Finite Group DatabasebetaFinite Group Databasebeta| order | 20032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C313 ⋊ #435 |
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 325 |
| transitive degree | μt(G) = 10016 |
A minimal faithful permutation representation — 3 generators on 325 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)(99,102,162,134)(100,127,138,131)(103,105,160,140)(106,125,144,137)(109,111,158,146)(112,123,150,143)(115,117,156,152)(118,121,154,149)(129,132,200,168)(130,161,172,165)(133,135,198,174)(136,159,178,171)(139,141,196,180)(142,157,184,177)(145,147,194,186)(148,155,190,183)(151,153,192,189)(163,166,242,206)(164,199,210,203)(167,169,240,212)(170,197,216,209)(173,175,238,218)(176,195,222,215)(179,181,236,224)(182,193,228,221)(185,187,234,230)(188,191,232,227)(201,204,288,248)(202,241,252,245)(205,207,286,254)(208,239,258,251)(211,213,284,260)(214,237,264,257)(217,219,282,266)(220,235,270,263)(223,225,280,272)(226,233,276,269)(229,231,278,275)(243,246,290,293)(244,287,292,291)(247,249,294,297)(250,285,296,295)(253,255,298,301)(256,283,300,299)(259,261,302,305)(262,281,304,303)(265,267,306,309)(268,279,308,307)(271,273,310,313)(274,277,312,311)(318,320,321,323,322,324,325,319);(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)(117,146)(120,148)(121,152)(122,151)(123,149)(124,145)(125,143)(126,139)(127,137)(128,133)(129,131)(132,164)(135,168)(138,170)(141,174)(144,176)(147,180)(150,182)(153,186)(154,188)(155,189)(156,185)(157,183)(158,179)(159,177)(160,173)(161,171)(162,167)(163,165)(166,202)(169,206)(172,208)(175,212)(178,214)(181,218)(184,220)(187,224)(190,226)(191,230)(192,229)(193,227)(194,223)(195,221)(196,217)(197,215)(198,211)(199,209)(200,205)(201,203)(204,244)(207,248)(210,250)(213,254)(216,256)(219,260)(222,262)(225,266)(228,268)(231,272)(232,274)(233,275)(234,271)(235,269)(236,265)(237,263)(238,259)(239,257)(240,253)(241,251)(242,247)(243,245)(246,290)(249,293)(252,294)(255,297)(258,298)(261,301)(264,302)(267,305)(270,306)(273,309)(276,310)(277,313)(278,312)(279,311)(280,308)(281,307)(282,304)(283,303)(284,300)(285,299)(286,296)(287,295)(288,292)(289,291)(315,317);(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)(114,125,142,143)(117,145,146,124)(120,123,148,149)(121,151,152,122)(132,163,164,165)(135,167,168,162)(138,161,170,171)(141,173,174,160)(144,159,176,177)(147,179,180,158)(150,157,182,183)(153,185,186,156)(154,155,188,189)(166,201,202,203)(169,205,206,200)(172,199,208,209)(175,211,212,198)(178,197,214,215)(181,217,218,196)(184,195,220,221)(187,223,224,194)(190,193,226,227)(191,229,230,192)(204,243,244,245)(207,247,248,242)(210,241,250,251)(213,253,254,240)(216,239,256,257)(219,259,260,238)(222,237,262,263)(225,265,266,236)(228,235,268,269)(231,271,272,234)(232,233,274,275)(246,289,290,291)(249,292,293,288)(252,287,294,295)(255,296,297,286)(258,285,298,299)(261,300,301,284)(264,283,302,303)(267,304,305,282)(270,281,306,307)(273,308,309,280)(276,279,310,311)(277,312,313,278)(314,315)(316,317)(318,319,321,320,322,323,325,324)Polycyclic presentation:
2^6,313|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^288,g^b=g^312,g^c=g^25,g^e=g^312808 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20032, 1581);