Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C101 · Schur multiplier (H2) = C24 |
| direct product | C101×#13015 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C101 | C2×D8 |
| commutator | C2×C8 | C22×C4×C101 |
| Frattini, cosocle | C22×C8 | C23×C101 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C101 ◁ C2×C42×C101 ◁ C2×C4×C8×C101 ◁ G | |
490 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 25856 |
A minimal faithful permutation representation — 3 generators on 141 points:
(2,4)(5,6)(7,8)(9,10,13,19,29,38,27,16,15,21,12,18,14,20,30,34)(11,22,24,40,32,37,28,36,26,33,23,35,25,39,31,17)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(1,2,3,4)(10,16)(12,27)(13,30)(14,29)(17,33)(18,20)(19,38)(21,34)(22,36)(23,28)(24,31)(25,32)(35,39)(37,40);(6,8)(9,11,15,26)(10,17,21,36)(12,28,13,31)(14,32,29,25)(16,33,34,22)(18,37,19,39)(20,40,38,35)(23,30,24,27)5858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 6003);