Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C101 · Schur multiplier (H2) = C25 |
| direct product | C101×#17621 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C101 |
| Frattini, cosocle | C22×C4 | C24×C101 |
| prime radical | C22×D4×C101 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C2×C4×D4×C101 ◁ G | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 4 generators on 133 points:
(2,7,9,22)(3,12)(4,16)(8,24,25,30)(10,23,11,17)(13,15)(18,20)(21,27,32,26)(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);(1,2,5,10)(3,8,12,26)(4,17,16,22)(6,11,19,9)(7,20,23,18)(13,25,15,27)(14,30,28,32)(21,29,24,31);(1,3)(2,8)(4,14)(5,12)(6,15)(7,21)(9,25)(10,26)(11,27)(13,19)(16,28)(17,30)(18,31)(20,29)(22,32)(23,24);(3,13)(8,25)(12,15)(14,29)(21,32)(24,30)(26,27)(28,31)4949 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 10609);