Finite Group DatabasebetaFinite Group Databasebeta| order | 26368 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C103 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#327×C103 |
816 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 6592 |
A minimal faithful permutation representation — 3 generators on 123 points:
(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(5,6)(7,11,12,9)(8,10)(13,14)(15,17)(16,19)(18,20);(5,7)(6,9)(8,12)(10,11)(14,17)(15,20)(18,19)7828 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26368, 1202);