Finite Group DatabasebetaFinite Group Databasebeta| order | 29824 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C233 · Schur multiplier (H2) = C22 |
| direct product | #2264×C233 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C233 | C2×D16 |
| commutator, Frattini, cosocle | C16 | C23×C233 |
| prime radical | #508×C233 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C233 ◁ C2×C4×C233 ◁ C2×C8×C233 ◁ C2×C16×C233 ◁ G | |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 297 |
| transitive degree | μt(G) = 14912 |
A minimal faithful permutation representation — 3 generators on 297 points:
(1,2)(3,13)(4,18)(5,24)(6,28)(7,9)(8,14)(10,21)(11,20)(12,26)(15,45)(16,48)(17,40)(19,37)(22,56)(23,39)(25,35)(27,58)(29,41)(30,44)(31,52)(32,51)(33,42)(34,46)(36,63)(38,43)(47,64)(49,54)(50,55)(53,62)(57,60)(59,61)(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);(1,3,7,17)(2,8,9,30)(4,19,23,53)(5,25,27,59)(6,29,26,16)(10,35,33,61)(11,37,34,62)(12,38,28,32)(13,39,40,18)(14,42,44,21)(15,46,47,20)(22,57,55,52)(24,31,58,60)(36,64,49,45)(41,50,48,56)(43,54,51,63);(2,9)(8,30)(10,33)(11,34)(12,28)(13,40)(18,39)(24,58)(31,60)(32,38)(35,61)(36,49)(37,62)(41,48)(45,64)(50,56)6058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29824, 996);