Finite Group DatabasebetaFinite Group Databasebeta| order | 26368 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C103 · Schur multiplier (H2) = C24 |
| direct product | C103×#33798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C103 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C103 |
| prime radical | #466×C103 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C2×C42×C103 ◁ C2×C4×C8×C103 ◁ G | |
468 conjugacy classes of subgroups.
| minimal degree | μ(G) = 151 |
| transitive degree | μt(G) = 13184 |
A minimal faithful permutation representation — 4 generators on 151 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18)(19,23)(20,24)(21,34)(22,27)(25,31)(26,32)(28,35)(29,44)(30,38)(33,40)(36,41)(37,42)(39,45)(43,47)(46,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,19,22,30)(18,23,27,38)(20,28,33,43)(21,29,32,42)(24,35,40,47)(25,36,39,46)(26,37,34,44)(31,41,45,48);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(18,24)(20,31)(21,32)(23,35)(25,26)(27,40)(28,41)(29,42)(33,45)(34,39)(36,37)(38,47)(43,48)(44,46);(2,8)(6,9)(7,16)(14,15)5356 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26368, 26786);