Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C109 · Schur multiplier (H2) = C23 |
| direct product | C109×#10691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | #401 |
| commutator, Frattini, cosocle | C25 | C23×C109 |
| prime radical | C25×C109 | C23 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C25×C109 ◁ G | |
372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 3488 |
A minimal faithful permutation representation — 3 generators on 141 points:
(1,2)(3,12,15,24)(4,16,19,25)(5,9)(6,11)(7,14,23,30)(8,18,26,20)(10,21)(13,27,17,32)(22,29,31,28)(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);(1,3)(2,7,11,24)(4,17,18,28)(5,15)(6,14)(8,22,26,27)(9,23,10,12)(13,19,29,20)(16,31,25,32)(21,30);(1,4)(2,8,9,25)(3,13,14,17)(5,18)(6,20)(7,22,12,27)(10,26,11,16)(15,29,30,28)(19,21)(23,32,24,31)2725 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 3679);