Finite Group Databasebeta

← Group #296281

Character table — Group #296281

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888882444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-11-1-111-111-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-11111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-11111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-1111-1-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-1-1111-1-111
χ12111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-111111-1-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111111-11-1-11111-1-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-11-111-1-1-1-111111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-11-11-1-111-1-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-11-111-1-1111-1-1-1-111
χ17222222222222222222-2-2-2-22222-2-2-2-222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ2122222222-2-2-2-22222-2-222-2-2000022-2-200000000000000000000002-2-20200000000000
χ2222222222-2-2-2-22222-2-222-2-2000022-2-20000000000000000000000-2220-200000000000
χ2322222222-2-2-2-22222-2-2-2-2220000-2-2220000000000000000000000000202-200-2000000
χ2422222222-2-2-2-22222-2-2-2-2220000-2-2220000000000000000000000000-20-22002000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000-2-222000000000000000000000000020-2200-2000000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000-2-2220000000000000000000000000-202-2002000000
χ2722222222-2-2-2-2-2-2-2-222-2-222000022-2-2000000000000000000000022-20-200000000000
χ2822222222-2-2-2-2-2-2-2-222-2-222000022-2-20000000000000000000000-2-220200000000000
χ29222-22-2-2-2-2-22200000000002i2i−2i−2i2-22-2002i−2i0000002i2i−2i−2i000022-2-20000000000000000
χ30222-22-2-2-2-2-22200000000002i2i−2i−2i2-22-2002i−2i000000−2i−2i2i2i0000-2-2220000000000000000
χ31222-22-2-2-2-2-22200000000002i2i−2i−2i-22-2200−2i2i002i2i−2i−2i000022-2-200000000000000000000
χ32222-22-2-2-2-2-22200000000002i2i−2i−2i-22-2200−2i2i00−2i−2i2i2i0000-2-22200000000000000000000
χ33222-22-2-2-2-2-2220000000000−2i−2i2i2i2-22-200−2i2i0000002i2i−2i−2i0000-2-2220000000000000000
χ34222-22-2-2-2-2-2220000000000−2i−2i2i2i2-22-200−2i2i000000−2i−2i2i2i000022-2-20000000000000000
χ35222-22-2-2-2-2-2220000000000−2i−2i2i2i-22-22002i−2i002i2i−2i−2i0000-2-22200000000000000000000
χ36222-22-2-2-2-2-2220000000000−2i−2i2i2i-22-22002i−2i00−2i−2i2i2i000022-2-200000000000000000000
χ372-222-2-2-222-22-20000002i−2i2i−2i2-22-2000000002i−2ii2−i2i2−i22−22−2i2−i2i2−i22−22−20000000000000000
χ382-222-2-2-222-22-20000002i−2i2i−2i2-22-2000000002i−2i−i2i2−i2i2−22−22−i2i2−i2i2−22−220000000000000000
χ392-222-2-2-222-22-20000002i−2i2i−2i-22-2200000000−2i2ii2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ402-222-2-2-222-22-20000002i−2i2i−2i-22-2200000000−2i2i−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ412-222-2-2-222-22-2000000−2i2i−2i2i2-22-200000000−2i2ii2−i2i2−i2−22−22i2−i2i2−i2−22−220000000000000000
χ422-222-2-2-222-22-2000000−2i2i−2i2i2-22-200000000−2i2i−i2i2−i2i22−22−2−i2i2−i2i22−22−20000000000000000
χ432-222-2-2-222-22-2000000−2i2i−2i2i-22-22000000002i−2ii2−i2i2−i2−22−22−i2i2−i2i22−22−20000000000000000
χ442-222-2-2-222-22-2000000−2i2i−2i2i-22-22000000002i−2i−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000000000000
χ452-22-2-222-2-222-22i2i−2i−2i2i−2i00002i−2i−2i2i00002-200002−2−22i2−i2−i2i2−i2i2i2−i22−2−220000000000000000
χ462-22-2-222-2-222-22i2i−2i−2i2i−2i00002i−2i−2i2i00002-20000−222−2−i2i2i2−i2i2−i2−i2i2−222−20000000000000000
χ472-22-2-222-2-222-22i2i−2i−2i2i−2i0000−2i2i2i−2i0000-2200002−2−22i2−i2−i2i2i2−i2−i2i2−222−20000000000000000
χ482-22-2-222-2-222-22i2i−2i−2i2i−2i0000−2i2i2i−2i0000-220000−222−2−i2i2i2−i2−i2i2i2−i22−2−220000000000000000
χ492-22-2-222-2-222-2−2i−2i2i2i−2i2i00002i−2i−2i2i0000-2200002−2−22−i2i2i2−i2−i2i2i2−i2−222−20000000000000000
χ502-22-2-222-2-222-2−2i−2i2i2i−2i2i00002i−2i−2i2i0000-220000−222−2i2−i2−i2i2i2−i2−i2i22−2−220000000000000000
χ512-22-2-222-2-222-2−2i−2i2i2i−2i2i0000−2i2i2i−2i00002-200002−2−22−i2i2i2−i2i2−i2−i2i22−2−220000000000000000
χ522-22-2-222-2-222-2−2i−2i2i2i−2i2i0000−2i2i2i−2i00002-20000−222−2i2−i2−i2i2−i2i2i2−i2−222−20000000000000000
χ53444-44-4-4-444-4-4000000000000004-4-4400000000000000000000000000000000000000
χ54444-44-4-4-444-4-400000000000000-444-400000000000000000000000000000000000000
χ5544-4-4-44-4400004i−4i4i−4i0000000000000000000000000000000000000000000000002i−2i2-2
χ5644-4-4-44-4400004i−4i4i−4i000000000000000000000000000000000000000000000000−2i2i-22
χ5744-4-4-44-440000−4i4i−4i4i0000000000000000000000000000000000000000000000002i−2i-22
χ5844-4-4-44-440000−4i4i−4i4i000000000000000000000000000000000000000000000000−2i2i2-2
χ594-444-4-4-44-44-440000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ604-444-4-4-44-44-44000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ614-44-4-444-44-4-444i4i−4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ624-44-4-444-44-4-44−4i−4i4i4i4i−4i00000000000000000000000000000000000000000000000000
χ634-4-4444-4-400004-4-4400000000000000000000000000000000000000000002i−2i02i−2i0000
χ644-4-4444-4-400004-4-440000000000000000000000000000000000000000000−2i2i0−2i2i0000
χ654-4-4444-4-40000-444-400000000000000000000000000000000000000000002i−2i0−2i2i0000
χ664-4-4444-4-40000-444-40000000000000000000000000000000000000000000−2i2i02i−2i0000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-88-888000000000000000000000000000000000000000000000000000000000000

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