Finite Group Databasebeta

← Group #306684

Character table — Group #306684

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-11-1-1-1-1-1-111-1-1-1
χ311111111111111111111111111-1-111111111-1-1111111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-111-11-1-111-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11-11111-1-11111-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-11
χ101111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1111-1-1111111-1
χ111111111111111111-1-1-1-1111111-1-1111111-1-111-1-1-1-111111111-1-11-1-1-1-1-111-1-111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-11111111-1-1-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111
χ151111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1111-1-1-1111111-1-1-1
χ17222222222-22-22-22-22222-2-2000022000000-2-222000000-2-20000000-200000000000
χ18222222222-22-22-22-22222-2-20000-2-2000000-2-2-2-2000000220000000200000000000
χ19222222222-22-22-22-2-2-2-2-2-2-200002200000022-2-2000000220000000-200000000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000-2-20000002222000000-2-20000000200000000000
χ2122222222-22-22-22-220000-2-222220022-2-22200000000-2-200000000-2000000000000
χ2222222222-22-22-22-220000-2-2222200-2-222-2-200000000-2-2000000002000000000000
χ2322222222-22-22-22-220000-2-2-2-2-2-20022-2-2-2-20000000022000000002000000000000
χ2422222222-22-22-22-220000-2-2-2-2-2-200-2-22222000000002200000000-2000000000000
χ252222-2-2-2-22020-20-2022-2-20022−2−22-2000000002-222−2−22−20022−2−200000000002−2000
χ262222-2-2-2-22020-20-2022-2-20022−2−2-2200000000-2222−2−22−200−2−2220000000000−22000
χ272222-2-2-2-22020-20-2022-2-200−2−2222-2000000002-2−2−222−2200−2−2220000000000−22000
χ282222-2-2-2-22020-20-2022-2-200−2−222-2200000000-22−2−222−220022−2−200000000002−2000
χ292222-2-2-2-22020-20-20-2-2220022−2−22-200000000-22−2−2222−200−2−22200000000002−2000
χ302222-2-2-2-22020-20-20-2-2220022−2−2-22000000002-2−2−2222−20022−2−20000000000−22000
χ312222-2-2-2-22020-20-20-2-22200−2−2222-200000000-2222−2−2−220022−2−20000000000−22000
χ322222-2-2-2-22020-20-20-2-22200−2−222-22000000002-222−2−2−2200−2−22200000000002−2000
χ332-22-2-222-22-2-222-2-220000-220000002-22-20000002i−2i2i−2i0000000000002i−2i000000000
χ342-22-2-222-22-2-222-2-220000-220000002-22-2000000−2i2i−2i2i000000000000−2i2i000000000
χ352-22-2-222-22-2-222-2-220000-22000000-22-220000002i−2i2i−2i000000000000−2i2i000000000
χ362-22-2-222-22-2-222-2-220000-22000000-22-22000000−2i2i−2i2i0000000000002i−2i000000000
χ372-22-2-222-2-222-2-222-22i−2i2i−2i-220000000000002i−2i000000000000000000002i−2i00002-20
χ382-22-2-222-2-222-2-222-22i−2i2i−2i-220000000000002i−2i00000000000000000000−2i2i0000-220
χ392-22-2-222-2-222-2-222-2−2i2i−2i2i-22000000000000−2i2i000000000000000000002i−2i0000-220
χ402-22-2-222-2-222-2-222-2−2i2i−2i2i-22000000000000−2i2i00000000000000000000−2i2i00002-20
χ412-22-2-222-2-2-222-2-2222i−2i2i−2i2-20000002-2-2200−2i2i000000000000002i−2i0000000000000
χ422-22-2-222-2-2-222-2-2222i−2i2i−2i2-2000000-222-200−2i2i00000000000000−2i2i0000000000000
χ432-22-2-222-2-2-222-2-222−2i2i−2i2i2-20000002-2-22002i−2i00000000000000−2i2i0000000000000
χ442-22-2-222-2-2-222-2-222−2i2i−2i2i2-2000000-222-2002i−2i000000000000002i−2i0000000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ464444-4-4-4-4-40-4040400000002222−22−220000000000000000−2222000000000000000000000
χ474444-4-4-4-4-40-404040000000−22−222222000000000000000022−22000000000000000000000
χ4844-4-44-44-404040-40-400000000000000000000000000000022−2222−22000000000000000
χ4944-4-44-44-404040-40-4000000000000000000000000000000−2222−2222000000000000000
χ5044-4-44-44-40-40-404040000004i−4i4i−4i000000000000000000000000000000000000000
χ5144-4-44-44-40-40-40404000000−4i4i−4i4i000000000000000000000000000000000000000
χ5244-4-4-44-44000000000000002i2−2i2−2i22i20000000000000000002i2−2i22-2-22000000000000000
χ5344-4-4-44-44000000000000002i2−2i2−2i22i2000000000000000000−2i22i2-222-2000000000000000
χ5444-4-4-44-4400000000000000−2i22i22i2−2i20000000000000000002i2−2i2-222-2000000000000000
χ5544-4-4-44-4400000000000000−2i22i22i2−2i2000000000000000000−2i22i22-2-22000000000000000
χ564-44-44-4-4440-40-404000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ574-44-44-4-4440-40-40400000000000000000000000−2i22i22i2−2i200000000000000000000000
χ584-44-44-4-44-404040-404i−4i−4i4i000000000000000000000000000000000000000000000
χ594-44-44-4-44-404040-40−4i4i4i−4i000000000000000000000000000000000000000000000
χ604-44-4-444-444-4-444-4-400004-40000000000000000000000000000000000000000000
χ614-4-44-4-444040-40-40400000000000000004-40000000000000000000000000000000
χ624-4-44-4-444040-40-4040000000000000000-440000000000000000000000000000000
χ634-4-44-4-4440-404040-400000000000000000000000000000000000000000022−2200000
χ644-4-44-4-4440-404040-4000000000000000000000000000000000000000000−222200000
χ658-8-8888-8-8000000000000000000000000000000000000000000000000000000000

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