Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C24 |
| direct product | C109×#26193 |
| 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)(11,22)(12,17)(13,30)(14,20)(15,21)(16,25)(18,29)(19,32)(23,36)(24,33)(26,34)(27,40)(28,37)(31,35)(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)(10,16)(12,27)(13,24)(14,31)(15,26)(17,36)(18,33)(19,34)(20,22)(21,35)(23,29)(25,32)(28,39)(30,38)(37,40);(1,4,5,3)(2,6,7,8)(9,12,15,13)(10,17,21,30)(11,23,26,39)(14,28,32,29)(16,33,35,40)(18,20,37,19)(22,36,34,38)(24,31,27,25);(9,13,15,12)(10,18,21,37)(11,24,26,27)(14,28,32,29)(16,33,35,40)(17,20,30,19)(22,38,34,36)(23,31,39,25)4687 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 19181);