Finite Group DatabasebetaFinite Group Databasebeta| order | 26368 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C103 · Schur multiplier (H2) = C24 |
| direct product | C103×#26650 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C103 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C103 |
| prime radical | #535×C103 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C22×C4×C103 ◁ G | |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 6592 |
A minimal faithful permutation representation — 4 generators on 143 points:
(1,2)(3,6)(4,5)(7,8)(9,10,13,18,14,19,29,33)(11,20,23,31,24,36,28,15)(12,16,25,34,27,35,26,17)(21,37,38,40,39,32,22,30)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143);(9,11,14,24)(10,15,19,31)(12,22,27,38)(13,28,29,23)(16,32,35,37)(17,30,34,40)(18,36,33,20)(21,25,39,26);(2,5)(6,8)(9,12)(10,16)(11,21)(13,25)(14,27)(15,30)(17,33)(18,34)(19,35)(20,37)(22,28)(23,38)(24,39)(26,29)(31,40)(32,36);(1,3,4,7)(2,6,5,8)(9,12)(10,17)(11,22)(13,26)(14,27)(15,30)(16,33)(18,35)(19,34)(20,32)(21,28)(23,39)(24,38)(25,29)(31,40)(36,37)4429 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26368, 19638);