Finite Group DatabasebetaFinite Group Databasebeta| order | 24256 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic6064 |
| Sylow | C379 ⋊ Q64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D6064 |
| commutator, cosocle | C16×C379 | C22 |
| Frattini | C16 | C2×D379 |
| Fitting | C32×C379 | C2 |
| socle, prime radical | C2×C379 | D16 |
| hypercenter | C32 | D379 |
| hypocenter | C379 | Q64 |
| LCS | G ▷ C16×C379 ▷ C8×C379 ▷ C4×C379 ▷ C2×C379 ▷ C379 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 443 |
| transitive degree | μt(G) = 24256 |
A minimal faithful permutation representation — 2 generators on 443 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)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443);(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)(66,443)(67,442)(68,441)(69,440)(70,439)(71,438)(72,437)(73,436)(74,435)(75,434)(76,433)(77,432)(78,431)(79,430)(80,429)(81,428)(82,427)(83,426)(84,425)(85,424)(86,423)(87,422)(88,421)(89,420)(90,419)(91,418)(92,417)(93,416)(94,415)(95,414)(96,413)(97,412)(98,411)(99,410)(100,409)(101,408)(102,407)(103,406)(104,405)(105,404)(106,403)(107,402)(108,401)(109,400)(110,399)(111,398)(112,397)(113,396)(114,395)(115,394)(116,393)(117,392)(118,391)(119,390)(120,389)(121,388)(122,387)(123,386)(124,385)(125,384)(126,383)(127,382)(128,381)(129,380)(130,379)(131,378)(132,377)(133,376)(134,375)(135,374)(136,373)(137,372)(138,371)(139,370)(140,369)(141,368)(142,367)(143,366)(144,365)(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)(152,357)(153,356)(154,355)(155,354)(156,353)(157,352)(158,351)(159,350)(160,349)(161,348)(162,347)(163,346)(164,345)(165,344)(166,343)(167,342)(168,341)(169,340)(170,339)(171,338)(172,337)(173,336)(174,335)(175,334)(176,333)(177,332)(178,331)(179,330)(180,329)(181,328)(182,327)(183,326)(184,325)(185,324)(186,323)(187,322)(188,321)(189,320)(190,319)(191,318)(192,317)(193,316)(194,315)(195,314)(196,313)(197,312)(198,311)(199,310)(200,309)(201,308)(202,307)(203,306)(204,305)(205,304)(206,303)(207,302)(208,301)(209,300)(210,299)(211,298)(212,297)(213,296)(214,295)(215,294)(216,293)(217,292)(218,291)(219,290)(220,289)(221,288)(222,287)(223,286)(224,285)(225,284)(226,283)(227,282)(228,281)(229,280)(230,279)(231,278)(232,277)(233,276)(234,275)(235,274)(236,273)(237,272)(238,271)(239,270)(240,269)(241,268)(242,267)(243,266)(244,265)(245,264)(246,263)(247,262)(248,261)(249,260)(250,259)(251,258)(252,257)(253,256)(254,255)Polycyclic presentation:
2^6,379|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^378,c^b=cd,d^b=de,e^b=ef,g^b=g^3786067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24256, 390);