Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C22×C4 |
| direct product | C109×#32695 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C109 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C109 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C109 ◁ C2×C4×Q8×C109 ◁ G | |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 27904 |
A minimal faithful permutation representation — 4 generators on 141 points:
(1,2,5,7)(3,4,8,6)(10,13)(11,15)(17,18)(19,22)(20,23)(21,24)(25,32)(26,30)(27,29)(28,31)(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);(1,3,5,8)(2,6,7,4)(9,10,12,13)(11,14,15,16)(17,19,20,26)(18,22,23,30)(21,25,28,27)(24,32,31,29);(9,11,12,15)(10,14,13,16)(18,23)(19,25)(21,28)(22,29)(26,27)(30,32);(1,4,5,6)(2,3,7,8)(10,13)(14,16)4360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 25683);