Finite Group DatabasebetaFinite Group Databasebeta| order | 20758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10379 |
| unambiguous semidirect product | C97⋊D107 |
| unambiguous semidirect product | C107⋊D97 |
| Fitting, socle, derived, Hall | C97×C107 ⋊ C2 |
| Sylow | C107 ⋊ D97 |
| Sylow | C97 ⋊ D107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C97×C107 | C2 |
| LCS | G ▷ C97×C107 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 204 |
| transitive degree | μt(G) = 10379 |
A minimal faithful permutation representation — 2 generators on 204 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);(2,97)(3,96)(4,95)(5,94)(6,93)(7,92)(8,91)(9,90)(10,89)(11,88)(12,87)(13,86)(14,85)(15,84)(16,83)(17,82)(18,81)(19,80)(20,79)(21,78)(22,77)(23,76)(24,75)(25,74)(26,73)(27,72)(28,71)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)(99,204)(100,203)(101,202)(102,201)(103,200)(104,199)(105,198)(106,197)(107,196)(108,195)(109,194)(110,193)(111,192)(112,191)(113,190)(114,189)(115,188)(116,187)(117,186)(118,185)(119,184)(120,183)(121,182)(122,181)(123,180)(124,179)(125,178)(126,177)(127,176)(128,175)(129,174)(130,173)(131,172)(132,171)(133,170)(134,169)(135,168)(136,167)(137,166)(138,165)(139,164)(140,163)(141,162)(142,161)(143,160)(144,159)(145,158)(146,157)(147,156)(148,155)(149,154)(150,153)(151,152)Polycyclic presentation:
2,97,107|b^a=b^96,c^a=c^1065191 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20758, 3);