Finite Group DatabasebetaFinite Group Databasebeta| order | 23488 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic5872 |
| Sylow | C367 ⋊ Q64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D5872 |
| commutator, cosocle | C16×C367 | C22 |
| Frattini | C16 | C2×D367 |
| Fitting | C32×C367 | C2 |
| socle, prime radical | C2×C367 | D16 |
| hypercenter | C32 | D367 |
| hypocenter | C367 | Q64 |
| LCS | G ▷ C16×C367 ▷ C8×C367 ▷ C4×C367 ▷ C2×C367 ▷ C367 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 431 |
| transitive degree | μt(G) = 23488 |
A minimal faithful permutation representation — 2 generators on 431 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)(33,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431);(1,33,17,49)(2,34,18,50)(3,35,19,51)(4,36,20,52)(5,37,21,53)(6,38,22,54)(7,39,23,55)(8,40,24,56)(9,41,25,57)(10,42,26,58)(11,43,27,59)(12,44,28,60)(13,45,29,61)(14,46,30,62)(15,47,31,63)(16,48,32,64)(66,431)(67,430)(68,429)(69,428)(70,427)(71,426)(72,425)(73,424)(74,423)(75,422)(76,421)(77,420)(78,419)(79,418)(80,417)(81,416)(82,415)(83,414)(84,413)(85,412)(86,411)(87,410)(88,409)(89,408)(90,407)(91,406)(92,405)(93,404)(94,403)(95,402)(96,401)(97,400)(98,399)(99,398)(100,397)(101,396)(102,395)(103,394)(104,393)(105,392)(106,391)(107,390)(108,389)(109,388)(110,387)(111,386)(112,385)(113,384)(114,383)(115,382)(116,381)(117,380)(118,379)(119,378)(120,377)(121,376)(122,375)(123,374)(124,373)(125,372)(126,371)(127,370)(128,369)(129,368)(130,367)(131,366)(132,365)(133,364)(134,363)(135,362)(136,361)(137,360)(138,359)(139,358)(140,357)(141,356)(142,355)(143,354)(144,353)(145,352)(146,351)(147,350)(148,349)(149,348)(150,347)(151,346)(152,345)(153,344)(154,343)(155,342)(156,341)(157,340)(158,339)(159,338)(160,337)(161,336)(162,335)(163,334)(164,333)(165,332)(166,331)(167,330)(168,329)(169,328)(170,327)(171,326)(172,325)(173,324)(174,323)(175,322)(176,321)(177,320)(178,319)(179,318)(180,317)(181,316)(182,315)(183,314)(184,313)(185,312)(186,311)(187,310)(188,309)(189,308)(190,307)(191,306)(192,305)(193,304)(194,303)(195,302)(196,301)(197,300)(198,299)(199,298)(200,297)(201,296)(202,295)(203,294)(204,293)(205,292)(206,291)(207,290)(208,289)(209,288)(210,287)(211,286)(212,285)(213,284)(214,283)(215,282)(216,281)(217,280)(218,279)(219,278)(220,277)(221,276)(222,275)(223,274)(224,273)(225,272)(226,271)(227,270)(228,269)(229,268)(230,267)(231,266)(232,265)(233,264)(234,263)(235,262)(236,261)(237,260)(238,259)(239,258)(240,257)(241,256)(242,255)(243,254)(244,253)(245,252)(246,251)(247,250)(248,249)Polycyclic presentation:
2^6,367|a^2=f,b^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^366,c^b=cd,d^b=de,e^b=ef,g^b=g^3665875 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23488, 390);