Finite Group Databasebeta

← Group #227246

Character table — Group #227246

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444442222222244444488888888888844444444448888888888888888882244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ511111111111111111111-1-1-1-1111111111111111111-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111
χ811111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-11111-1-11111-1-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111
χ111111111111111111-1-1-1-111111-1-1-1-1111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ171-111-1-1-1111-1-111-1-111-1-111-1-1-1ii−i−i1ii−i−iii−i−iii−i−i1-1i−ii−ii−i1-1i−i11-1-1ii−i−iii−i−i11-1-11-1i−ii−i1-11-1
χ181-111-1-1-1111-1-111-1-111-1-111-1-1-1ii−i−i1−i−iiiii−i−i−i−iii1-1i−i−ii−ii1-1i−i-1-111ii−i−i−i−iii-1-1111-1i−i−ii-11-11
χ191-111-1-1-1111-1-111-1-111-1-111-1-1-1−i−iii1ii−i−i−i−iiiii−i−i1-1−iii−ii−i1-1−ii-1-111−i−iiiii−i−i-1-1111-1−iii−i-11-11
χ201-111-1-1-1111-1-111-1-111-1-111-1-1-1−i−iii1−i−iii−i−iii−i−iii1-1−ii−ii−ii1-1−ii11-1-1−i−iii−i−iii11-1-11-1−ii−ii1-11-1
χ211-111-1-1-1111-1-111-1-111-1-1-1-111-1ii−i−i1ii−i−iii−i−iii−i−i-11i−i−ii−ii1-1i−i11-1-1−i−iiiii−i−i11-1-1-11−ii−ii-11-11
χ221-111-1-1-1111-1-111-1-111-1-1-1-111-1ii−i−i1−i−iiiii−i−i−i−iii-11i−ii−ii−i1-1i−i-1-111−i−iii−i−iii-1-111-11−iii−i1-11-1
χ231-111-1-1-1111-1-111-1-111-1-1-1-111-1−i−iii1ii−i−i−i−iiiii−i−i-11−ii−ii−ii1-1−ii-1-111ii−i−iii−i−i-1-111-11i−i−ii1-11-1
χ241-111-1-1-1111-1-111-1-111-1-1-1-111-1−i−iii1−i−iii−i−iii−i−iii-11−iii−ii−i1-1−ii11-1-1ii−i−i−i−iii11-1-1-11i−ii−i-11-11
χ251-111-1-1-1111-1-111-1-1-1-11111-1-1-1ii−i−i1ii−i−i−i−iiiii−i−i1-1i−ii−ii−i-11−ii11-1-1−i−iii−i−iii-1-111-11i−i−ii1-1-11
χ261-111-1-1-1111-1-111-1-1-1-11111-1-1-1ii−i−i1−i−iii−i−iii−i−iii1-1i−i−ii−ii-11−ii-1-111−i−iiiii−i−i11-1-1-11i−ii−i-111-1
χ271-111-1-1-1111-1-111-1-1-1-11111-1-1-1−i−iii1ii−i−iii−i−iii−i−i1-1−iii−ii−i-11i−i-1-111ii−i−i−i−iii11-1-1-11−ii−ii-111-1
χ281-111-1-1-1111-1-111-1-1-1-11111-1-1-1−i−iii1−i−iiiii−i−i−i−iii1-1−ii−ii−ii-11i−i11-1-1ii−i−iii−i−i-1-111-11−iii−i1-1-11
χ291-111-1-1-1111-1-111-1-1-1-111-1-111-1ii−i−i1ii−i−i−i−iiiii−i−i-11i−i−ii−ii-11−ii11-1-1ii−i−i−i−iii-1-1111-1−iii−i-111-1
χ301-111-1-1-1111-1-111-1-1-1-111-1-111-1ii−i−i1−i−iii−i−iii−i−iii-11i−ii−ii−i-11−ii-1-111ii−i−iii−i−i11-1-11-1−ii−ii1-1-11
χ311-111-1-1-1111-1-111-1-1-1-111-1-111-1−i−iii1ii−i−iii−i−iii−i−i-11−ii−ii−ii-11i−i-1-111−i−iii−i−iii11-1-11-1i−ii−i1-1-11
χ321-111-1-1-1111-1-111-1-1-1-111-1-111-1−i−iii1−i−iiiii−i−i−i−iii-11−iii−ii−i-11i−i11-1-1−i−iiiii−i−i-1-1111-1i−i−ii-111-1
χ33222222222-22-22-22-222220000-22222-200002222000000-2-20000-2-2-2-200000000000000000000000000
χ34222222222-22-22-22-222220000-2-2-2-2-2-20000-2-2-2-2000000220000-2-22200000000000000000000000000
χ35222222222-22-22-22-2-2-2-2-20000-22222-20000-2-2-2-2000000-2-20000222200000000000000000000000000
χ36222222222-22-22-22-2-2-2-2-20000-2-2-2-2-2-20000222200000022000022-2-200000000000000000000000000
χ3722222222-22-22-22-2200002222-20000-222220000-2-2-2-2-2-20022-2-2000000000000000000000000000000
χ3822222222-22-22-22-2200002222-20000-2-2-2-2-200002222-2-200-2-222000000000000000000000000000000
χ3922222222-22-22-22-220000-2-2-2-2-20000-222220000-2-2-2-22200-2-222000000000000000000000000000000
χ4022222222-22-22-22-220000-2-2-2-2-20000-2-2-2-2-200002222220022-2-2000000000000000000000000000000
χ4122-22-22-2-220-20-20202-22-2000002-22-20i2−i2i2−i22-22-2i2−i2i2−i2000000000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000000000
χ4222-22-22-2-220-20-20202-22-2000002-22-20−i2i2−i2i22-22-2−i2i2−i2i2000000000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000000000
χ4322-22-22-2-220-20-20202-22-200000-22-220i2−i2i2−i2-22-22i2−i2i2−i2000000000000−i2i2−i2i20000i2−i2i2−i2−i2i2−i2i20000000000
χ4422-22-22-2-220-20-20202-22-200000-22-220−i2i2−i2i2-22-22−i2i2−i2i2000000000000i2−i2i2−i20000−i2i2−i2i2i2−i2i2−i20000000000
χ4522-22-22-2-220-20-2020-22-22000002-22-20i2−i2i2−i2-22-22i2−i2i2−i2000000000000i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i20000000000
χ4622-22-22-2-220-20-2020-22-22000002-22-20−i2i2−i2i2-22-22−i2i2−i2i2000000000000−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i20000000000
χ4722-22-22-2-220-20-2020-22-2200000-22-220i2−i2i2−i22-22-2i2−i2i2−i2000000000000−i2i2−i2i20000−i2i2−i2i2i2−i2i2−i20000000000
χ4822-22-22-2-220-20-2020-22-2200000-22-220−i2i2−i2i22-22-2−i2i2−i2i2000000000000i2−i2i2−i20000i2−i2i2−i2−i2i2−i2i20000000000
χ492-222-2-2-222-2-222-2-2222-2-2000022i2i−2i−2i-200002i2i−2i−2i000000−2i2i0000-22−2i2i00000000000000000000000000
χ502-222-2-2-222-2-222-2-2222-2-200002−2i−2i2i2i-20000−2i−2i2i2i0000002i−2i0000-222i−2i00000000000000000000000000
χ512-222-2-2-222-2-222-2-22-2-222000022i2i−2i−2i-20000−2i−2i2i2i000000−2i2i00002-22i−2i00000000000000000000000000
χ522-222-2-2-222-2-222-2-22-2-22200002−2i−2i2i2i-200002i2i−2i−2i0000002i−2i00002-2−2i2i00000000000000000000000000
χ532-222-2-2-22-222-2-222-2000022-2-220000-22i2i−2i−2i0000−2i−2i2i2i-22002i−2i−2i2i000000000000000000000000000000
χ542-222-2-2-22-222-2-222-2000022-2-220000-2−2i−2i2i2i00002i2i−2i−2i-2200−2i2i2i−2i000000000000000000000000000000
χ552-222-2-2-22-222-2-222-20000-2-22220000-22i2i−2i−2i0000−2i−2i2i2i2-200−2i2i2i−2i000000000000000000000000000000
χ562-222-2-2-22-222-2-222-20000-2-22220000-2−2i−2i2i2i00002i2i−2i−2i2-2002i−2i−2i2i000000000000000000000000000000
χ572-2-222-22-22020-20-202-2-22000002i−2i−2i2i02−2−222i−2i−2i2i2−2−22000000000000−i2i2i2−i200002−2−22−i2i2i2−i20000000000
χ582-2-222-22-22020-20-202-2-22000002i−2i−2i2i0−222−22i−2i−2i2i−222−2000000000000i2−i2−i2i20000−222−2i2−i2−i2i20000000000
χ592-2-222-22-22020-20-202-2-2200000−2i2i2i−2i02−2−22−2i2i2i−2i2−2−22000000000000i2−i2−i2i200002−2−22i2−i2−i2i20000000000
χ602-2-222-22-22020-20-202-2-2200000−2i2i2i−2i0−222−2−2i2i2i−2i−222−2000000000000−i2i2i2−i20000−222−2−i2i2i2−i20000000000
χ612-2-222-22-22020-20-20-222-2000002i−2i−2i2i02−2−22−2i2i2i−2i2−2−22000000000000−i2i2i2−i20000−222−2i2−i2−i2i20000000000
χ622-2-222-22-22020-20-20-222-2000002i−2i−2i2i0−222−2−2i2i2i−2i−222−2000000000000i2−i2−i2i200002−2−22−i2i2i2−i20000000000
χ632-2-222-22-22020-20-20-222-200000−2i2i2i−2i02−2−222i−2i−2i2i2−2−22000000000000i2−i2−i2i20000−222−2−i2i2i2−i20000000000
χ642-2-222-22-22020-20-20-222-200000−2i2i2i−2i0−222−22i−2i−2i2i−222−2000000000000−i2i2i2−i200002−2−22i2−i2−i2i20000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ6644-44-44-4-4-404040-40000000000000002i2−2i22i2−2i20000−2i22i2−2i22i200000000000000000000000000000000000000
χ6744-44-44-4-4-404040-4000000000000000−2i22i2−2i22i200002i2−2i22i2−2i200000000000000000000000000000000000000
χ6844-4-4-4-44404040-40-40000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ6944-4-4-4-44404040-40-4000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ7044-4-4-4-4440-40-4040400004-44-400000000000000000000000000000000000000000000000000000000
χ7144-4-4-4-4440-40-404040000-44-4400000000000000000000000000000000000000000000000000000000
χ724-444-4-4-44-4-444-4-44400000000-40000400000000000000000000000000000000000000000000000000
χ734-4-444-44-4-40-4040400000000000000022−22−22220000−222222−2200000000000000000000000000000000000000
χ744-4-444-44-4-40-40404000000000000000−222222−22000022−22−222200000000000000000000000000000000000000
χ754-4-4-444-44040-40-40400000000000000000000000000000000000000000022−22−2222000000000000000000
χ764-4-4-444-44040-40-404000000000000000000000000000000000000000000−222222−22000000000000000000
χ774-4-4-444-440-404040-400004-4-4400000000000000000000000000000000000000000000000000000000
χ784-4-4-444-440-404040-40000-444-400000000000000000000000000000000000000000000000000000000
χ79888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000

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