Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1346 ⋊ C2 |
| Sylow | C53 ⋊ #12201 |
380 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 points:
(3,7)(5,8)(9,12)(10,16,18,32)(11,19)(13,25)(14,24)(15,28,30,31)(17,22,26,37)(20,35)(21,23)(27,40)(29,34,33,38)(36,39)(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)(85,86)(87,88)(89,90)(91,92);(1,2)(3,8)(4,6)(5,7)(9,11,14,21)(10,15,18,30)(12,23,24,19)(13,20,27,36)(16,31,32,28)(17,33,26,29)(22,34,37,38)(25,39,40,35);(2,5)(3,7)(6,8)(9,10)(11,15)(12,22)(13,26)(14,18)(16,25)(17,27)(19,34)(20,33)(21,30)(23,38)(24,37)(28,35)(29,36)(31,39)(32,40)(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)(86,87)(88,89)(90,91)(92,93)Polycyclic presentation:
2^8,53|b^2=h,c^2=fgh,d^2=f,e^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,g^a=gh,i^a=i^52,c^b=ch,d^b=df,e^b=egh,d^c=dg,i^c=i^52,e^d=eh623 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 82280);