Finite Group Databasebeta

← Group #312357

Character table — Group #312357

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-1
χ311111111111111111111111111-1-11111111111-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ51111111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-11-111-1-11111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1111
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111111111-1-1-1
χ91111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11
χ101111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1111111-1
χ111111111111111111-1-1-1-1111111-1-11111-1-1111111-1-1-1-1111111-11-1-1-1-1-1-111-1-111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111111-1-1-11111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1111-1-111-1-11111-1
χ17222222222-22-22-22-20000-2-2222200222200-2-2-2-20000000000000-20000000000000
χ18222222222-22-22-22-20000-2-2222200-2-2-2-20022-2-2000000000000020000000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-20022-2-200-2-222000000000000020000000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-200-2-2220022220000000000000-20000000000000
χ2122222222-22-22-22-222222-2-20000220000-2-20000220000-2-20000-200000000000000
χ2222222222-22-22-22-222222-2-20000-2-20000-2-20000-2-20000220000200000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000220000220000-2-20000220000-200000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000-2-20000220000220000-2-20000200000000000000
χ25222-2-2-2-222-2-222-2-222i2i−2i−2i-2200000000002i−2i00000000000000000000002-22i−2i00000
χ26222-2-2-2-222-2-222-2-222i2i−2i−2i-2200000000002i−2i0000000000000000000000-22−2i2i00000
χ27222-2-2-2-222-2-222-2-22−2i−2i2i2i-220000000000−2i2i00000000000000000000002-2−2i2i00000
χ28222-2-2-2-222-2-222-2-22−2i−2i2i2i-220000000000−2i2i0000000000000000000000-222i−2i00000
χ29222-2-2-2-22-222-2-222-20000-220000002i−2i00002i−2i00002i2i−2i−2i00000000002-2000000000
χ30222-2-2-2-22-222-2-222-20000-220000002i−2i00002i−2i0000−2i−2i2i2i0000000000-22000000000
χ31222-2-2-2-22-222-2-222-20000-22000000−2i2i0000−2i2i00002i2i−2i−2i0000000000-22000000000
χ32222-2-2-2-22-222-2-222-20000-22000000−2i2i0000−2i2i0000−2i−2i2i2i00000000002-2000000000
χ33222-2-2-2-22-2-222-2-2222i2i−2i−2i2-20000002i−2i00−2i2i−2i2i00000000000000002-200000000000
χ34222-2-2-2-22-2-222-2-2222i2i−2i−2i2-2000000−2i2i00−2i2i2i−2i0000000000000000-2200000000000
χ35222-2-2-2-22-2-222-2-222−2i−2i2i2i2-20000002i−2i002i−2i−2i2i0000000000000000-2200000000000
χ36222-2-2-2-22-2-222-2-222−2i−2i2i2i2-2000000−2i2i002i−2i2i−2i00000000000000002-200000000000
χ3722-222-2-2-202020-20-22-22-20022−2−22-2000000002−22-22−22−20022−2−200000000002−2000
χ3822-222-2-2-202020-20-22-22-20022−2−2-22000000002−2-222−22−200−2−2220000000000−22000
χ3922-222-2-2-202020-20-22-22-200−2−2222-200000000−222-2−22−2200−2−2220000000000−22000
χ4022-222-2-2-202020-20-22-22-200−2−222-2200000000−22-22−22−220022−2−200000000002−2000
χ4122-222-2-2-202020-20-2-22-220022−2−22-2000000002−2-22−22−2200−2−22200000000002−2000
χ4222-222-2-2-202020-20-2-22-220022−2−2-22000000002−22-2−22−220022−2−20000000000−22000
χ4322-222-2-2-202020-20-2-22-2200−2−2222-200000000−22-222−22−20022−2−20000000000−22000
χ4422-222-2-2-202020-20-2-22-2200−2−222-2200000000−222-22−22−200−2−22200000000002−2000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-4-4444-4-444-4-400004-40000000000000000000000000000000000000000000
χ4744-444-4-4-40-40-404040000002222−22−220000000000−2222000000000000000000000000000
χ4844-444-4-4-40-40-40404000000−22−222222000000000022−22000000000000000000000000000
χ4944-4-4-444-4040-40-4040000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5044-4-4-444-4040-40-404000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5144-4-4-444-40-404040-44i−4i−4i4i000000000000000000000000000000000000000000000
χ5244-4-4-444-40-404040-4−4i4i4i−4i000000000000000000000000000000000000000000000
χ534-444-44-4-440-40-40400000004-44-4000000000000000000000000000000000000000
χ544-444-44-4-440-40-4040000000-44-44000000000000000000000000000000000000000
χ554-444-44-4-4-404040-4000000000000000000000000000000022−2222−22000000000000000
χ564-444-44-4-4-404040-40000000000000000000000000000000−2222−2222000000000000000
χ574-44-44-44-44040-40-40000000000000000000000000000000000000000000000022−220
χ584-44-44-44-44040-40-400000000000000000000000000000000000000000000000−22220
χ594-44-44-44-4-40-404040000000000000004i−4i000000000000000000000000000000000
χ604-44-44-44-4-40-40404000000000000000−4i4i000000000000000000000000000000000
χ614-4-44-4-4440000000000000022−22−222200000000000000000022−222-2-22000000000000000
χ624-4-44-4-4440000000000000022−22−2222000000000000000000−2222-222-2000000000000000
χ634-4-44-4-44400000000000000−222222−2200000000000000000022−22-222-2000000000000000
χ644-4-44-4-44400000000000000−222222−22000000000000000000−22222-2-22000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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