Finite Group Databasebeta

← Group #242897

Character table — Group #242897

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222444444444444224444442244444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ91111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ111111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111
χ121111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ131111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1
χ141111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ151111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111-1-111
χ161111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-111-1-1
χ17222222222-2222222-2-22-2-2-2-2-222-2-2000000000000000022-2-222-2-20000000000000000
χ18222222222-2222222-2-22-2-2-2-2-222-2-20000000000000000-2-222-2-2220000000000000000
χ19222222222-2-2-2-2-222-2-22-222-2-2-2-222000000000000000022-2-2-2-2220000000000000000
χ20222222222-2-2-2-2-222-2-22-222-2-2-2-2220000000000000000-2-22222-2-20000000000000000
χ2122222222-222222-2-222-22-2-2-2-2-2-22222-2-222-2-200000000000000000000000000000000
χ2222222222-222222-2-222-22-2-2-2-2-2-222-2-222-2-22200000000000000000000000000000000
χ2322222222-22-2-2-2-2-2-222-2222-2-222-2-222-2-2-2-22200000000000000000000000000000000
χ2422222222-22-2-2-2-2-2-222-2222-2-222-2-2-2-22222-2-200000000000000000000000000000000
χ2522222222-2-22222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000002i−2i2i−2i0000
χ2622222222-2-22222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000−2i2i−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000000000000000−2i2i2i−2i0000
χ292-2-2222-2-22222-2-2-2-2-2-2222-22-22-22-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ302-2-2222-2-22222-2-2-2-2-2-2222-22-22-22-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312-2-2222-2-222-2-222-2-2-2-222-222-2-22-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ322-2-2222-2-222-2-222-2-2-2-222-222-2-22-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ332-2-2222-2-22-222-2-2-2-2222-2-22-222-2-220000000000000000000000000000000000002i−2i2i−2i
χ342-2-2222-2-22-222-2-2-2-2222-2-22-222-2-22000000000000000000000000000000000000−2i2i−2i2i
χ352-2-2222-2-22-2-2-222-2-2222-22-2-22-222-20000000000000000000000000000000000002i−2i−2i2i
χ362-2-2222-2-22-2-2-222-2-2222-22-2-22-222-2000000000000000000000000000000000000−2i2i2i−2i
χ372-2-2222-2-2-2222-2-222-2-2-22-22-22-222-20000000000000000000000002i−2i2i−2i000000000000
χ382-2-2222-2-2-2222-2-222-2-2-22-22-22-222-2000000000000000000000000−2i2i−2i2i000000000000
χ392-2-2222-2-2-22-2-22222-2-2-222-2-222-2-220000000000000000000000002i−2i−2i2i000000000000
χ402-2-2222-2-2-22-2-22222-2-2-222-2-222-2-22000000000000000000000000−2i2i2i−2i000000000000
χ412-2-2222-2-2-2-222-2-22222-2-22-22-2-22-2200000000000000000000000000002i−2i2i−2i00000000
χ422-2-2222-2-2-2-222-2-22222-2-22-22-2-22-220000000000000000000000000000−2i2i−2i2i00000000
χ432-2-2222-2-2-2-2-2-2222222-2-2-222-22-22-200000000000000000000000000002i−2i−2i2i00000000
χ442-2-2222-2-2-2-2-2-2222222-2-2-222-22-22-20000000000000000000000000000−2i2i2i−2i00000000
χ454444-4-4-4-4004-44-40000000000000000000000000000000022−220022−220000000000000000
χ464444-4-4-4-4004-44-400000000000000000000000000000000−222200−22220000000000000000
χ474444-4-4-4-400-44-440000000000000000000000000000000022−2200−22220000000000000000
χ484444-4-4-4-400-44-4400000000000000000000000000000000−22220022−220000000000000000
χ4944-4-44-44-4040000004-40-4000000000000004-400000000000000000000000000000000
χ5044-4-44-44-4040000004-40-400000000000000-4400000000000000000000000000000000
χ5144-4-44-44-40-4000000-44040000000000004i−4i0000000000000000000000000000000000
χ5244-4-44-44-40-4000000-4404000000000000−4i4i0000000000000000000000000000000000
χ5344-4-4-44-444000004-400-4000000000000000002i2−2i22i2−2i20000000000000000000000000000
χ5444-4-4-44-444000004-400-400000000000000000−2i22i2−2i22i20000000000000000000000000000
χ5544-4-4-44-44-400000-4400400000000000000000000022−2222−22000000000000000000000000
χ5644-4-4-44-44-400000-44004000000000000000000000−2222−2222000000000000000000000000
χ574-44-44-4-4404000000-440-400000000004i−4i000000000000000000000000000000000000
χ584-44-44-4-4404000000-440-40000000000−4i4i000000000000000000000000000000000000
χ594-44-44-4-440-40000004-404000000004-400000000000000000000000000000000000000
χ604-44-44-4-440-40000004-40400000000-4400000000000000000000000000000000000000
χ614-44-4-444-4400000-4400-40000000000000000022−22−22220000000000000000000000000000
χ624-44-4-444-4400000-4400-400000000000000000−222222−220000000000000000000000000000
χ634-44-4-444-4-4000004-40040000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ644-44-4-444-4-4000004-4004000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ654-4-44-4-444004-4-4400000000000000000000000000000022−220022−22000000000000000000
χ664-4-44-4-444004-4-44000000000000000000000000000000−222200−2222000000000000000000
χ674-4-44-4-44400-444-400000000000000000000000000000022−2200−2222000000000000000000
χ684-4-44-4-44400-444-4000000000000000000000000000000−22220022−22000000000000000000

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