Finite Group DatabasebetaFinite Group Databasebeta| order | 26368 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C103 · Schur multiplier (H2) = C23 |
| direct product | C103×#13264 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C103 | C23 |
| commutator | C23 | C22×C8×C103 |
| Frattini, cosocle | C22×C8 | C23×C103 |
| socle, prime radical | C23×C103 | C22×C8 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C103 ◁ G | |
386 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 26368 |
A minimal faithful permutation representation — 3 generators on 131 points:
(2,4)(5,6)(7,11)(8,9)(10,12)(13,14,18,23,19,21,26,28,17,22,24,27,16,15,20,25)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131);(1,2,3,4)(6,9)(10,11)(13,15,24,28,19,14,20,27,17,21,18,25,16,22,26,23);(5,7,8,12)(6,10,9,11)(13,16,17,19)(14,21,22,15)(18,20,24,26)(23,28,27,25)9064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26368, 6252);