Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C25 |
| direct product | C101×#18354 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C101 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G | |
1022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 4 generators on 133 points:
(2,8)(3,12)(4,14)(5,17)(9,22)(10,18)(11,24)(13,27)(15,31)(16,19)(20,29)(23,25)(26,32)(28,30)(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);(1,2)(3,9)(4,15)(5,18)(6,11)(7,10)(8,17)(12,25)(13,28)(14,30)(16,23)(19,31)(20,32)(21,26)(22,27)(24,29);(1,3,7,4)(2,9,10,15)(5,19,17,27)(6,12,21,14)(8,22,18,31)(11,25,26,30)(13,29,16,20)(23,32,28,24);(1,4,7,3)(2,9,10,15)(5,16,17,13)(6,14,21,12)(8,23,18,28)(11,25,26,30)(19,20,27,29)(22,32,31,24)3434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 11342);