Finite Group DatabasebetaFinite Group Databasebeta| order | 26368 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C103 · Schur multiplier (H2) = C22 |
| direct product | C103×#11656 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C103 | C2×#102 |
| commutator | C2×C8 | C22×C4×C103 |
| Frattini, cosocle | C4×C8 | C23×C103 |
| prime radical | #466×C103 | C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C2×C42×C103 ◁ C2×C4×C8×C103 ◁ G | |
306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 151 |
| transitive degree | μt(G) = 13184 |
A minimal faithful permutation representation — 3 generators on 151 points:
(1,2,4,7,5,8,11,14)(3,6,10,13,9,12,15,16)(17,18)(19,28,31,44)(20,24)(21,35)(22,27)(23,30,39,48)(25,33)(26,34)(29,42,32,45)(36,38,46,40)(37,41)(43,47)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151);(1,3)(2,6)(4,10)(5,9)(7,13)(8,12)(11,15)(14,16)(17,19)(18,23)(20,32)(21,36)(22,31)(24,40)(25,42)(26,38)(27,39)(28,41)(29,34)(30,47)(33,48)(35,44)(37,46)(43,45);(3,9)(6,12)(10,15)(13,16)(17,20,22,34)(18,24,27,26)(19,29,31,32)(21,33,37,47)(23,38,39,40)(25,41,43,35)(28,42,44,45)(30,46,48,36)4738 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26368, 4644);