 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57086);