Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C101 · Schur multiplier (H2) = C22×C4 |
| direct product | C101×#13234 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C101 | #1964 |
| commutator | C22×C4 | C22×C4×C101 |
| Frattini, cosocle | C2×#41 | C23×C101 |
| prime radical | C101×#3058 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C101 ◁ C2×C4×C101 ◁ C2×#131×C101 ◁ G | |
464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 3 generators on 133 points:
(1,2,7,11,8,12,6,24)(3,5,10,22,16,23,15,13)(4,17,20,26,21,31,19,9)(14,28,25,32,30,27,29,18)(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);(1,3,13,2)(4,14,27,9)(5,11,6,15)(7,10,23,24)(8,16,22,12)(17,19,29,18)(20,25,32,31)(21,30,28,26);(1,4,7,20,8,21,6,19)(2,9,24,31,12,26,11,17)(3,14,10,25,16,30,15,29)(5,18,13,27,23,32,22,28)3434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 6222);