Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C25 |
| direct product | C101×#24808 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C101 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C101 |
| prime radical | C101×#3068 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C101 ◁ C22×C4×C101 ◁ G | |
820 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 4 generators on 133 points:
(1,2,5,10,6,11,21,9)(3,12,15,7,17,13,16,23)(4,18,19,8,20,24,32,25)(14,28,29,26,31,22,30,27)(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);(1,3,5,15,6,17,21,16)(2,7,9,12,11,23,10,13)(4,14,19,29,20,31,32,30)(8,22,18,26,25,28,24,27);(1,2)(3,13)(4,8)(5,9)(6,11)(7,15)(10,21)(12,17)(14,27)(16,23)(18,19)(20,25)(22,29)(24,32)(26,31)(28,30);(1,4,5,19,6,20,21,32)(2,8,9,18,11,25,10,24)(3,14,15,29,17,31,16,30)(7,22,12,26,23,28,13,27)4040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 17796);