Finite Group DatabasebetaFinite Group Databasebeta| order | 20294 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10147 |
| unambiguous semidirect product | C73⋊D139 |
| unambiguous semidirect product | C139⋊D73 |
| Fitting, socle, derived, Hall | C73×C139 ⋊ C2 |
| Sylow | C139 ⋊ D73 |
| Sylow | C73 ⋊ D139 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C73×C139 | C2 |
| LCS | G ▷ C73×C139 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 212 |
| transitive degree | μt(G) = 10147 |
A minimal faithful permutation representation — 2 generators on 212 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)(74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212);(2,73)(3,72)(4,71)(5,70)(6,69)(7,68)(8,67)(9,66)(10,65)(11,64)(12,63)(13,62)(14,61)(15,60)(16,59)(17,58)(18,57)(19,56)(20,55)(21,54)(22,53)(23,52)(24,51)(25,50)(26,49)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)(75,212)(76,211)(77,210)(78,209)(79,208)(80,207)(81,206)(82,205)(83,204)(84,203)(85,202)(86,201)(87,200)(88,199)(89,198)(90,197)(91,196)(92,195)(93,194)(94,193)(95,192)(96,191)(97,190)(98,189)(99,188)(100,187)(101,186)(102,185)(103,184)(104,183)(105,182)(106,181)(107,180)(108,179)(109,178)(110,177)(111,176)(112,175)(113,174)(114,173)(115,172)(116,171)(117,170)(118,169)(119,168)(120,167)(121,166)(122,165)(123,164)(124,163)(125,162)(126,161)(127,160)(128,159)(129,158)(130,157)(131,156)(132,155)(133,154)(134,153)(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)(143,144)Polycyclic presentation:
2,73,139|b^a=b^72,c^a=c^1385075 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20294, 3);