Finite Group DatabasebetaFinite Group Databasebeta| order | 26368 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C103 · Schur multiplier (H2) = C26 |
| direct product | C103×#10988 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C103 | #386 |
| commutator | C22×C4 | C22×C4×C103 |
| Frattini, cosocle | C23×C4 | C23×C103 |
| prime radical | C22×#41×C103 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G | |
1274 conjugacy classes of subgroups.
| minimal degree | μ(G) = 139 |
| transitive degree | μt(G) = 6592 |
A minimal faithful permutation representation — 3 generators on 139 points:
(1,2)(3,4)(5,6)(7,15)(8,19,21,12)(9,22)(10,14)(11,17)(13,25)(16,33,35,32)(18,30)(20,29,24,31)(23,27)(26,36,28,34)(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);(5,7,10,18)(6,11,14,27)(8,16,21,35)(9,23,25,17)(12,28,19,26)(13,30,22,15)(20,36,24,34)(29,33,31,32);(2,4)(5,8)(6,12)(7,16)(9,24)(10,21)(11,26)(13,31)(14,19)(15,32)(17,36)(18,35)(20,25)(22,29)(23,34)(27,28)(30,33)4738 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26368, 3976);