Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C26 |
| direct product | C101×#23994 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C101 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C101 |
| socle | C2×C101 | #2404 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C101 ◁ C22×C4×C101 ◁ G | |
1250 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 1616 |
A minimal faithful permutation representation — 4 generators on 117 points:
(6,14)(9,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117);(1,2)(3,9,10,16)(4,8)(5,7)(6,11,14,12)(13,15);(1,3)(2,6)(4,12)(5,10)(7,14)(8,16)(9,15)(11,13);(1,2)(3,6)(4,8)(5,7)(9,11)(10,14)(12,16)(13,15)4646 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 16982);