Finite Group DatabasebetaFinite Group Databasebeta| order | 34028 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8507 |
| unambiguous semidirect product | C47⋊Dic181 |
| derived, Hall | C47×C181 ⋊ C4 |
| Sylow | C181 ⋊ Dic47 |
| Sylow | C47 ⋊ Dic181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8507 |
| commutator, hypocenter | C47×C181 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C47×C181 | C2 |
| LCS | G ▷ C47×C181 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 232 |
| transitive degree | μt(G) = 34028 |
A minimal faithful permutation representation — 2 generators on 232 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)(52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232);(1,3,2,4)(6,51)(7,50)(8,49)(9,48)(10,47)(11,46)(12,45)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(53,232)(54,231)(55,230)(56,229)(57,228)(58,227)(59,226)(60,225)(61,224)(62,223)(63,222)(64,221)(65,220)(66,219)(67,218)(68,217)(69,216)(70,215)(71,214)(72,213)(73,212)(74,211)(75,210)(76,209)(77,208)(78,207)(79,206)(80,205)(81,204)(82,203)(83,202)(84,201)(85,200)(86,199)(87,198)(88,197)(89,196)(90,195)(91,194)(92,193)(93,192)(94,191)(95,190)(96,189)(97,188)(98,187)(99,186)(100,185)(101,184)(102,183)(103,182)(104,181)(105,180)(106,179)(107,178)(108,177)(109,176)(110,175)(111,174)(112,173)(113,172)(114,171)(115,170)(116,169)(117,168)(118,167)(119,166)(120,165)(121,164)(122,163)(123,162)(124,161)(125,160)(126,159)(127,158)(128,157)(129,156)(130,155)(131,154)(132,153)(133,152)(134,151)(135,150)(136,149)(137,148)(138,147)(139,146)(140,145)(141,144)(142,143)Polycyclic presentation:
2,47,181,2|a^2=d,b^a=b^46,c^a=c^1808510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34028, 4);