Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C23 |
| direct product | C109×#32696 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C109 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C109 |
| prime radical | #535×C109 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C109 ◁ C22×C4×C109 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 3488 |
A minimal faithful permutation representation — 4 generators on 141 points:
(1,2,5,10,6,9,20,26)(3,11,14,27,13,7,19,22)(4,15,18,31,17,8,23,25)(12,28,16,30,29,21,32,24)(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)(4,16)(5,19)(6,13)(8,24)(9,11)(10,27)(12,18)(14,20)(15,30)(17,32)(21,25)(22,26)(23,29)(28,31);(1,4)(2,8,9,15)(3,12,13,29)(5,18)(6,17)(7,21)(10,25,26,31)(11,28)(14,16,19,32)(20,23)(22,24)(27,30);(2,9)(5,20)(8,15)(14,19)(16,32)(18,23)(22,27)(24,30)3706 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 25684);