Finite Group DatabasebetaFinite Group Databasebeta| order | 38396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic9599 |
| unambiguous semidirect product | C331⋊Dic29 |
| derived, Hall | C29×C331 ⋊ C4 |
| Sylow | C331 ⋊ Dic29 |
| Sylow | C29 ⋊ Dic331 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D9599 |
| commutator, hypocenter | C29×C331 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C29×C331 | C2 |
| LCS | G ▷ C29×C331 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 364 |
| transitive degree | μt(G) = 38396 |
A minimal faithful permutation representation — 2 generators on 364 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)(34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364);(1,3,2,4)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(35,364)(36,363)(37,362)(38,361)(39,360)(40,359)(41,358)(42,357)(43,356)(44,355)(45,354)(46,353)(47,352)(48,351)(49,350)(50,349)(51,348)(52,347)(53,346)(54,345)(55,344)(56,343)(57,342)(58,341)(59,340)(60,339)(61,338)(62,337)(63,336)(64,335)(65,334)(66,333)(67,332)(68,331)(69,330)(70,329)(71,328)(72,327)(73,326)(74,325)(75,324)(76,323)(77,322)(78,321)(79,320)(80,319)(81,318)(82,317)(83,316)(84,315)(85,314)(86,313)(87,312)(88,311)(89,310)(90,309)(91,308)(92,307)(93,306)(94,305)(95,304)(96,303)(97,302)(98,301)(99,300)(100,299)(101,298)(102,297)(103,296)(104,295)(105,294)(106,293)(107,292)(108,291)(109,290)(110,289)(111,288)(112,287)(113,286)(114,285)(115,284)(116,283)(117,282)(118,281)(119,280)(120,279)(121,278)(122,277)(123,276)(124,275)(125,274)(126,273)(127,272)(128,271)(129,270)(130,269)(131,268)(132,267)(133,266)(134,265)(135,264)(136,263)(137,262)(138,261)(139,260)(140,259)(141,258)(142,257)(143,256)(144,255)(145,254)(146,253)(147,252)(148,251)(149,250)(150,249)(151,248)(152,247)(153,246)(154,245)(155,244)(156,243)(157,242)(158,241)(159,240)(160,239)(161,238)(162,237)(163,236)(164,235)(165,234)(166,233)(167,232)(168,231)(169,230)(170,229)(171,228)(172,227)(173,226)(174,225)(175,224)(176,223)(177,222)(178,221)(179,220)(180,219)(181,218)(182,217)(183,216)(184,215)(185,214)(186,213)(187,212)(188,211)(189,210)(190,209)(191,208)(192,207)(193,206)(194,205)(195,204)(196,203)(197,202)(198,201)(199,200)Polycyclic presentation:
2,29,331,2|a^2=d,b^a=b^28,c^a=c^3309602 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38396, 4);