Finite Group DatabasebetaFinite Group Databasebeta| order | 26368 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C103 · Schur multiplier (H2) = C23 |
| direct product | C103×#13388 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C103 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C103 |
| prime radical | C2×#41×C103 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C2×#131×C103 ◁ G | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 139 |
| transitive degree | μt(G) = 13184 |
A minimal faithful permutation representation — 3 generators on 139 points:
(2,3)(5,6,10,15)(7,11,19,28)(8,12,23,31)(9,24,22,14)(13,32,30,21)(16,26,18,27)(17,35,20,29)(25,36,33,34)(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);(1,2)(3,4)(5,7)(6,11)(8,20)(9,16)(10,19)(12,29)(13,33)(14,27)(15,28)(17,23)(18,22)(21,36)(24,26)(25,30)(31,35)(32,34);(1,3,4,2)(6,12)(7,16)(8,21)(9,22)(11,25)(13,14)(15,31)(17,20)(18,19)(23,32)(24,30)(26,35)(27,29)(28,33)4120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26368, 6376);