Finite Group DatabasebetaFinite Group Databasebeta| order | 33812 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8453 |
| unambiguous semidirect product | C79⋊Dic107 |
| unambiguous semidirect product | C107⋊Dic79 |
| derived, Hall | C79×C107 ⋊ C4 |
| Sylow | C107 ⋊ Dic79 |
| Sylow | C79 ⋊ Dic107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8453 |
| commutator, hypocenter | C79×C107 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C79×C107 | C2 |
| LCS | G ▷ C79×C107 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 190 |
| transitive degree | μt(G) = 33812 |
A minimal faithful permutation representation — 2 generators on 190 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);(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)(85,190)(86,189)(87,188)(88,187)(89,186)(90,185)(91,184)(92,183)(93,182)(94,181)(95,180)(96,179)(97,178)(98,177)(99,176)(100,175)(101,174)(102,173)(103,172)(104,171)(105,170)(106,169)(107,168)(108,167)(109,166)(110,165)(111,164)(112,163)(113,162)(114,161)(115,160)(116,159)(117,158)(118,157)(119,156)(120,155)(121,154)(122,153)(123,152)(124,151)(125,150)(126,149)(127,148)(128,147)(129,146)(130,145)(131,144)(132,143)(133,142)(134,141)(135,140)(136,139)(137,138)Polycyclic presentation:
2,79,107,2|a^2=d,b^a=b^78,c^a=c^1068456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33812, 4);