Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD32×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:
(1,2,8,5)(3,6,18,14)(4,7,16,11)(9,12,32,24)(10,17,28,21)(13,15,30,27)(19,22,50,38)(20,31,42,35)(23,25,48,44)(26,29,46,41)(33,36,72,56)(34,49,60,53)(37,39,70,62)(40,47,66,59)(43,45,68,65)(51,54,98,78)(52,71,82,75)(55,57,96,84)(58,69,88,81)(61,63,94,90)(64,67,92,87)(73,76,128,104)(74,97,108,101)(77,79,126,110)(80,95,114,107)(83,85,124,116)(86,93,120,113)(89,91,122,119)(99,102,146,134)(100,127,138,131)(103,105,147,140)(106,125,143,137)(109,111,144,145)(112,123,129,132)(115,117,139,141)(118,121,133,135)(130,149,152,142)(136,148,154,151)(150,155,157,153)(158,160,168,171,162,169,161,167)(159,164,166,163,165,173,170,172);(2,4)(3,5)(6,10)(7,14)(8,13)(9,11)(12,20)(15,24)(16,26)(17,27)(18,23)(19,21)(22,34)(25,38)(28,40)(29,44)(30,43)(31,41)(32,37)(33,35)(36,52)(39,56)(42,58)(45,62)(46,64)(47,65)(48,61)(49,59)(50,55)(51,53)(54,74)(57,78)(60,80)(63,84)(66,86)(67,90)(68,89)(69,87)(70,83)(71,81)(72,77)(73,75)(76,100)(79,104)(82,106)(85,110)(88,112)(91,116)(92,118)(93,119)(94,115)(95,113)(96,109)(97,107)(98,103)(99,101)(102,130)(105,134)(108,136)(111,140)(114,142)(117,145)(120,146)(121,141)(122,147)(123,135)(124,144)(125,132)(126,139)(127,137)(128,133)(129,131)(138,150)(143,153)(148,152)(149,151)(154,156)(155,157)(158,159)(160,164)(161,170)(162,165)(163,171)(166,168)(167,172)(169,173);(2,3,4,5)(6,9,10,11)(7,13,14,8)(12,19,20,21)(15,23,24,18)(16,17,26,27)(22,33,34,35)(25,37,38,32)(28,31,40,41)(29,43,44,30)(36,51,52,53)(39,55,56,50)(42,49,58,59)(45,61,62,48)(46,47,64,65)(54,73,74,75)(57,77,78,72)(60,71,80,81)(63,83,84,70)(66,69,86,87)(67,89,90,68)(76,99,100,101)(79,103,104,98)(82,97,106,107)(85,109,110,96)(88,95,112,113)(91,115,116,94)(92,93,118,119)(102,129,130,131)(105,133,134,128)(108,127,136,137)(111,139,140,126)(114,125,142,132)(117,144,145,124)(120,123,146,135)(121,147,141,122)(138,149,150,151)(143,148,153,152)(154,155,156,157)(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,h^b=h^156,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, 20922);