Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9280 |
382 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 101 points:
(1,2)(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)(54,56)(55,60)(57,65)(58,63)(59,67)(61,69)(62,66)(64,68)(70,73,75,86)(71,77,79,84)(72,81,83,97)(74,88,89,85)(76,90,91,100)(78,93,87,92)(80,94,95,101)(82,98,99,96);(54,55,57,64,58,61,66,59)(56,60,65,68,63,69,62,67)(70,72,74,82,75,83,89,99)(71,76,78,80,79,91,87,95)(73,81,88,98,86,97,85,96)(77,90,93,94,84,100,92,101);(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)(55,59,61,64)(56,62,63,65)(70,71)(72,80)(73,84,86,77)(74,87)(75,79)(76,82)(78,89)(81,94,97,101)(83,95)(85,92,88,93)(90,96,100,98)(91,99)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=g,d^2=gh,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^52,d^b=dh,e^b=egh,f^b=fh,d^c=dgh,e^c=eh,f^c=fgh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 66163);