Finite Group Databasebeta

← Group #408634

Character table — Group #408634

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222224444444488888888882244444444448888888888882224444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-1
χ61111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-111-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-111111-1-1-1-1
χ9111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-11-1-1-1111-1-111-1-1
χ10111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1111-1-1-111-1-111
χ11111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-11-1-1-11-1-111-1-111
χ12111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11-1111-111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111111-11-1-1-111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-11-1111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-11-1-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-11-111111-1-1-1-111
χ17222222-2-2-2-22222-2-2-2-200000000002200-2-2002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ18222222-2-2-2-22222-2-2-2-200000000002200-2-200−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ19222222-2-2-2-22222-2-2-2-20000000000-2-20022002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ20222222-2-2-2-22222-2-2-2-20000000000-2-2002200−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ21222222-2-2-2-2-2-2-2-22222222222-2-2-2-2000000000000000000000000002-2-200200000000
χ22222222-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000-22200-200000000
χ23222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000022-200-200000000
χ24222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222200000000000000000000000000-2-2200200000000
χ252222-2-222-2-22-2-222-2-222222-2-222-2-22-2002-20000000000000022-2-20000000000000000
χ262222-2-222-2-22-2-222-2-222222-2-222-2-2-2200-2200000000000000-2-2220000000000000000
χ272222-2-222-2-22-2-222-2-22-2-2-2-222-2-2222-2002-200000000000000-2-2220000000000000000
χ282222-2-222-2-22-2-222-2-22-2-2-2-222-2-222-2200-220000000000000022-2-20000000000000000
χ292222-2-2-2-2222-2-22-222-200000000002-222-22-2-20000000022-2-200000000000000000000
χ302222-2-2-2-2222-2-22-222-200000000002-2-2-2-222200000000-2-22200000000000000000000
χ312222-2-2-2-2222-2-22-222-20000000000-22222-2-2-200000000-2-22200000000000000000000
χ322222-2-2-2-2222-2-22-222-20000000000-22-2-22-2220000000022-2-200000000000000000000
χ332222-2-2-2-222-222-22-2-222222-2-2-2-2220000000000000000000000002-20002-2000000000
χ342222-2-2-2-222-222-22-2-222222-2-2-2-222000000000000000000000000-22000-22000000000
χ352222-2-2-2-222-222-22-2-22-2-2-2-22222-2-20000000000000000000000002-2000-22000000000
χ362222-2-2-2-222-222-22-2-22-2-2-2-22222-2-2000000000000000000000000-220002-2000000000
χ372-22-22-22-22-222-2-2-22-2200000000000000000000002i−2i2i−2i2i−2i2i−2i2-22-20000000000000000
χ382-22-22-22-22-222-2-2-22-2200000000000000000000002i−2i2i−2i−2i2i−2i2i-22-220000000000000000
χ392-22-22-22-22-222-2-2-22-220000000000000000000000−2i2i−2i2i2i−2i2i−2i-22-220000000000000000
χ402-22-22-22-22-222-2-2-22-220000000000000000000000−2i2i−2i2i−2i2i−2i2i2-22-20000000000000000
χ412-22-22-22-22-2-2-2222-22-22i2i−2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000002-22i−2i
χ422-22-22-22-22-2-2-2222-22-22i2i−2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000-22−2i2i
χ432-22-22-22-22-2-2-2222-22-2−2i−2i2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000002-2−2i2i
χ442-22-22-22-22-2-2-2222-22-2−2i−2i2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000-222i−2i
χ452-22-22-2-22-2222-2-22-22-22i2i−2i−2i2i−2i−2i2i−2i2i002i−2i002i−2i00002-2-22000000000000000000000000
χ462-22-22-2-22-2222-2-22-22-22i2i−2i−2i2i−2i−2i2i−2i2i00−2i2i00−2i2i0000-222-2000000000000000000000000
χ472-22-22-2-22-2222-2-22-22-2−2i−2i2i2i−2i2i2i−2i2i−2i002i−2i002i−2i0000-222-2000000000000000000000000
χ482-22-22-2-22-2222-2-22-22-2−2i−2i2i2i−2i2i2i−2i2i−2i00−2i2i00−2i2i00002-2-22000000000000000000000000
χ492-22-2-222-2-222-22-2-2-2220000000000002i−2i00−2i2i2i−2i2i−2i000000002-2-220000000000000000
χ502-22-2-222-2-222-22-2-2-2220000000000002i−2i00−2i2i−2i2i−2i2i00000000-222-20000000000000000
χ512-22-2-222-2-222-22-2-2-222000000000000−2i2i002i−2i2i−2i2i−2i00000000-222-20000000000000000
χ522-22-2-222-2-222-22-2-2-222000000000000−2i2i002i−2i−2i2i−2i2i000000002-2-220000000000000000
χ532-22-2-222-2-22-22-2222-2-22i2i−2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000002i−2i2-20000
χ542-22-2-222-2-22-22-2222-2-22i2i−2i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000−2i2i-220000
χ552-22-2-222-2-22-22-2222-2-2−2i−2i2i2i2i−2i−2i2i2i−2i000000000000000000000000000000002i−2i-220000
χ562-22-2-222-2-22-22-2222-2-2−2i−2i2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000−2i2i2-20000
χ572-22-2-22-222-22-22-222-2-22i2i−2i−2i−2i2i−2i2i2i−2i000000002-2-2200002i−2i−2i2i00000000000000000000
χ582-22-2-22-222-22-22-222-2-22i2i−2i−2i−2i2i−2i2i2i−2i00000000-222-20000−2i2i2i−2i00000000000000000000
χ592-22-2-22-222-22-22-222-2-2−2i−2i2i2i2i−2i2i−2i−2i2i000000002-2-220000−2i2i2i−2i00000000000000000000
χ602-22-2-22-222-22-22-222-2-2−2i−2i2i2i2i−2i2i−2i−2i2i00000000-222-200002i−2i−2i2i00000000000000000000
χ614444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ624444-4-444-4-4-444-4-444-400000000000000000000000000000000000000000000000000
χ634-44-44-4-44-44-4-444-44-4400000000000000000000000000000000000000000000000000
χ644-44-4-44-444-4-44-44-4-44400000000000000000000000000000000000000000000000000
χ6588-8-8000000000000004i2−4i24i2−4i20000000000000000000000000000000000000000000000
χ6688-8-800000000000000−4i24i2−4i24i20000000000000000000000000000000000000000000000
χ678-8-880000000000000042−42−42420000000000000000000000000000000000000000000000
χ688-8-8800000000000000−424242−420000000000000000000000000000000000000000000000

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