Finite Group DatabasebetaFinite Group Databasebeta| order | 29056 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C227 · Schur multiplier (H2) = C22 |
| direct product | #2179×C227 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C227 | C2×D8 |
| commutator | C8 | C22×C4×C227 |
| Frattini, cosocle | C2×C8 | C23×C227 |
| socle | C2×C227 | C4×D8 |
| prime radical | #508×C227 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C227 ◁ C2×C8×C227 ◁ C4×C8×C227 ◁ G | |
144 conjugacy classes of subgroups.
| minimal degree | μ(G) = 259 |
| transitive degree | μt(G) = 7264 |
A minimal faithful permutation representation — 3 generators on 259 points:
(1,2,6,11,7,13,23,12)(3,14,16,29,18,31,17,25)(4,10,19,28,20,9,5,21)(8,24,26,32,27,22,30,15)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259);(1,3)(2,8)(4,15)(5,22)(6,16)(7,18)(9,25)(10,29)(11,26)(12,30)(13,27)(14,21)(17,23)(19,24)(20,32)(28,31);(1,4,6,19,7,20,23,5)(2,9,11,21,13,10,12,28)(3,15,16,24,18,32,17,22)(8,25,26,14,27,29,30,31)7264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29056, 911);