Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #510×C157 ⋊ C2 |
| Sylow | C157 ⋊ #3417 |
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 221 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 4 generators on 221 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)(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)(93,94)(95,96)(97,98)(99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(161,175)(166,189)(171,199)(176,203)(177,204)(186,212)(190,214)(191,208)(197,219)(200,211)(201,209)(205,218)(206,221)(207,215)(213,217)(216,220);(158,161)(159,166)(160,171)(162,176)(163,177)(164,175)(165,186)(167,190)(168,191)(169,189)(170,197)(172,200)(173,201)(174,199)(178,205)(179,206)(180,204)(181,207)(182,203)(183,208)(184,209)(185,211)(187,213)(188,212)(192,215)(193,216)(194,214)(195,217)(196,218)(198,219)(202,220)(210,221);(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)(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)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)(128,129)(130,131)(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)(146,147)(148,149)(150,151)(152,153)(154,155)(156,157)(158,160,164,174)(159,165,169,188)(161,171,175,199)(162,179,182,210)(163,184,180,173)(166,186,189,212)(167,193,194,202)(168,195,183,187)(170,196,198,178)(172,192,185,181)(176,206,203,221)(177,209,204,201)(190,216,214,220)(191,217,208,213)(197,218,219,205)(200,215,211,207);(158,159,164,169)(160,170,174,198)(161,166,175,189)(162,178,182,196)(163,183,180,168)(165,185,188,172)(167,192,194,181)(171,197,199,219)(173,202,184,193)(176,205,203,218)(177,208,204,191)(179,195,210,187)(186,211,212,200)(190,215,214,207)(201,220,209,216)(206,217,221,213)Polycyclic presentation:
2^7,157|a^2=g,b^2=g,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,e^b=ef,f^b=fg,h^b=h^156,d^c=dg,h^d=h^1561280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 17662);