Finite Group Databasebeta

← Group #290707

Character table — Group #290707

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444488888888888888882444444444444444
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
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-11-1-111-111-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-11111111-1-1-1-1
χ91111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-1-1111-1-111-1-1
χ101111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1111-1-1-111-1-111
χ111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-1-1-1-1-1111-1-111
χ121111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-111111-1-1-111-1-1
χ131111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-111
χ141111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1111-1-1-1-111111-1-1
χ151111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-111-1-1-111-1-1-11111-1-1
χ161111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1111-1-1111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-22200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-222222222-2-2-2-222-2-200000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ2122222222-2-22222-2-2-2-22-222-2-200002-200000000000000000000002-2-20200000000000
χ2222222222-2-22222-2-2-2-22-222-2-200002-20000000000000000000000-2220-200000000000
χ2322222222-2-22222-2-2-2-2-22-2-2220000-220000000000000000000000000202-200-2000000
χ2422222222-2-22222-2-2-2-2-22-2-2220000-220000000000000000000000000-20-22002000000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-22200002-200000000000000000000002-220-200000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-22200002-20000000000000000000000-22-20200000000000
χ2722222222-2-2-2-2-2-2-2-222-2222-2-20000-22000000000000000000000000020-2200-2000000
χ2822222222-2-2-2-2-2-2-2-222-2222-2-20000-220000000000000000000000000-202-2002000000
χ29222-22-2-2-2-2-222-2-2222-20000002i2i−2i−2i0000002i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ30222-22-2-2-2-2-222-2-2222-20000002i2i−2i−2i0000002i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ31222-22-2-2-2-2-222-2-2222-2000000−2i−2i2i2i000000−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ32222-22-2-2-2-2-222-2-2222-2000000−2i−2i2i2i000000−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ33222-22-2-2-2-2-2-2-22222-220000002i2i−2i−2i000000−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ34222-22-2-2-2-2-2-2-22222-220000002i2i−2i−2i000000−2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ35222-22-2-2-2-2-2-2-22222-22000000−2i−2i2i2i0000002i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ36222-22-2-2-2-2-2-2-22222-22000000−2i−2i2i2i0000002i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ3722-22-2-2-222-200002-200002i−2i2i−2i2-22-200002i−2i00i2−i2i2−i22−22−2i2−i2i2−i22−22−20000000000000000
χ3822-22-2-2-222-200002-200002i−2i2i−2i2-22-200002i−2i00−i2i2−i2i2−22−22−i2i2−i2i2−22−220000000000000000
χ3922-22-2-2-222-200002-200002i−2i2i−2i-22-220000−2i2i00i2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ4022-22-2-2-222-200002-200002i−2i2i−2i-22-220000−2i2i00−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ4122-22-2-2-222-200002-20000−2i2i−2i2i2-22-20000−2i2i00i2−i2i2−i2−22−22i2−i2i2−i2−22−220000000000000000
χ4222-22-2-2-222-200002-20000−2i2i−2i2i2-22-20000−2i2i00−i2i2−i2i22−22−2−i2i2−i2i22−22−20000000000000000
χ4322-22-2-2-222-200002-20000−2i2i−2i2i-22-2200002i−2i00i2−i2i2−i2−22−22−i2i2−i2i22−22−20000000000000000
χ4422-22-2-2-222-200002-20000−2i2i−2i2i-22-2200002i−2i00−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000000000000
χ4522-2-2-222-2-2200002-2002-200002i−2i−2i2i-222i−2i000000002i−2i−2i2i00002-2-220000000000000000
χ4622-2-2-222-2-2200002-2002-200002i−2i−2i2i-222i−2i00000000−2i2i2i−2i0000-222-20000000000000000
χ4722-2-2-222-2-2200002-2002-20000−2i2i2i−2i-22−2i2i000000002i−2i−2i2i0000-222-20000000000000000
χ4822-2-2-222-2-2200002-2002-20000−2i2i2i−2i-22−2i2i00000000−2i2i2i−2i00002-2-220000000000000000
χ4922-2-2-222-2-2200002-200-2200002i−2i−2i2i2-2−2i2i00002-2-220000−2i2i2i−2i00000000000000000000
χ5022-2-2-222-2-2200002-200-2200002i−2i−2i2i2-2−2i2i0000-222-200002i−2i−2i2i00000000000000000000
χ5122-2-2-222-2-2200002-200-220000−2i2i2i−2i2-22i−2i00002-2-2200002i−2i−2i2i00000000000000000000
χ5222-2-2-222-2-2200002-200-220000−2i2i2i−2i2-22i−2i0000-222-20000−2i2i2i−2i00000000000000000000
χ53444-44-4-4-44444-4-4-4-4-4400000000000000000000000000000000000000000000000000
χ54444-44-4-4-444-4-444-4-44-400000000000000000000000000000000000000000000000000
χ5544-44-4-4-44-440000-4400004i−4i−4i4i00000000000000000000000000000000000000000000
χ5644-44-4-4-44-440000-440000−4i4i4i−4i00000000000000000000000000000000000000000000
χ5744-4-4-444-44-40000-44004400000000-4-400000000000000000000000000000000000000
χ5844-4-4-444-44-40000-4400-4-4000000004400000000000000000000000000000000000000
χ594-4-4444-4-4004-44-40000000000000000000000000000000000000000000002i−2i02i−2i0000
χ604-4-4444-4-4004-44-4000000000000000000000000000000000000000000000−2i2i0−2i2i0000
χ614-4-4444-4-400-44-440000000000000000000000000000000000000000000002i−2i0−2i2i0000
χ624-4-4444-4-400-44-44000000000000000000000000000000000000000000000−2i2i02i−2i0000
χ634-4-4-44-444004-4-44000000000000000000000000000000000000000000000000002-22-2
χ644-4-4-44-444004-4-4400000000000000000000000000000000000000000000000000-22-22
χ654-4-4-44-44400-444-4000000000000000000000000000000000000000000000000002-2-22
χ664-4-4-44-44400-444-400000000000000000000000000000000000000000000000000-222-2
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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