Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C23×C8 |
| direct product | C2×C101×#1717 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C101 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C101 |
| prime radical | C2×#493×C101 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C101 ◁ C2×C42×C101 ◁ G | |
966 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 12928 |
A minimal faithful permutation representation — 4 generators on 119 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(4,7)(5,9)(8,10)(12,17)(13,18)(14,15);(3,4,5,7,6,8,9,10)(11,12,15,13,16,18,14,17);(4,8)(7,10)(11,13,15,18,16,17,14,12)5252 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 12597);