Finite Group DatabasebetaFinite Group Databasebeta| order | 26368 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C103 · Schur multiplier (H2) = C25 |
| direct product | C103×#33435 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C103 | C24 |
| commutator | C22 | C23×C8×C103 |
| Frattini, cosocle | C2×C8 | C24×C103 |
| socle | C22×C103 | C23×C8 |
| prime radical | #532×C103 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C103 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 139 |
| transitive degree | μt(G) = 13184 |
A minimal faithful permutation representation — 4 generators on 139 points:
(1,2)(3,4)(5,6,9,15,10,16,24,32,11,14,25,30,26,31,27,36)(7,12,18,28,19,8,20,21,17,22,33,35,34,23,13,29)(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);(2,4)(5,7)(6,12)(8,16)(9,18)(10,19)(11,17)(13,27)(14,22)(15,28)(20,24)(21,32)(23,31)(25,33)(26,34)(29,36)(30,35);(5,8,9,21,10,22,24,35,11,23,25,29,26,12,27,28)(6,13,15,7,16,18,32,19,14,20,30,17,31,33,36,34);(6,14)(7,17)(13,20)(15,30)(16,31)(18,33)(19,34)(32,36)9064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26368, 26423);