Finite Group DatabasebetaFinite Group Databasebeta| order | 34036 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8509 |
| unambiguous semidirect product | C67⋊Dic127 |
| unambiguous semidirect product | C127⋊Dic67 |
| derived, Hall | C67×C127 ⋊ C4 |
| Sylow | C127 ⋊ Dic67 |
| Sylow | C67 ⋊ Dic127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8509 |
| commutator, hypocenter | C67×C127 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C67×C127 | C2 |
| LCS | G ▷ C67×C127 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 198 |
| transitive degree | μt(G) = 34036 |
A minimal faithful permutation representation — 2 generators on 198 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);(1,3,2,4)(6,71)(7,70)(8,69)(9,68)(10,67)(11,66)(12,65)(13,64)(14,63)(15,62)(16,61)(17,60)(18,59)(19,58)(20,57)(21,56)(22,55)(23,54)(24,53)(25,52)(26,51)(27,50)(28,49)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,39)(73,198)(74,197)(75,196)(76,195)(77,194)(78,193)(79,192)(80,191)(81,190)(82,189)(83,188)(84,187)(85,186)(86,185)(87,184)(88,183)(89,182)(90,181)(91,180)(92,179)(93,178)(94,177)(95,176)(96,175)(97,174)(98,173)(99,172)(100,171)(101,170)(102,169)(103,168)(104,167)(105,166)(106,165)(107,164)(108,163)(109,162)(110,161)(111,160)(112,159)(113,158)(114,157)(115,156)(116,155)(117,154)(118,153)(119,152)(120,151)(121,150)(122,149)(123,148)(124,147)(125,146)(126,145)(127,144)(128,143)(129,142)(130,141)(131,140)(132,139)(133,138)(134,137)(135,136)Polycyclic presentation:
2,67,127,2|a^2=d,b^a=b^66,c^a=c^1268512 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34036, 4);