Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C25 |
| direct product | C101×#18352 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C101 |
| prime radical | C101×#2635 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G | |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 4 generators on 133 points:
(2,7)(3,11)(4,15)(8,21)(9,19)(10,16)(12,27)(13,29)(14,26)(17,31)(20,22)(23,32)(24,28)(25,30)(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);(1,2,5,10)(3,12,14,8)(4,16,15,7)(6,9,18,23)(11,24,26,22)(13,20,30,28)(17,32,31,19)(21,29,27,25);(4,17)(7,19)(13,25)(15,31)(16,32)(20,21)(27,28)(29,30);(1,3,5,14)(2,8,10,12)(4,13,15,30)(6,11,18,26)(7,20,16,28)(9,22,23,24)(17,25,31,29)(19,21,32,27)3434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 11340);