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×#10905 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C101 | #386 |
| commutator | C2×C4 | C2×C42×C101 |
| Frattini, cosocle | C23×C4 | C23×C101 |
| socle | C2×C101 | #1436 |
| prime radical | C24×C101 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C101 ◁ C23×C4×C101 ◁ G | |
672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 3 generators on 133 points:
(1,2,6,10,7,11,5,20)(3,12,15,24,16,23,14,8)(4,17,18,9,19,25,21,26)(13,28,29,32,31,22,30,27)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133);(1,3)(2,8,11,24)(4,13)(5,14)(6,15)(7,16)(9,22,26,28)(10,12,20,23)(17,32,25,27)(18,29)(19,31)(21,30);(1,4,6,18,7,19,5,21)(2,9,10,25,11,26,20,17)(3,13,15,29,16,31,14,30)(8,22,12,27,24,28,23,32)5858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 3893);