Finite Group DatabasebetaFinite Group Databasebeta| order | 20698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10349 |
| unambiguous semidirect product | C79⋊D131 |
| unambiguous semidirect product | C131⋊D79 |
| Fitting, socle, derived, Hall | C79×C131 ⋊ C2 |
| Sylow | C131 ⋊ D79 |
| Sylow | C79 ⋊ D131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C79×C131 | C2 |
| LCS | G ▷ C79×C131 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 210 |
| transitive degree | μt(G) = 10349 |
A minimal faithful permutation representation — 2 generators on 210 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);(2,79)(3,78)(4,77)(5,76)(6,75)(7,74)(8,73)(9,72)(10,71)(11,70)(12,69)(13,68)(14,67)(15,66)(16,65)(17,64)(18,63)(19,62)(20,61)(21,60)(22,59)(23,58)(24,57)(25,56)(26,55)(27,54)(28,53)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)(81,210)(82,209)(83,208)(84,207)(85,206)(86,205)(87,204)(88,203)(89,202)(90,201)(91,200)(92,199)(93,198)(94,197)(95,196)(96,195)(97,194)(98,193)(99,192)(100,191)(101,190)(102,189)(103,188)(104,187)(105,186)(106,185)(107,184)(108,183)(109,182)(110,181)(111,180)(112,179)(113,178)(114,177)(115,176)(116,175)(117,174)(118,173)(119,172)(120,171)(121,170)(122,169)(123,168)(124,167)(125,166)(126,165)(127,164)(128,163)(129,162)(130,161)(131,160)(132,159)(133,158)(134,157)(135,156)(136,155)(137,154)(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)(145,146)Polycyclic presentation:
2,79,131|b^a=b^78,c^a=c^1305176 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20698, 3);