Finite Group DatabasebetaFinite Group Databasebeta| order | 26368 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C103 · Schur multiplier (H2) = C25 |
| direct product | C103×#25435 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C103 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C103 |
| prime radical | C2×#41×C103 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C22×C4×C103 ◁ G | |
880 conjugacy classes of subgroups.
| minimal degree | μ(G) = 139 |
| transitive degree | μt(G) = 6592 |
A minimal faithful permutation representation — 4 generators on 139 points:
(1,2,4,3)(5,6,12,17)(7,18,8,14)(9,23,26,36)(10,27,11,16)(13,22,29,20)(15,25,31,24)(19,33,21,28)(30,34,32,35)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139);(1,3,4,2)(5,7,11,22,12,8,10,20)(6,13,27,14,17,29,16,18)(9,19,25,35,26,21,24,34)(15,28,36,30,31,33,23,32);(2,3)(5,8)(6,14)(7,12)(9,21)(10,22)(11,20)(13,16)(15,30)(17,18)(19,26)(23,28)(24,35)(25,34)(27,29)(31,32)(33,36);(5,9,11,25,12,26,10,24)(6,15,27,36,17,31,16,23)(7,19,22,35,8,21,20,34)(13,28,14,30,29,33,18,32)4738 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26368, 18423);