Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C101 · Schur multiplier (H2) = C25×C4 |
| direct product | C101×#21253 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C101 | C22×D4 |
| commutator | C2×C4 | C23×C4×C101 |
| Frattini, cosocle | C22×C4 | C24×C101 |
| socle | C22×C101 | C22×C22⋊C4 |
| prime radical | C101×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C101 ◁ C2×#117×C101 ◁ G | |
1562 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 4 generators on 121 points:
(2,4)(6,10,12,15)(11,17,18,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121);(5,6,8,15,9,12,16,10)(7,11,14,20,13,18,19,17);(1,2,3,4)(5,7)(6,11)(8,14)(9,13)(10,17)(12,18)(15,20)(16,19);(7,13)(11,18)(14,19)(17,20)6464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 14241);