Finite Group DatabasebetaFinite Group Databasebeta| order | 29094 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C373⋊C3)⋊D13 |
| Fitting, socle, derived, Hall | C13×C373 ⋊ C2×C3 |
| Hall | C13×C373⋊C3 ⋊ C2 |
| Hall | D4849 ⋊ C3 |
| Hall | C373⋊C3 ⋊ D13 |
| Sylow | C373 ⋊ C3×D13 |
| Sylow | C13 ⋊ D373⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C373 | C2×C3 |
| LCS | G ▷ C13×C373 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 386 |
| transitive degree | μt(G) = 4849 |
A minimal faithful permutation representation — 2 generators on 386 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,19,20,16,17,21)(18,27,28,22,23,37)(24,40,41,30,31,54)(25,39,35,33,29,26)(32,59,60,43,44,77)(34,57,58,46,42,51)(36,38,56,48,49,52)(45,82,83,62,63,106)(47,80,81,65,61,74)(50,55,79,67,68,75)(53,95,93,71,72,70)(64,111,112,85,86,141)(66,109,110,88,84,103)(69,78,108,90,91,104)(73,124,125,96,97,99)(76,130,122,100,101,94)(87,146,147,114,115,182)(89,144,145,117,113,138)(92,107,143,119,120,139)(98,159,160,126,127,134)(102,166,164,131,132,129)(105,171,157,135,136,123)(116,187,188,149,150,229)(118,185,186,152,148,179)(121,142,184,154,155,180)(128,200,201,161,162,175)(133,207,208,167,168,170)(137,213,205,172,173,165)(140,218,198,176,177,158)(151,234,235,190,191,282)(153,232,233,193,189,226)(156,183,231,195,196,227)(163,247,248,202,203,222)(169,254,255,209,210,217)(174,261,259,214,215,212)(178,266,252,219,220,206)(181,271,245,223,224,199)(192,287,288,237,238,334)(194,285,286,240,236,279)(197,230,284,242,243,280)(204,298,299,249,250,275)(211,304,305,256,257,270)(216,309,310,262,263,265)(221,313,307,267,268,260)(225,318,302,272,273,253)(228,323,296,276,277,246)(239,311,317,264,290,350)(241,337,338,291,289,331)(244,283,336,293,294,332)(251,343,344,300,301,327)(258,339,347,292,306,322)(269,353,351,314,315,312)(274,355,348,319,320,308)(278,359,345,324,325,303)(281,363,341,328,329,297)(295,335,354,316,340,370)(321,378,375,356,357,352)(326,379,373,360,361,349)(330,380,371,364,365,346)(333,377,358,367,368,342)(362,384,385,372,369,376)(366,386,383,381,382,374);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,18,24,32,45,64,87,116,151,192,239,262,214,172,135,91,44,61,72,75,77,103,134,170,212,260,308,349,374,381,364,328,243,150,189,203,210,215,220,224,227,229,279,327,338,235,284,323,318,313,309,304,298,285,234,283,333,369,382,385,375,351,310,255,201,145,83,108,130,124,109,82,107,140,178,221,269,316,293,242,195,154,119,90,67,48,35,20,19,25,34,47,66,89,118,153,194,241,292,256,209,167,131,100,68,31,42,52,54,74,99,129,165,206,253,303,346,372,360,324,276,196,115,148,162,168,173,177,180,182,226,275,322,288,336,363,359,355,353,290,339,343,337,287,335,357,361,365,368,370,350,305,248,186,112,143,171,166,159,144,111,142,181,225,274,321,358,341,296,245,198,157,122,93,58,28,39,27,38,53,73,98,128,163,204,251,300,249,202,161,126,96,71,49,23,29,37,51,70,94,123,158,199,246,297,342,356,319,272,223,155,86,113,127,132,136,139,141,179,222,270,317,354,377,380,379,378,340,238,289,301,306,311,315,320,325,329,332,334,347,299,233,147,184,218,213,207,200,185,146,183,228,278,326,362,371,345,302,252,205,164,125,81,41,56,57,40,55,76,102,133,169,211,258,291,240,193,152,117,88,65,46,33,17,21,26,36,50,69,92,121,156,197,244,295,314,267,219,176,120,63,84,97,101,104,106,138,175,217,265,312,352,376,386,384,367,294,191,236,250,257,263,268,273,277,280,282,331,344,286,188,231,271,266,261,254,247,232,187,230,281,330,366,383,373,348,307,259,208,160,110,60,79,95,80,59,78,105,137,174,216,264,237,190,149,114,85,62,43,30,22,16)Polycyclic presentation:
2,3,13,373|c^a=c^12,d^a=d^372,d^b=d^284830 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29094, 21);