Finite Group Databasebeta

← Group #290621

Character table — Group #290621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1111-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1111-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-11111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-111-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-111-1-11-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-111-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-111-1-1111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-11111-111-1-1-1-111
χ172222222222222222-2-2-2-2-2-2222222-2-2-2-222-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ2122222222-2-2-2-2222222-2-22-2-2-200002-2000000000000000000000020-22-200000000000
χ2222222222-2-2-2-2222222-2-22-2-2-200002-20000000000000000000000-202-2200000000000
χ2322222222-2-2-2-22222-2-222-22-2-20000-220000000000000000000000020002-2-200000000
χ2422222222-2-2-2-22222-2-222-22-2-20000-2200000000000000000000000-2000-22200000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-22220000-22000000000000000000000002000-22-200000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-22220000-2200000000000000000000000-20002-2200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222-22200002-2000000000000000000000020-2-2200000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222-22200002-20000000000000000000000-2022-200000000000
χ2922-222-2-2-22-22-2000000002-2002i2i−2i−2i-222i−2i000000002i2i−2i−2i000022-2-20000000000000000
χ3022-222-2-2-22-22-2000000002-2002i2i−2i−2i-222i−2i00000000−2i−2i2i2i0000-2-2220000000000000000
χ3122-222-2-2-22-22-2000000002-200−2i−2i2i2i-22−2i2i000000002i2i−2i−2i0000-2-2220000000000000000
χ3222-222-2-2-22-22-2000000002-200−2i−2i2i2i-22−2i2i00000000−2i−2i2i2i000022-2-20000000000000000
χ3322-222-2-2-22-22-200000000-22002i2i−2i−2i2-2−2i2i000022-2-200002i2i−2i−2i00000000000000000000
χ3422-222-2-2-22-22-200000000-22002i2i−2i−2i2-2−2i2i0000-2-2220000−2i−2i2i2i00000000000000000000
χ3522-222-2-2-22-22-200000000-2200−2i−2i2i2i2-22i−2i000022-2-20000−2i−2i2i2i00000000000000000000
χ3622-222-2-2-22-22-200000000-2200−2i−2i2i2i2-22i−2i0000-2-22200002i2i−2i−2i00000000000000000000
χ372-222-22-2-22-2-2200002i−2i2i−2i00002i−2i2i−2i0000002-2i2−i2i2−i22−22−22−22−2i2−i2i2−i20000000000000000
χ382-222-22-2-22-2-2200002i−2i2i−2i00002i−2i2i−2i0000002-2−i2i2−i2i2−22−22−22−22−i2i2−i2i20000000000000000
χ392-222-22-2-22-2-2200002i−2i2i−2i0000−2i2i−2i2i000000-22i2−i2i2−i22−22−2−22−22−i2i2−i2i20000000000000000
χ402-222-22-2-22-2-2200002i−2i2i−2i0000−2i2i−2i2i000000-22−i2i2−i2i2−22−222−22−2i2−i2i2−i20000000000000000
χ412-222-22-2-22-2-220000−2i2i−2i2i00002i−2i2i−2i000000-22i2−i2i2−i2−22−222−22−2−i2i2−i2i20000000000000000
χ422-222-22-2-22-2-220000−2i2i−2i2i00002i−2i2i−2i000000-22−i2i2−i2i22−22−2−22−22i2−i2i2−i20000000000000000
χ432-222-22-2-22-2-220000−2i2i−2i2i0000−2i2i−2i2i0000002-2i2−i2i2−i2−22−22−22−22i2−i2i2−i20000000000000000
χ442-222-22-2-22-2-220000−2i2i−2i2i0000−2i2i−2i2i0000002-2−i2i2−i2i22−22−22−22−2−i2i2−i2i20000000000000000
χ452-2-22-2-22222-2-222-2-20000002-22-2-2200002-200i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ462-2-22-2-22222-2-222-2-20000002-22-2-2200002-200−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ472-2-22-2-22222-2-222-2-20000002-2-222-20000-2200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ482-2-22-2-22222-2-222-2-20000002-2-222-20000-2200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ492-2-22-2-22222-2-2-2-222000000-222-2-220000-2200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ502-2-22-2-22222-2-2-2-222000000-222-2-220000-2200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ512-2-22-2-22222-2-2-2-222000000-22-222-200002-200i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ522-2-22-2-22222-2-2-2-222000000-22-222-200002-200−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ5344-444-4-4-4-44-440000000044000000-4-400000000000000000000000000000000000000
χ5444-444-4-4-4-44-4400000000-4-40000004400000000000000000000000000000000000000
χ5544-4-4-444-400004i−4i4i−4i0000000000000000000000000000000000000000000000002-22i−2i
χ5644-4-4-444-400004i−4i4i−4i000000000000000000000000000000000000000000000000-22−2i2i
χ5744-4-4-444-40000−4i4i−4i4i0000000000000000000000000000000000000000000000002-2−2i2i
χ5844-4-4-444-40000−4i4i−4i4i000000000000000000000000000000000000000000000000-222i−2i
χ594-444-44-4-4-444-400004i−4i−4i4i000000000000000000000000000000000000000000000000
χ604-444-44-4-4-444-40000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ614-44-44-44-400004i−4i−4i4i000000000000000000000000000000000000000000002-22i−2i0000
χ624-44-44-44-400004i−4i−4i4i00000000000000000000000000000000000000000000-22−2i2i0000
χ634-44-44-44-40000−4i4i4i−4i000000000000000000000000000000000000000000002-2−2i2i0000
χ644-44-44-44-40000−4i4i4i−4i00000000000000000000000000000000000000000000-222i−2i0000
χ654-4-44-4-444-4-44444-4-4000000-4400000000000000000000000000000000000000000000
χ664-4-44-4-444-4-444-4-4440000004-400000000000000000000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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