Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C24 |
| direct product | C109×#26192 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C109 |
| prime radical | C2×#135×C109 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C22×C4×C109 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 149 |
| transitive degree | μt(G) = 6976 |
A minimal faithful permutation representation — 4 generators on 149 points:
(1,2)(3,6)(4,8)(5,7)(9,10)(11,21)(12,27)(13,30)(14,20)(15,19)(16,24)(17,29)(18,28)(22,35)(23,33)(25,37)(26,34)(31,36)(32,40)(38,39)(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);(1,3,5,4)(2,6,7,8)(9,11,14,25)(10,16,20,34)(12,23,29,40)(13,26,15,24)(17,35,27,38)(18,33,36,32)(19,37,30,21)(22,31,39,28);(1,4,5,3)(2,6,7,8)(9,12)(10,17)(11,22)(13,28)(14,29)(15,31)(16,32)(18,19)(20,27)(21,38)(23,24)(25,39)(26,40)(30,36)(33,34)(35,37);(9,12)(10,18)(11,23)(13,31)(14,29)(15,28)(16,33)(17,19)(20,36)(21,38)(22,24)(25,40)(26,39)(27,30)(32,34)(35,37)4687 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 19180);