Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C24 |
| direct product | C101×#20285 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C101 |
| prime radical | #127×C101 | C23 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C42×C101 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 12928 |
A minimal faithful permutation representation — 4 generators on 133 points:
(1,2,7,5)(3,10,13,16)(4,9,6,14)(8,11,15,12)(17,18)(19,26)(20,24)(21,29)(22,25)(23,28)(27,32)(30,31)(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);(1,3,7,13)(2,8,5,15)(4,12,6,11)(9,16,14,10)(19,27)(23,31)(26,32)(28,30);(1,4,7,6)(2,9,5,14)(3,11,13,12)(8,10,15,16)(17,19,22,27)(18,23,25,31)(20,28,21,30)(24,32,29,26);(1,5,7,2)(3,10,13,16)(4,14,6,9)(8,11,15,12)(17,20,22,21)(18,24,25,29)(19,28,27,30)(23,32,31,26)3434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 13273);