Finite Group Databasebeta

← Group #72241345

Character table — Group #72241345

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11114448888888888881616161616161616161616161632323232323232323232323232323232323232323232646464646464646464646464128128
order12222222222224444442222222222244444444444444448888888844444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111111-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-11-1
χ3111111111111111111111111-1-111111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-11
χ4111111111111111111111111-1-1-1-1111111-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ511111111111111111111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111-1-1-1-111-1-11111-1-11-111-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-111-11
χ711111111111111111111-1-1-1-1-1-1111111-1-1-1111-1-1-1-1-1-1-1-111111111-11-1-111-1-111-1-11-1
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111111-1-1-1-111111111111-1-1111111-1-11-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-11
χ101111111-1-1-1-111111111111-1-111-1-111-1-11-11-1-1-111-1-11111-1-1-1-111111-1-1-111-1-11111-1-1
χ111111111-1-1-1-111111111111-1-1-1-11111-1-11-1-11-1-111-1-11111-1-1-1-11111-1111-1-1-1-1-1-1-1-111
χ121111111-1-1-1-111111111111-1-1-1-1-1-111-1-11-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1111-1
χ131111111-1-1-1-1111111111-1-111111111-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ141111111-1-1-1-1111111111-1-11111-1-111-1-1-111-1-1-1-1-11111111111-1-1-1-11-1-1-111-1-1-1-1-1-111
χ151111111-1-1-1-1111111111-1-111-1-11111-1-1-11-11-1-1-1-11111111111-1-1-1-1-1111-1-1-1-11111-1-1
χ161111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-11
χ1722222220000-2-2-22-22-2-22002200002-20002000000-2-22i2i−2i−2i2i2i−2i−2i000000000000000000
χ1822222220000-2-2-22-22-2-22002200002-20002000000-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000
χ1922222220000-2-2-22-22-2-2200-2-200002-2000-2000000222i2i−2i−2i−2i−2i2i2i000000000000000000
χ2022222220000-2-2-22-22-2-2200-2-200002-2000-200000022−2i−2i2i2i2i2i−2i−2i000000000000000000
χ2122222220000-2-2-2-22-22-2222000000-2200200000-2-2002i−2i2i−2i00002i2i−2i−2i00000000000000
χ2222222220000-2-2-2-22-22-2222000000-2200200000-2-200−2i2i−2i2i0000−2i−2i2i2i00000000000000
χ2322222220000-2-2-2-22-22-22-2-2000000-2200-20000022002i−2i2i−2i0000−2i−2i2i2i00000000000000
χ2422222220000-2-2-2-22-22-22-2-2000000-2200-2000002200−2i2i−2i2i00002i2i−2i−2i00000000000000
χ2522222222222222-2-2-2-22200000000-2-2220000-2-200002-2-22000000000000002-2000000
χ2622222222222222-2-2-2-22200000000-2-2220000-2-20000-222-200000000000000-22000000
χ27222222222-2-222-22-22-2-2-200000022-222-200022-200000000000000000-2002-200000000
χ28222222222-2-222-22-22-2-2-2000000-2-2-222-2000-22-200000000000000000200-2200000000
χ29222222222-2-222-2-22-22-2-2000022002-22-20020-220000000000000000-202-20000000000
χ30222222222-2-222-2-22-22-2-20000-2-2002-22-200-20-22000000000000000020-220000000000
χ312222222-2-22222-22-22-2-2-200000022-22-220002-2200000000000000000-200-2200000000
χ322222222-2-22222-22-22-2-2-2000000-2-2-22-22000-2-22000000000000000002002-200000000
χ332222222-2-22222-2-22-22-2-2000022002-2-2200202-20000000000000000-20-220000000000
χ342222222-2-22222-2-22-22-2-20000-2-2002-2-2200-202-20000000000000000202-20000000000
χ352222222-2-2-2-2222-2-2-2-22200000000-2-2-2-200002200002-2-2200000000000000-22000000
χ362222222-2-2-2-2222-2-2-2-22200000000-2-2-2-20000220000-222-2000000000000002-2000000
χ3744444440000-4-4444444-400000000-4-400000000000000000000000000000000000000
χ3844444440000-4-44-4-4-4-44-4000000004400000000000000000000000000000000000000
χ394444-4-4400444-4000000022220000000-4-2-200002-22-200000000000000000000000000
χ404444-4-4400444-40000000-2-2-2-20000000-4220000-22-2200000000000000000000000000
χ414444-4-4400-4-44-4000000022-2-200000004-2200002-2-2200000000000000000000000000
χ424444-4-4400-4-44-40000000-2-222000000042-20000-222-200000000000000000000000000
χ434444-4-444400-4400000002222000000-40-2-20000-22-2200000000000000000000000000
χ444444-4-444400-440000000-2-2-2-2000000-402200002-22-200000000000000000000000000
χ454444-4-44-4-400-44000000022-2-200000040-220000-222-200000000000000000000000000
χ464444-4-44-4-400-440000000-2-222000000402-200002-2-2200000000000000000000000000
χ4788888-8-80000000000000000000440000000-400000000000000000000000000000000
χ4888888-8-80000000000000000000-4-40000000400000000000000000000000000000000
χ498888-88-8000000000000000004400000000-4000000000000000000000000000000000
χ508888-88-800000000000000000-4-4000000004000000000000000000000000000000000
χ5188-8-80004-44-40040000-40000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000
χ5288-8-80004-44-40040000-4000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ5388-8-80004-4-4400-4000040000000000000000000000000002-2-222-2-2200000000000000
χ5488-8-80004-4-4400-400004000000000000000000000000000-222-2-222-200000000000000
χ5588-8-8000-444-400-4000040000000000000000000000000002-2-22-222-200000000000000
χ5688-8-8000-444-400-400004000000000000000000000000000-222-22-2-2200000000000000
χ5788-8-8000-44-440040000-40000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000
χ5888-8-8000-44-440040000-4000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000
χ598-88-800000000000-404004-4004-40000000000000000000000000000000000002-20000
χ608-88-800000000000-404004-400-44000000000000000000000000000000000000-220000
χ618-88-800000000000-40400-44004-4000000000000000000000000000000000000-220000
χ628-88-800000000000-40400-4400-440000000000000000000000000000000000002-20000
χ638-8-880000000000-404000004-4004-40000000000000000000000000000000000002-200
χ648-8-880000000000-404000004-400-44000000000000000000000000000000000000-2200
χ658-8-880000000000-40400000-44004-4000000000000000000000000000000000000-2200
χ668-8-880000000000-40400000-4400-440000000000000000000000000000000000002-200
χ6716-1616-160000000000080-800000000000000000000000000000000000000000000000000
χ6816-16-1616000000000080-8000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).