Finite Group Databasebeta

← Group #404080

Character table — Group #404080

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222444444444444888888888888888888888816161616161616161616161616161616
order12222222224444444444444444444422444444444444444444442244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-11-111-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11-1-1111111-1-1-1-1
χ9111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-1-11111-1-1-1-111
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1111-1-1-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11-11-1-1-111-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-11-1111-1-111-1-1-1-111
χ172222222222-2-2-2-2-2-2-2-22222-2-2-2-200000022-2-20000000022-2-200000000000000000000
χ182222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000-2-22200000000-2-22200000000000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000022-2-200000000-2-22200000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000-2-2220000000022-2-200000000000000000000
χ21222222-2-2-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000020-2002i−2i00000000
χ22222222-2-2-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000-20200−2i2i00000000
χ23222222-2-2-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000020-200−2i2i00000000
χ24222222-2-2-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000-202002i−2i00000000
χ25222222-2-2-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000020-202i−2i0000000000
χ26222222-2-2-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000-2020−2i2i0000000000
χ27222222-2-2-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000020-20−2i2i0000000000
χ28222222-2-2-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000-20202i−2i0000000000
χ292222-2-2-222-22-22-22-22-2000000000000222-22-20000-2-200000022-2-20000000000000000
χ302222-2-2-222-22-22-22-22-200000000000022-22-220000-2-2000000-2-2220000000000000000
χ312222-2-2-222-22-22-22-22-2000000000000-2-22-22-2000022000000-2-2220000000000000000
χ322222-2-2-222-22-22-22-22-2000000000000-2-2-22-2200002200000022-2-20000000000000000
χ332222-2-2-222-2-22-22-22-22000000002222002-2-2222-2-200-2-2000000000000000000000000
χ342222-2-2-222-2-22-22-22-2200000000222200-222-2-2-22200-2-2000000000000000000000000
χ352222-2-2-222-2-22-22-22-2200000000-2-2-2-2002-2-22-2-2220022000000000000000000000000
χ362222-2-2-222-2-22-22-22-2200000000-2-2-2-200-222-222-2-20022000000000000000000000000
χ372-2-222-222-2-222-2-2-2-2222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000002i−2i2-20000
χ382-2-222-222-2-222-2-2-2-2222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−2i2i-220000
χ392-2-222-222-2-222-2-2-2-222−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000002i−2i-220000
χ402-2-222-222-2-222-2-2-2-222−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−2i2i2-20000
χ412-2-222-222-2-2-2-22222-2-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000002i−2i2-2
χ422-2-222-222-2-2-2-22222-2-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000−2i2i-22
χ432-2-222-222-2-2-2-22222-2-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000002i−2i-22
χ442-2-222-222-2-2-2-22222-2-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000−2i2i2-2
χ452-2-222-2-2-2222222-2-2-2-22-2-222-2-2200000000002i−2i2i−2i000000002i−2i2i−2i0000000000000000
χ462-2-222-2-2-2222222-2-2-2-22-2-222-2-220000000000−2i2i−2i2i00000000−2i2i−2i2i0000000000000000
χ472-2-222-2-2-2222222-2-2-2-2-222-2-222-200000000002i−2i2i−2i00000000−2i2i−2i2i0000000000000000
χ482-2-222-2-2-2222222-2-2-2-2-222-2-222-20000000000−2i2i−2i2i000000002i−2i2i−2i0000000000000000
χ492-2-222-2-2-222-2-2-2-222222-2-22-222-222-2-22-2000000002-22-2000000000000000000000000
χ502-2-222-2-2-222-2-2-2-222222-2-22-222-2-2-222-2200000000-22-22000000000000000000000000
χ512-2-222-2-2-222-2-2-2-22222-222-22-2-2222-2-2-2200000000-222-2000000000000000000000000
χ522-2-222-2-2-222-2-2-2-22222-222-22-2-22-2-2222-2000000002-2-22000000000000000000000000
χ532-2-22-222-22-22-22-2-22-220000000022-2-2000000000000-222i−2i2i−2i2i−2i−2i2i0000000000000000
χ542-2-22-222-22-22-22-2-22-220000000022-2-2000000000000-22−2i2i−2i2i−2i2i2i−2i0000000000000000
χ552-2-22-222-22-22-22-2-22-2200000000-2-2220000000000002-22i−2i2i−2i−2i2i2i−2i0000000000000000
χ562-2-22-222-22-22-22-2-22-2200000000-2-2220000000000002-2−2i2i−2i2i2i−2i−2i2i0000000000000000
χ572-2-22-222-22-2-22-222-22-20000000000002-200002i−2i−2i2i-22002i−2i−2i2i00000000000000000000
χ582-2-22-222-22-2-22-222-22-20000000000002-20000−2i2i2i−2i-2200−2i2i2i−2i00000000000000000000
χ592-2-22-222-22-2-22-222-22-2000000000000-2200002i−2i−2i2i2-200−2i2i2i−2i00000000000000000000
χ602-2-22-222-22-2-22-222-22-2000000000000-220000−2i2i2i−2i2-2002i−2i−2i2i00000000000000000000
χ614444-4-44-4-444-4-444-4-4400000000000000000000000000000000000000000000000000
χ624444-4-44-4-44-444-4-444-400000000000000000000000000000000000000000000000000
χ634-4-44-44-44-444-4-44-444-400000000000000000000000000000000000000000000000000
χ644-4-44-44-44-44-444-44-4-4400000000000000000000000000000000000000000000000000
χ6588-8-800000000000000000000004i−4i4i−4i00000000000000000000000000000000000000
χ6688-8-80000000000000000000000−4i4i−4i4i00000000000000000000000000000000000000
χ678-88-800000000000000000000004i−4i−4i4i00000000000000000000000000000000000000
χ688-88-80000000000000000000000−4i4i4i−4i00000000000000000000000000000000000000

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