Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C23 |
| direct product | C109×#32697 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C109 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C109 |
| prime radical | C2×#41×C109 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C109 ◁ C22×C4×C109 ◁ G | |
528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 3488 |
A minimal faithful permutation representation — 4 generators on 141 points:
(1,2,7,11,6,12,24,32)(3,8,16,28,15,27,25,30)(4,17,20,21,19,9,29,14)(5,10,23,13,22,18,26,31)(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)(2,8)(4,18)(5,21)(6,15)(7,25)(9,26)(10,19)(11,30)(12,27)(13,20)(14,22)(16,24)(17,23)(28,32)(29,31);(1,4,6,19)(2,9)(3,13)(5,8,22,27)(7,20,24,29)(10,25)(11,14)(12,17)(15,31)(16,18)(21,32)(23,28,26,30);(1,5,6,22)(2,10,12,18)(3,14,15,21)(4,8,19,27)(7,26,24,23)(9,25,17,16)(11,31,32,13)(20,30,29,28)3706 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 25685);