Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C101 · Schur multiplier (H2) = C23×C4 |
| direct product | C101×#10914 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C101 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C101 |
| Frattini, cosocle | C23×C4 | C23×C101 |
| socle | C22×C101 | C4×C22⋊C4 |
| prime radical | C24×C101 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C101 ◁ C23×C8×C101 ◁ G | |
698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 3 generators on 137 points:
(1,2)(3,4)(5,6,9,13,10,14,21,27)(7,15,18,29,17,11,22,24)(8,12,19,25,20,26,32,35)(16,28,31,36,30,23,33,34)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137);(5,7)(6,11,14,15)(8,16)(9,18)(10,17)(12,23,26,28)(13,24,27,29)(19,31)(20,30)(21,22)(25,34,35,36)(32,33);(2,4)(5,8,9,19,10,20,21,32)(6,12,13,25,14,26,27,35)(7,16,18,31,17,30,22,33)(11,23,24,34,15,28,29,36)6464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 3902);