Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23×C4 |
| direct product | C73×#33789 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| prime radical | C2×#135×C73 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ #117×C73 ◁ #405×C73 ◁ G | |
562 conjugacy classes of subgroups.
| minimal degree | μ(G) = 145 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 145 points:
(1,2)(3,7)(4,6)(5,8)(9,10,15,20)(11,16,22,37)(12,25,28,59)(13,29,33,58)(14,34,31,19)(17,40,42,26)(18,43,45,32)(21,47,48,70)(23,53,51,69)(24,56,52,39)(27,60,35,44)(30,46,61,41)(36,62,63,49)(38,66,65,55)(50,71,57,67)(54,68,72,64)(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);(1,3,4,8)(2,5,6,7)(9,11)(10,16)(12,21)(13,23)(14,24)(15,22)(17,36)(18,38)(19,39)(20,37)(25,47)(26,49)(27,50)(28,48)(29,53)(30,54)(31,52)(32,55)(33,51)(34,56)(35,57)(40,62)(41,64)(42,63)(43,66)(44,67)(45,65)(46,68)(58,69)(59,70)(60,71)(61,72);(3,8)(5,7)(9,12,15,28)(10,17,20,42)(11,21,22,48)(13,30,33,61)(14,35,31,27)(16,36,37,63)(18,44,45,60)(19,46,34,41)(23,54,51,72)(24,57,52,50)(25,58,59,29)(26,43,40,32)(38,67,65,71)(39,68,56,64)(47,69,70,53)(49,66,62,55);(2,6)(5,7)(11,22)(16,37)(21,48)(23,51)(24,52)(36,63)(38,65)(39,56)(47,70)(49,62)(50,57)(53,69)(54,72)(55,66)(64,68)(67,71)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26777);