Finite Group DatabasebetaFinite Group Databasebeta| order | 26368 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C103 · Schur multiplier (H2) = C2×C4 |
| direct product | C103×#13289 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C103 | C2×#102 |
| commutator | C2×C8 | C22×C4×C103 |
| Frattini, cosocle | C22×C8 | C23×C103 |
| prime radical | C23×C103 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C2×C42×C103 ◁ C2×C4×C8×C103 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 13184 |
A minimal faithful permutation representation — 3 generators on 143 points:
(1,2)(3,7)(4,5)(6,8)(9,10,14,21,16,22,15,20)(11,23,28,40,29,39,27,35)(12,30,24,18,31,19,13,32)(17,34,36,26,38,25,37,33)(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);(2,5)(6,7)(9,11,24,26,15,28,12,25,16,29,13,33,14,27,31,34)(10,17,19,39,21,37,32,40,22,38,30,23,20,36,18,35);(1,3,4,8)(2,6,5,7)(9,12,14,24,16,31,15,13)(10,18,20,30,22,32,21,19)(11,25,27,26,29,34,28,33)(17,35,36,23,38,40,37,39)5356 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26368, 6277);