Finite Group DatabasebetaFinite Group Databasebeta| order | 35456 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C277 · Schur multiplier (H2) = C22 |
| direct product | #2258×C277 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C277 | C22 |
| commutator | C2 | C22×C16×C277 |
| Frattini, cosocle | C16 | C23×C277 |
| socle | C2×C277 | C22×C16 |
| prime radical | #41×C277 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C32×C277 ◁ G | |
106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 341 |
| transitive degree | μt(G) = 17728 |
A minimal faithful permutation representation — 3 generators on 341 points:
(1,2,4,9,5,10,17,27,6,11,18,28,20,30,39,49,7,12,19,29,21,31,40,50,22,32,41,51,42,52,57,62)(3,8,14,24,15,25,36,46,16,26,37,47,38,48,56,61,13,23,33,43,34,44,53,58,35,45,54,59,55,60,63,64)(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);(1,3)(2,8)(4,14)(5,15)(6,16)(7,13)(9,24)(10,25)(11,26)(12,23)(17,36)(18,37)(19,33)(20,38)(21,34)(22,35)(27,46)(28,47)(29,43)(30,48)(31,44)(32,45)(39,56)(40,53)(41,54)(42,55)(49,61)(50,58)(51,59)(52,60)(57,63)(62,64);(3,13)(8,23)(14,33)(15,34)(16,35)(24,43)(25,44)(26,45)(36,53)(37,54)(38,55)(46,58)(47,59)(48,60)(56,63)(61,64)22160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35456, 990);