Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C109 · Schur multiplier (H2) = C24 |
| direct product | C109×#10185 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C109 |
| prime radical | #532×C109 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G | |
550 conjugacy classes of subgroups.
| minimal degree | μ(G) = 149 |
| transitive degree | μt(G) = 13952 |
A minimal faithful permutation representation — 3 generators on 149 points:
(1,2)(3,7)(4,6)(5,8)(9,10,15,20)(11,16,23,32)(12,24,26,35)(13,19,14,18)(17,28,34,27)(21,33,37,40)(22,36,29,31)(25,30,38,39)(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);(2,6)(3,4)(7,8)(9,11)(10,16)(12,25)(13,22)(14,29)(15,23)(17,33)(18,31)(19,36)(20,32)(21,28)(24,39)(26,38)(27,37)(30,35)(34,40);(1,3,5,4)(2,7,8,6)(9,12)(10,17)(11,21)(13,28)(14,27)(15,26)(16,30)(18,35)(19,24)(20,34)(22,38)(23,37)(25,29)(31,40)(32,39)(33,36)4033 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 3173);