Finite Group DatabasebetaFinite Group Databasebeta| order | 13143 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C337 ⋊ C3 |
| Sylow | C337 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ C337⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C337 | C3 |
| LCS | G ▷ C13×C337 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 350 |
| transitive degree | μt(G) = 4381 |
A minimal faithful permutation representation — 2 generators on 350 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,184)(151,180,206)(154,183,203)(157,186,200)(160,189,197)(163,192,194)(166,195,191)(169,198,188)(172,201,185)(175,204,182)(177,207,179)(181,211,213)(187,215,232)(190,218,229)(193,221,226)(196,224,223)(199,227,220)(202,230,217)(205,233,214)(208,235,212)(209,216,210)(219,241,255)(222,244,252)(225,247,249)(228,250,246)(231,253,243)(234,256,240)(236,258,239)(237,242,238)(245,264,275)(248,267,272)(251,270,269)(254,273,266)(257,276,263)(259,278,262)(260,265,261)(268,284,292)(271,287,289)(274,290,286)(277,293,283)(279,295,282)(280,285,281)(288,301,306)(291,304,303)(294,307,300)(296,309,299)(297,302,298)(305,315,317)(308,318,314)(310,320,313)(311,316,312)(319,326,325)(321,328,324)(322,327,323)(329,333,332)(330,334,331)(335,337,336)(339,340,342)(341,344,347)(343,346,345)(348,350,349);(1,2,4,8,15,25,38,54,73,95,120,148,150,94,118,144,172,202,231,254,274,291,305,316,295,256,201,140,90,51,67,86,108,133,161,191,220,243,263,282,298,284,244,189,128,78,40,14,23,34,47,63,82,104,129,157,187,216,176,206,178,209,237,260,280,297,311,322,330,335,337,328,307,273,227,165,109,65,33,12,19,29,42,58,77,99,124,152,182,212,238,215,153,97,53,71,91,113,138,166,196,225,248,268,285,258,204,143,92,114,139,167,197,226,249,269,286,300,313,323,315,287,247,192,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,181,180,119,146,175,205,234,257,277,294,308,319,327,309,276,230,168,112,68,35,48,64,83,105,130,158,188,217,240,262,281,264,218,156,100,56,24,36,50,66,85,107,132,160,190,219,242,207,145,173,203,232,255,275,292,306,317,325,332,336,333,318,290,250,195,134,84,46,20,5,9,16,26,39,55,74,96,121,149,179,210,183,122,72,93,116,141,169,199,228,251,271,288,302,278,233,171,115,70,89,111,136,164,194,223,246,266,283,299,312,301,267,221,159,103,59,27,7,13,21,31,44,60,79,101,126,154,184,213,211,147,177,208,236,259,279,296,310,321,329,334,320,293,253,198,137,87,49,22,32,45,61,80,102,127,155,185,214,239,261,241,186,125,75,37,52,69,88,110,135,163,193,222,245,265,235,174,117,142,170,200,229,252,272,289,303,314,324,331,326,304,270,224,162,106,62,30,10)(338,339,341,340,343,347,344,348,350,342,345,349,346)Polycyclic presentation:
3,13,337|b^a=b^3,c^a=c^1281463 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#27190355, #39911397, #39911401, … |
| maximal normal subgroup of | C2×#27190355, #39911397, #39911401, … |
| maximal quotient of | C2×#27190355 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13143, 3);