Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C101 · Schur multiplier (H2) = C24 |
| direct product | C101×#22951 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C101 | C22×D4 |
| commutator | C2×C4 | C23×C4×C101 |
| Frattini, cosocle | C22×C4 | C24×C101 |
| socle | C22×C101 | C2×C4×D4 |
| prime radical | #525×C101 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C101 ◁ C2×C22⋊C8×C101 ◁ G | |
730 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 4 generators on 141 points:
(2,5)(6,8)(9,10,14,18,15,19,13,27)(11,16,23,31,21,30,22,37)(12,24,26,17,25,33,28,32)(20,34,35,29,36,39,38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(1,2)(3,6)(4,5)(7,8)(9,11,14,23,15,21,13,22)(10,16,18,31,19,30,27,37)(12,20,26,35,25,36,28,38)(17,29,33,39,32,40,24,34);(1,3,4,7)(2,6,5,8)(9,12)(10,17)(11,20)(13,28)(14,26)(15,25)(16,29)(18,33)(19,32)(21,36)(22,38)(23,35)(24,27)(30,40)(31,39)(34,37);(2,5)(6,8)(11,21)(12,25)(16,30)(17,32)(22,23)(24,33)(26,28)(31,37)5858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 15939);