Finite Group DatabasebetaFinite Group Databasebeta| order | 26368 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C103 · Schur multiplier (H2) = C24 |
| direct product | C103×#33884 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C103 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C103 |
| prime radical | C103×#3287 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C4×D4×C103 ◁ C8×D4×C103 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 13184 |
A minimal faithful permutation representation — 4 generators on 143 points:
(1,2,4,6)(3,7,8,5)(9,10,15,19)(11,20,21,37)(12,17,14,29)(13,25,28,38)(16,31,32,23)(18,24,36,27)(22,39,30,35)(26,33,40,34)(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);(1,3)(2,5)(4,8)(6,7)(11,21)(16,32)(20,37)(22,30)(23,31)(26,40)(33,34)(35,39);(9,11,15,21)(10,16,19,32)(12,22,14,30)(13,26,28,40)(17,33,29,34)(18,35,36,39)(20,38,37,25)(23,24,31,27);(3,8)(5,7)(9,12,15,14)(10,17,19,29)(11,22,21,30)(13,24,28,27)(16,33,32,34)(18,25,36,38)(20,39,37,35)(23,26,31,40)4429 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26368, 26872);