Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D16×C157 ⋊ C4 |
| Sylow | C157 ⋊ AGL(1,ℤ/16) |
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 2512 |
A minimal faithful permutation representation — 3 generators on 173 points:
(1,2,8,4)(3,6,18,14)(5,7,16,10)(9,12,32,24)(11,17,28,20)(13,15,30,26)(19,22,50,38)(21,31,42,34)(23,25,48,44)(27,29,46,40)(33,36,72,56)(35,49,60,52)(37,39,70,62)(41,47,66,58)(43,45,68,64)(51,54,98,78)(53,71,82,74)(55,57,96,84)(59,69,88,80)(61,63,94,90)(65,67,92,86)(73,76,128,104)(75,97,108,100)(77,79,126,110)(81,95,114,106)(83,85,124,116)(87,93,120,112)(89,91,122,118)(99,102,146,134)(101,127,138,130)(103,105,147,140)(107,125,143,136)(109,111,144,145)(113,123,129,132)(115,117,139,141)(119,121,133,135)(131,149,152,142)(137,148,154,150)(151,155,156,153)(158,160,168,171,162,169,161,167)(159,164,166,163,165,173,170,172);(158,159)(160,164)(161,170)(162,165)(163,171)(166,168)(167,172)(169,173);(2,3,5,4)(6,9,11,10)(7,13,14,8)(12,19,21,20)(15,23,24,18)(16,17,27,26)(22,33,35,34)(25,37,38,32)(28,31,41,40)(29,43,44,30)(36,51,53,52)(39,55,56,50)(42,49,59,58)(45,61,62,48)(46,47,65,64)(54,73,75,74)(57,77,78,72)(60,71,81,80)(63,83,84,70)(66,69,87,86)(67,89,90,68)(76,99,101,100)(79,103,104,98)(82,97,107,106)(85,109,110,96)(88,95,113,112)(91,115,116,94)(92,93,119,118)(102,129,131,130)(105,133,134,128)(108,127,137,136)(111,139,140,126)(114,125,142,132)(117,144,145,124)(120,123,146,135)(121,147,141,122)(138,149,151,150)(143,148,153,152)(154,155,157,156)(159,163,165,172)(160,167)(161,168)(164,170,173,166)(169,171)Polycyclic presentation:
2^7,157|a^2=e,c^2=efg,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,h^a=h^129,d^b=dfg,e^b=eg,f^b=fg,d^c=dg,h^c=h^28,h^e=h^156452 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 20920);