Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C25 |
| direct product | C109×#24023 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C109 |
| prime radical | C109×#3486 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G | |
1214 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)(4,5)(7,8)(9,10)(11,15)(12,22)(13,25)(14,18)(16,24)(17,28)(19,36)(20,34)(21,31)(23,35)(26,30)(27,33)(29,38)(32,39)(37,40)(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);(2,5)(6,8)(9,11,14,21)(10,15,18,31)(12,19,23,37)(13,26,28,20)(16,32,33,29)(17,34,25,30)(22,36,35,40)(24,39,27,38);(1,3,4,7)(2,6,5,8)(9,12)(10,16)(11,19)(13,27)(14,23)(15,29)(17,35)(18,33)(20,39)(21,37)(22,25)(24,28)(26,38)(30,40)(31,32)(34,36);(2,5)(6,8)(12,23)(16,33)(19,37)(22,35)(24,27)(29,32)(36,40)(38,39)4360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 17011);