Finite Group DatabasebetaFinite Group Databasebeta| order | 29824 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C233 · Schur multiplier (H2) = C1 |
| direct product | #1425×C233 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C233 | D16 |
| commutator | C16 | C2×C4×C233 |
| Frattini, cosocle | C2×C16 | C22×C233 |
| socle | C2×C233 | #366 |
| prime radical | C22×C233 | Q32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C233 ◁ C2×C4×C233 ◁ C2×C8×C233 ◁ C2×C16×C233 ◁ G | |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 297 |
| transitive degree | μt(G) = 14912 |
A minimal faithful permutation representation — 2 generators on 297 points:
(1,2,5,11,8,13,7,29)(3,14,17,39,20,41,19,51)(4,21,23,52,25,54,24,55)(6,27,26,37,28,56,22,12)(9,30,31,47,33,46,57,16)(10,34,35,44,36,43,53,15)(18,49,48,61,50,64,45,40)(32,42,38,58,59,63,60,62)(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);(1,3,15,42,6,18,23,30,5,17,34,58,26,48,25,47,8,20,44,63,28,50,24,46,7,19,43,62,22,45,4,16)(2,9,21,40,12,32,53,51,29,57,55,64,56,60,36,41,13,33,54,61,37,59,35,39,11,31,52,49,27,38,10,14)8854 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29824, 157);