Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C26 |
| direct product | C101×#23992 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C101 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C101 |
| prime radical | #585×C101 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C101 ◁ C22×C4×C101 ◁ G | |
1128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 4 generators on 133 points:
(1,2,6,10)(3,7,13,21)(4,8,14,22)(5,16,18,9)(11,24,17,19)(12,26,27,20)(15,29,28,23)(25,31,30,32)(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);(3,11,13,17)(7,19,21,24)(12,25,27,30)(20,31,26,32);(1,3)(2,7)(4,12)(5,17)(6,13)(8,20)(9,24)(10,21)(11,18)(14,27)(15,30)(16,19)(22,26)(23,32)(25,28)(29,31);(1,4)(2,8)(3,12)(5,15)(6,14)(7,20)(9,23)(10,22)(11,25)(13,27)(16,29)(17,30)(18,28)(19,31)(21,26)(24,32)4040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 16980);