Finite Group Databasebeta

← Group #306921

Character table — Group #306921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444442222448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-11111-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111-1-111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-1-11-1-11111-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1111111-1-1-1
χ91111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11
χ101111111111111111-1-1-1-111111111-1-111-1-1111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1111-1-111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-1111111-1-111-1
χ17222222222-22-22-22-20000-2-222222200-2-200-2-2-2-2000000000000200000000000000
χ18222222222-22-22-22-20000-2-22222-2-200220022-2-2000000000000-200000000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-222002200-2-222000000000000-200000000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2-2-200-2-2002222000000000000200000000000000
χ2122222222-22-22-22-222222-2-2000000-2-200220000-2-200002200000-20000000000000
χ2222222222-22-22-22-222222-2-2000000-2-200-2-20000220000-2-20000020000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000002200220000220000-2-200000-20000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000002200-2-20000-2-20000220000020000000000000
χ2522-2-2-222-2020-20-20222-2-200i2i2−i2−i20000002-200i2−i200i2i2−i2−i22-2i2i2−i2−i200000000i2−i200000
χ2622-2-2-222-2020-20-20222-2-200i2i2−i2−i2000000-2200i2−i200i2i2−i2−i2-22−i2−i2i2i200000000−i2i200000
χ2722-2-2-222-2020-20-20222-2-200−i2−i2i2i20000002-200−i2i200−i2−i2i2i22-2−i2−i2i2i200000000−i2i200000
χ2822-2-2-222-2020-20-20222-2-200−i2−i2i2i2000000-2200−i2i200−i2−i2i2i2-22i2i2−i2−i200000000i2−i200000
χ2922-2-2-222-2020-20-202-2-22200i2i2−i2−i20000002-200i2−i200−i2−i2i2i2-22−i2−i2i2i200000000i2−i200000
χ3022-2-2-222-2020-20-202-2-22200i2i2−i2−i2000000-2200i2−i200−i2−i2i2i22-2i2i2−i2−i200000000−i2i200000
χ3122-2-2-222-2020-20-202-2-22200−i2−i2i2i20000002-200−i2i200i2i2−i2−i2-22i2i2−i2−i200000000−i2i200000
χ3222-2-2-222-2020-20-202-2-22200−i2−i2i2i2000000-2200−i2i200i2i2−i2−i22-2−i2−i2i2i200000000i2−i200000
χ332-2-222-22-22-2-222-2-222-22-2-220000002-2000000000000000000000000002i−2i002i−2i000
χ342-2-222-22-22-2-222-2-222-22-2-220000002-200000000000000000000000000−2i2i00−2i2i000
χ352-2-222-22-22-2-222-2-22-22-22-22000000-22000000000000000000000000002i−2i00−2i2i000
χ362-2-222-22-22-2-222-2-22-22-22-22000000-2200000000000000000000000000−2i2i002i−2i000
χ372-2-222-22-2-222-2-222-20000-2200002i−2i0000002i−2i00002-22-2000000002i−2i00000000000
χ382-2-222-22-2-222-2-222-20000-2200002i−2i0000002i−2i0000-22-2200000000−2i2i00000000000
χ392-2-222-22-2-222-2-222-20000-220000−2i2i000000−2i2i00002-22-200000000−2i2i00000000000
χ402-2-222-22-2-222-2-222-20000-220000−2i2i000000−2i2i0000-22-22000000002i−2i00000000000
χ412-2-222-22-2-2-222-2-2222-22-22-200002i−2i-220000−2i2i0000000000000000002i−2i000000000
χ422-2-222-22-2-2-222-2-2222-22-22-20000−2i2i-2200002i−2i000000000000000000−2i2i000000000
χ432-2-222-22-2-2-222-2-222-22-222-200002i−2i2-20000−2i2i000000000000000000−2i2i000000000
χ442-2-222-22-2-2-222-2-222-22-222-20000−2i2i2-200002i−2i0000000000000000002i−2i000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ464444-4-4-4-440-40-40400000004-44-4000000000000000000000000000000000000000
χ474444-4-4-4-440-40-4040000000-44-44000000000000000000000000000000000000000
χ484444-4-4-4-4-404040-4000000000000000000000000000000022−2222−22000000000000000
χ494444-4-4-4-4-404040-40000000000000000000000000000000−2222−2222000000000000000
χ5044-4-44-4-44000000000000002i2−2i2−2i22i200000000000022−220000002i−2i−2i2i000000000000000
χ5144-4-44-4-44000000000000002i2−2i2−2i22i2000000000000−2222000000−2i2i2i−2i000000000000000
χ5244-4-44-4-4400000000000000−2i22i22i2−2i200000000000022−22000000−2i2i2i−2i000000000000000
χ5344-4-44-4-4400000000000000−2i22i22i2−2i2000000000000−22220000002i−2i−2i2i000000000000000
χ5444-4-4-444-40-404040-40000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ5544-4-4-444-40-404040-4000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ564-44-4-4-44404040-40-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ574-44-4-4-44404040-40-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ584-44-4-4-4440-40-404044-4-44000000000000000000000000000000000000000000000
χ594-44-4-4-4440-40-40404-444-4000000000000000000000000000000000000000000000
χ604-4-444-44-444-4-444-4-400004-40000000000000000000000000000000000000000000
χ614-4-44-44-444040-40-4000000000000000000000000000000000000000000000002i2−2i20
χ624-4-44-44-444040-40-400000000000000000000000000000000000000000000000−2i22i20
χ634-4-44-44-44-40-404040000000000000004-4000000000000000000000000000000000
χ644-4-44-44-44-40-40404000000000000000-44000000000000000000000000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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