Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C23×C4 |
| direct product | C101×#19714 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C101 |
| prime radical | #532×C101 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G | |
690 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 12928 |
A minimal faithful permutation representation — 4 generators on 133 points:
(1,2,6,9)(3,10,8,5)(4,7,12,14)(11,16,15,13)(17,18,23,28)(19,29,30,25)(20,32,31,24)(21,27,22,26)(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);(1,3,5,2,6,8,10,9)(4,11,13,7,12,15,16,14)(17,19,21,31,23,30,22,20)(18,24,26,29,28,32,27,25);(1,4)(2,7)(3,11)(5,13)(6,12)(8,15)(9,14)(10,16)(17,20,22,30,23,31,21,19)(18,25,27,32,28,29,26,24);(4,12)(7,14)(11,15)(13,16)(19,30)(20,31)(24,32)(25,29)4040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 12702);