Finite Group Databasebeta

?

← Prev (#44576991) Next (#44576993) →

C₁₂₇×#13319 #44576992

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 163 points:

(5,6)(7,18)(8,12)(9,16)(10,15)(11,17)(13,20)(14,22)(19,32)(21,33)(23,30)(24,28)(25,29)(26,31)(27,36)(34,35)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163);(1,2)(3,4)(6,12)(8,22)(9,10)(13,27)(14,16)(15,28)(17,29)(18,32)(19,35)(20,26)(23,36)(24,25)(30,33)(31,34);(2,4)(5,7)(6,13)(8,23)(9,26)(10,20)(11,21)(12,27)(14,32)(15,33)(16,18)(17,31)(19,25)(22,36)(24,35)(28,30)(29,34)

Conjugacy classes & character table

5080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32512, 6307);