Finite Group Databasebeta

← Group #232256

Character table — Group #232256

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222222224444224444442222222244444444888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-11-1-11-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-11-1-111-1-1
χ101111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-111-111-1-111
χ111111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-111-11-1-111
χ121111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-11-1-11-111-1-1
χ131111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-11-1-11-1-1-111
χ141111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-111-1111-1-1
χ151111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-111-11111-1-1
χ161111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-11-1-11-1-1-1-111
χ172222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000002-22-20000000000
χ182222222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000000000-22-220000000000
χ192222222222-2-2-2-2222222-2-2-2-222-2-2000000000000000000000000002-2-220000000000
χ202222222222-2-2-2-2222222-2-2-2-222-2-200000000000000000000000000-222-20000000000
χ2122222222-2-22222-2-22222-2-22-2-2-22-2000000000000000000000000000000220-2-200000
χ2222222222-2-22222-2-22222-2-22-2-2-22-2000000000000000000000000000000-2-202200000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2222-220000000000000000000000002-2000000200-20000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2222-22000000000000000000000000-22000000-20020000
χ2522222222-2-2-2-2-2-2-2-2222222-22-2-2-220000000000000000000000002-2000000-20020000
χ2622222222-2-2-2-2-2-2-2-2222222-22-2-2-22000000000000000000000000-22000000200-20000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222-2222-20000000000000000000000000000002-20-2200000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222-2222-2000000000000000000000000000000-2202-200000
χ292-2-22-2-2222222-2-2-2-222-2-22-2222-2-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ302-2-22-2-2222222-2-2-2-222-2-22-2222-2-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312-2-22-2-2222222-2-2-2-2-2-2222-2-2-2-222222-2-222-2-200000000000000000000000000000000
χ322-2-22-2-2222222-2-2-2-2-2-2222-2-2-2-2222-2-222-2-22200000000000000000000000000000000
χ332-2-22-2-22222-2-222-2-222-2-2-22-2-22-22222-2-2-2-22200000000000000000000000000000000
χ342-2-22-2-22222-2-222-2-222-2-2-22-2-22-222-2-22222-2-200000000000000000000000000000000
χ352-2-22-2-22222-2-222-2-2-2-222-2222-22-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362-2-22-2-22222-2-222-2-2-2-222-2222-22-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ372-2-22-2-222-2-222-2-22222-2-2-222-2-22-220000000000000000000000000000000000002-22-2
χ382-2-22-2-222-2-222-2-22222-2-2-222-2-22-22000000000000000000000000000000000000-22-22
χ392-2-22-2-222-2-222-2-222-2-222-22-222-22-2000000000000000022-2-222-2-20000000000000000
χ402-2-22-2-222-2-222-2-222-2-222-22-222-22-20000000000000000-2-222-2-2220000000000000000
χ412-2-22-2-222-2-2-2-2222222-2-22-2-22-222-2000000000000000022-2-2-2-2220000000000000000
χ422-2-22-2-222-2-2-2-2222222-2-22-2-22-222-20000000000000000-2-22222-2-20000000000000000
χ432-2-22-2-222-2-2-2-22222-2-2222-22-22-2-220000000000000000000000000000000000002-2-22
χ442-2-22-2-222-2-2-2-22222-2-2222-22-22-2-22000000000000000000000000000000000000-222-2
χ45444-4-4-44-4004-44-400000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ46444-4-4-44-4004-44-40000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ47444-4-4-44-400-44-4400000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ48444-4-4-44-400-44-440000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4944-444-4-4-44-400004-4000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ5044-444-4-4-44-400004-400000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ5144-444-4-4-4-440000-4400000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ5244-444-4-4-4-440000-440000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ5344-4-4-44-44000000004-44-4000000002-22-22-22-200000000000000000000000000000000
χ5444-4-4-44-44000000004-44-400000000-22-22-22-2200000000000000000000000000000000
χ5544-4-4-44-4400000000-44-44000000002-22-2-22-2200000000000000000000000000000000
χ5644-4-4-44-4400000000-44-4400000000-22-222-22-200000000000000000000000000000000
χ574-444-44-4-44-40000-4400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ584-444-44-4-44-40000-440000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ594-444-44-4-4-4400004-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ604-444-44-4-4-4400004-400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ614-44-44-4-44000000004-4-44000000002-2-22-222-200000000000000000000000000000000
χ624-44-44-4-44000000004-4-4400000000-222-22-2-2200000000000000000000000000000000
χ634-44-44-4-4400000000-444-4000000002-2-222-2-2200000000000000000000000000000000
χ644-44-44-4-4400000000-444-400000000-222-2-222-200000000000000000000000000000000
χ654-4-4-4444-4004-4-4400000000000000000000002-2-222-2-22000000000000000000000000
χ664-4-4-4444-4004-4-440000000000000000000000-222-2-222-2000000000000000000000000
χ674-4-4-4444-400-444-400000000000000000000002-2-22-222-2000000000000000000000000
χ684-4-4-4444-400-444-40000000000000000000000-222-22-2-22000000000000000000000000

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