Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C101 · Schur multiplier (H2) = C27 |
| direct product | C101×#20954 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C2×#120 |
| commutator | C2×C4 | C23×C4×C101 |
| Frattini, cosocle | C22×C4 | C24×C101 |
| prime radical | C22×#41×C101 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G | |
1694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 4 generators on 137 points:
(2,4)(5,6,10,16,11,14,9,15)(7,17,21,12,20,28,19,27)(8,22,24,29,25,13,23,30)(18,31,34,35,33,36,32,26)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137);(1,2,3,4)(5,7)(6,12)(8,18)(9,21)(10,19)(11,20)(13,26)(14,27)(15,28)(16,17)(22,35)(23,34)(24,32)(25,33)(29,31)(30,36);(5,8,11,25)(6,13,14,22)(7,18,20,33)(9,24,10,23)(12,26,27,35)(15,30,16,29)(17,31,28,36)(19,34,21,32);(6,14)(12,27)(13,22)(15,16)(17,28)(26,35)(29,30)(31,36)5858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 13942);