Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C101 · Schur multiplier (H2) = C23 |
| direct product | C101×#22292 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C101 | C24 |
| commutator | C23 | C23×C4×C101 |
| Frattini, cosocle | C22×C4 | C24×C101 |
| socle | C23×C101 | C23×C4 |
| prime radical | C24×C101 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C101 ◁ G | |
702 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 12928 |
A minimal faithful permutation representation — 4 generators on 133 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,14)(12,16)(13,15)(17,18,22,25,21,24,26,19)(20,28,31,27,30,23,32,29)(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)(2,5)(4,8)(6,7)(9,11,13,12)(10,14,15,16)(17,19,26,24,21,25,22,18)(20,29,32,23,30,27,31,28);(3,8)(5,7)(9,12,13,11)(10,14,15,16)(17,20,21,30)(18,23,24,28)(19,27,25,29)(22,31,26,32);(2,6)(5,7)(20,30)(23,28)(27,29)(31,32)6464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 15280);