Finite Group DatabasebetaFinite Group Databasebeta| order | 35708 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8927 |
| unambiguous semidirect product | C79⋊Dic113 |
| derived, Hall | C79×C113 ⋊ C4 |
| Sylow | C113 ⋊ Dic79 |
| Sylow | C79 ⋊ Dic113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8927 |
| commutator, hypocenter | C79×C113 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C79×C113 | C2 |
| LCS | G ▷ C79×C113 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 196 |
| transitive degree | μt(G) = 35708 |
A minimal faithful permutation representation — 2 generators on 196 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);(1,3,2,4)(6,83)(7,82)(8,81)(9,80)(10,79)(11,78)(12,77)(13,76)(14,75)(15,74)(16,73)(17,72)(18,71)(19,70)(20,69)(21,68)(22,67)(23,66)(24,65)(25,64)(26,63)(27,62)(28,61)(29,60)(30,59)(31,58)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)(85,196)(86,195)(87,194)(88,193)(89,192)(90,191)(91,190)(92,189)(93,188)(94,187)(95,186)(96,185)(97,184)(98,183)(99,182)(100,181)(101,180)(102,179)(103,178)(104,177)(105,176)(106,175)(107,174)(108,173)(109,172)(110,171)(111,170)(112,169)(113,168)(114,167)(115,166)(116,165)(117,164)(118,163)(119,162)(120,161)(121,160)(122,159)(123,158)(124,157)(125,156)(126,155)(127,154)(128,153)(129,152)(130,151)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)(140,141)Polycyclic presentation:
2,79,113,2|a^2=d,b^a=b^78,c^a=c^1128930 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35708, 4);