Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C101 · Schur multiplier (H2) = C25 |
| direct product | C101×#17597 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C101 |
| Frattini, cosocle | C22×C4 | C24×C101 |
| prime radical | C101×#3519 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C2×C4×D4×C101 ◁ G | |
1060 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 4 generators on 133 points:
(2,7,9,20)(3,12)(4,15)(8,22,24,31)(10,21,11,16)(13,26)(14,29)(17,30)(19,23,32,25)(27,28)(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)(3,8)(4,16)(5,10)(6,11)(7,17)(9,18)(12,25)(13,23)(14,22)(15,20)(19,27)(21,30)(24,26)(28,32)(29,31);(1,3)(2,8)(4,14)(5,13)(6,12)(7,19)(9,24)(10,23)(11,25)(15,28)(16,22)(17,27)(18,26)(20,32)(21,31)(29,30);(3,13)(8,23)(12,26)(14,28)(19,31)(22,32)(24,25)(27,29)4949 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 10585);