Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C101 · Schur multiplier (H2) = C23 |
| direct product | C101×#13417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C101 | #2041 |
| commutator, Frattini, cosocle | C22×C8 | C23×C101 |
| prime radical | C101×#3155 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C101 ◁ C22×C4×C101 ◁ #405×C101 ◁ G | |
454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 3 generators on 133 points:
(1,2)(3,15)(4,9)(5,21)(6,12)(7,11)(8,14)(10,18)(13,23)(16,26)(17,29)(19,27)(20,31)(22,28)(24,30)(25,32)(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);(2,9)(3,16)(4,7)(5,6)(10,27)(11,14)(12,31)(15,30)(17,18)(19,22)(20,23)(24,25)(26,29)(28,32);(1,3,4,17,8,19,7,25)(2,10,11,28,14,30,9,26)(5,22,20,18,23,16,6,24)(12,29,13,15,31,32,21,27)3434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 6405);