Finite Group Databasebeta

← Group #324997

Character table — Group #324997

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444444444888844448888888888888888888888888844884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-1
χ91111111111111111-1-111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-11-1
χ101111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-11-11
χ111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-11
χ121111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111-11-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-111-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-11-1-11
χ17222222222-2-2-2222-222-2-222-2-2-2-2000022-2-2000000000000000000000000002-2000000
χ18222222222-2-2-2222-222-2-222-2-2-2-20000-2-22200000000000000000000000000-22000000
χ19222222222-2-2-2222-2-2-2-2-2-2-22222000022-2-200000000000000000000000000-22000000
χ20222222222-2-2-2222-2-2-2-2-2-2-222220000-2-222000000000000000000000000002-2000000
χ2122222222-2222-2-2-2222-2-2-2-2-2-22222220000-2-2220000000000000000-2-2000000000000
χ2222222222-2222-2-2-2222-2-2-2-2-2-222-2-2-2-2000022-2-2000000000000000022000000000000
χ2322222222-2222-2-2-22-2-2-2-22222-2-222220000-2-2-2-2000000000000000022000000000000
χ2422222222-2222-2-2-22-2-2-2-22222-2-2-2-2-2-2000022220000000000000000-2-2000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-222-2-20000000000000000000000000000002i2i−2i−2i002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-222-2-2000000000000000000000000000000−2i−2i2i2i00−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000000000000000002i2i−2i−2i00−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-222000000000000000000000000000000−2i−2i2i2i002i−2i0000
χ29222-2-2-2-2202-2-200022-20000002-22i2i−2i−2i0000002i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000000000
χ30222-2-2-2-2202-2-200022-20000002-22i2i−2i−2i0000002i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i200000000000000
χ31222-2-2-2-2202-2-200022-20000002-2−2i−2i2i2i000000−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000000000
χ32222-2-2-2-2202-2-200022-20000002-2−2i−2i2i2i000000−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i200000000000000
χ33222-2-2-2-2202-2-20002-22000000-222i2i−2i−2i000000−2i2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i200000000000000
χ34222-2-2-2-2202-2-20002-22000000-222i2i−2i−2i000000−2i2i−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000000000
χ35222-2-2-2-2202-2-20002-22000000-22−2i−2i2i2i0000002i−2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i200000000000000
χ36222-2-2-2-2202-2-20002-22000000-22−2i−2i2i2i0000002i−2i−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000000000
χ3722-222-2-2-20-22-2000200002-22-2002-22-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-2000000000000
χ3822-222-2-2-20-22-2000200002-22-2002-22-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-2000000000000
χ3922-222-2-2-20-22-2000200002-22-200-22-2200000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2-22000000000000
χ4022-222-2-2-20-22-2000200002-22-200-22-2200000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2-22000000000000
χ4122-222-2-2-20-22-200020000-22-22002-22-200000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2-22000000000000
χ4222-222-2-2-20-22-200020000-22-22002-22-200000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2-22000000000000
χ4322-222-2-2-20-22-200020000-22-2200-22-2200000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i22-2000000000000
χ4422-222-2-2-20-22-200020000-22-2200-22-2200000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i22-2000000000000
χ4522-2-2-222-22-2-22-2-222002-20000002i−2i−2i2i00002i−2i002i−2i−2i2i00000000-222-200000000000000
χ4622-2-2-222-22-2-22-2-222002-20000002i−2i−2i2i00002i−2i00−2i2i2i−2i000000002-2-2200000000000000
χ4722-2-2-222-22-2-22-2-222002-2000000−2i2i2i−2i0000−2i2i002i−2i−2i2i000000002-2-2200000000000000
χ4822-2-2-222-22-2-22-2-222002-2000000−2i2i2i−2i0000−2i2i00−2i2i2i−2i00000000-222-200000000000000
χ4922-2-2-222-2-2-2-2222-2200-220000002i−2i−2i2i0000−2i2i0000002-2-22−2i2i2i−2i000000000000000000
χ5022-2-2-222-2-2-2-2222-2200-220000002i−2i−2i2i0000−2i2i000000-222-22i−2i−2i2i000000000000000000
χ5122-2-2-222-2-2-2-2222-2200-22000000−2i2i2i−2i00002i−2i0000002-2-222i−2i−2i2i000000000000000000
χ5222-2-2-222-2-2-2-2222-2200-22000000−2i2i2i−2i00002i−2i000000-222-2−2i2i2i−2i000000000000000000
χ53444-4-4-4-440-444000-44-4000000-44000000000000000000000000000000000000000000
χ54444-4-4-4-440-444000-4-440000004-4000000000000000000000000000000000000000000
χ5544-444-4-4-404-44000-400004-4-4400000000000000000000000000000000000000000000
χ5644-444-4-4-404-44000-40000-444-400000000000000000000000000000000000000000000
χ5744-4-4-444-4444-4-4-44-400-44000000000000000000000000000000000000000000000000
χ5844-4-4-444-4-444-444-4-4004-4000000000000000000000000000000000000000000000000
χ594-444-44-4-440004-4-4000000000000000004-40000000000000000000000000000000000
χ604-444-44-4-440004-4-400000000000000000-440000000000000000000000000000000000
χ614-444-44-4-4-4000-4440000000000000004i−4i000000000000000000000000000000000000
χ624-444-44-4-4-4000-444000000000000000−4i4i000000000000000000000000000000000000
χ634-4-4-444-444000-44-4000000000000000000000000000000000000000002i2−2i22i2−2i200000000
χ644-4-4-444-444000-44-400000000000000000000000000000000000000000−2i22i2−2i22i200000000
χ654-4-4-444-44-40004-440000000000000000000000000000000000000000022−22−222200000000
χ664-4-4-444-44-40004-4400000000000000000000000000000000000000000−222222−2200000000
χ678-88-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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