Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C109 · Schur multiplier (H2) = C2×C4 |
| direct product | C109×#8246 |
376 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 13952 |
A minimal faithful permutation representation — 3 generators on 141 points:
(1,2,5,9,6,10,4,7)(3,8,12,15,13,16,11,14)(17,18,20,23)(19,25,26,22)(21,29,28,24)(27,30,32,31)(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);(2,7,10,9)(8,14,16,15)(17,19,21,27,20,26,28,32)(18,22,24,30,23,25,29,31);(1,3,5,12,6,13,4,11)(2,8,9,15,10,16,7,14)(19,26)(22,25)(27,32)(30,31)6976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 1234);