Finite Group Databasebeta

← Group #227208

Character table — Group #227208

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888822444444448888888888888888882244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-11111-1-111-1-111-1-1
χ91111111111111111-1-1-1-11111111111-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111
χ111111111111111111-1-1-1-11111-1-1-1-111111111111111-1-11111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111111111-1-111-1-1-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-11111
χ171-11-11-11-111-1-111-1-111-1-111-1-1ii−i−i-11ii−i−iii−i−iii−i−i1-1i−i1-1i−ii−i11-1-1i−iii−i−iii−i−i11-1-11-1i−i1-1i−i1-1
χ181-11-11-11-111-1-111-1-111-1-111-1-1ii−i−i-11ii−i−i−i−iii−i−iii1-1−ii1-1i−i−ii-1-111i−iii−i−i−i−iii-1-1111-1−ii-11i−i-11
χ191-11-11-11-111-1-111-1-111-1-111-1-1−i−iii-11−i−iiiii−i−iii−i−i1-1i−i1-1−iii−i-1-111−ii−i−iiiii−i−i-1-1111-1i−i-11−ii-11
χ201-11-11-11-111-1-111-1-111-1-111-1-1−i−iii-11−i−iii−i−iii−i−iii1-1−ii1-1−ii−ii11-1-1−ii−i−iii−i−iii11-1-11-1−ii1-1−ii1-1
χ211-11-11-11-111-1-111-1-111-1-1-1-111ii−i−i-11ii−i−iii−i−iii−i−i1-1−ii-11i−i−ii11-1-1i−i−i−iiiii−i−i11-1-1-11−ii-11−ii-11
χ221-11-11-11-111-1-111-1-111-1-1-1-111ii−i−i-11ii−i−i−i−iii−i−iii1-1i−i-11i−ii−i-1-111i−i−i−iii−i−iii-1-111-11i−i1-1−ii1-1
χ231-11-11-11-111-1-111-1-111-1-1-1-111−i−iii-11−i−iiiii−i−iii−i−i1-1−ii-11−ii−ii-1-111−iiii−i−iii−i−i-1-111-11−ii1-1i−i1-1
χ241-11-11-11-111-1-111-1-111-1-1-1-111−i−iii-11−i−iii−i−iii−i−iii1-1i−i-11−iii−i11-1-1−iiii−i−i−i−iii11-1-1-11i−i-11i−i-11
χ251-11-11-11-111-1-111-1-1-1-11111-1-1ii−i−i-11−i−iiiii−i−iii−i−i-11i−i1-1i−ii−i11-1-1−ii−i−iii−i−iii-1-111-11−ii1-1i−i-11
χ261-11-11-11-111-1-111-1-1-1-11111-1-1ii−i−i-11−i−iii−i−iii−i−iii-11−ii1-1i−i−ii-1-111−ii−i−iiiii−i−i11-1-1-11i−i-11i−i1-1
χ271-11-11-11-111-1-111-1-1-1-11111-1-1−i−iii-11ii−i−iii−i−iii−i−i-11i−i1-1−iii−i-1-111i−iii−i−i−i−iii11-1-1-11−ii-11−ii1-1
χ281-11-11-11-111-1-111-1-1-1-11111-1-1−i−iii-11ii−i−i−i−iii−i−iii-11−ii1-1−ii−ii11-1-1i−iii−i−iii−i−i-1-111-11i−i1-1−ii-11
χ291-11-11-11-111-1-111-1-1-1-111-1-111ii−i−i-11−i−iiiii−i−iii−i−i-11−ii-11i−i−ii11-1-1−iiii−i−i−i−iii-1-1111-1i−i-11−ii1-1
χ301-11-11-11-111-1-111-1-1-1-111-1-111ii−i−i-11−i−iii−i−iii−i−iii-11i−i-11i−ii−i-1-111−iiii−i−iii−i−i11-1-11-1−ii1-1−ii-11
χ311-11-11-11-111-1-111-1-1-1-111-1-111−i−iii-11ii−i−iii−i−iii−i−i-11−ii-11−ii−ii-1-111i−i−i−iii−i−iii11-1-11-1i−i1-1i−i-11
χ321-11-11-11-111-1-111-1-1-1-111-1-111−i−iii-11ii−i−i−i−iii−i−iii-11i−i-11−iii−i11-1-1i−i−i−iiiii−i−i-1-1111-1−ii-11i−i1-1
χ33222222222-22-22-22-2222200002222-2-2222200000000-2-20000-2-2000000-2-20000000000000000000000
χ34222222222-22-22-22-222220000-2-2-2-2-2-2-2-2-2-200000000-2-2000022000000220000000000000000000000
χ35222222222-22-22-22-2-2-2-2-200002222-2-2-2-2-2-200000000220000-2-2000000220000000000000000000000
χ36222222222-22-22-22-2-2-2-2-20000-2-2-2-2-2-222220000000022000022000000-2-20000000000000000000000
χ3722222222-22-22-22-22000022220000-2-200002222-2-2-2-20022-2-200-2-20000000000000000000000000000
χ3822222222-22-22-22-22000022220000-2-20000-2-2-2-2222200-2-2-2-200220000000000000000000000000000
χ3922222222-22-22-22-220000-2-2-2-20000-2-200002222-2-2-2-200-2-22200220000000000000000000000000000
χ4022222222-22-22-22-220000-2-2-2-20000-2-20000-2-2-2-2222200222200-2-20000000000000000000000000000
χ41222-2-22-2-2-20-2020202i−2i2i−2i00002-22-2002i−2i2i−2i2−22−22−22−200000000002−22−2000000i2−i2i2−i2i2−i2i2−i20000000000
χ42222-2-22-2-2-20-2020202i−2i2i−2i00002-22-2002i−2i2i−2i−22−22−22−220000000000−22−22000000−i2i2−i2i2−i2i2−i2i20000000000
χ43222-2-22-2-2-20-2020202i−2i2i−2i0000-22-2200−2i2i−2i2i2−22−22−22−20000000000−22−22000000i2−i2i2−i2−i2i2−i2i20000000000
χ44222-2-22-2-2-20-2020202i−2i2i−2i0000-22-2200−2i2i−2i2i−22−22−22−2200000000002−22−2000000−i2i2−i2i2i2−i2i2−i20000000000
χ45222-2-22-2-2-20-202020−2i2i−2i2i00002-22-200−2i2i−2i2i2−22−22−22−200000000002−22−2000000−i2i2−i2i2−i2i2−i2i20000000000
χ46222-2-22-2-2-20-202020−2i2i−2i2i00002-22-200−2i2i−2i2i−22−22−22−220000000000−22−22000000i2−i2i2−i2i2−i2i2−i20000000000
χ47222-2-22-2-2-20-202020−2i2i−2i2i0000-22-22002i−2i2i−2i2−22−22−22−20000000000−22−22000000−i2i2−i2i2i2−i2i2−i20000000000
χ48222-2-22-2-2-20-202020−2i2i−2i2i0000-22-22002i−2i2i−2i−22−22−22−2200000000002−22−2000000i2−i2i2−i2−i2i2−i2i20000000000
χ492-222-2-2-22-202020-202i−2i−2i2i00002i−2i−2i2i00-222-2i2−i2−i2i2i2−i2−i2i200000000002−2−22000000−222−2i2−i2−i2i20000000000
χ502-222-2-2-22-202020-202i−2i−2i2i00002i−2i−2i2i00-222-2−i2i2i2−i2−i2i2i2−i20000000000−222−20000002−2−22−i2i2i2−i20000000000
χ512-222-2-2-22-202020-202i−2i−2i2i0000−2i2i2i−2i002-2-22i2−i2−i2i2i2−i2−i2i20000000000−222−2000000−222−2−i2i2i2−i20000000000
χ522-222-2-2-22-202020-202i−2i−2i2i0000−2i2i2i−2i002-2-22−i2i2i2−i2−i2i2i2−i200000000002−2−220000002−2−22i2−i2−i2i20000000000
χ532-222-2-2-22-202020-20−2i2i2i−2i00002i−2i−2i2i002-2-22i2−i2−i2i2i2−i2−i2i200000000002−2−220000002−2−22−i2i2i2−i20000000000
χ542-222-2-2-22-202020-20−2i2i2i−2i00002i−2i−2i2i002-2-22−i2i2i2−i2−i2i2i2−i20000000000−222−2000000−222−2i2−i2−i2i20000000000
χ552-222-2-2-22-202020-20−2i2i2i−2i0000−2i2i2i−2i00-222-2i2−i2−i2i2i2−i2−i2i20000000000−222−20000002−2−22i2−i2−i2i20000000000
χ562-222-2-2-22-202020-20−2i2i2i−2i0000−2i2i2i−2i00-222-2−i2i2i2−i2−i2i2i2−i200000000002−2−22000000−222−2−i2i2i2−i20000000000
χ572-22-22-22-22-2-222-2-2222-2-200002i2i−2i−2i2-22i2i−2i−2i00000000-220000−2i2i000000−2i2i0000000000000000000000
χ582-22-22-22-22-2-222-2-2222-2-20000−2i−2i2i2i2-2−2i−2i2i2i00000000-2200002i−2i0000002i−2i0000000000000000000000
χ592-22-22-22-22-2-222-2-22-2-22200002i2i−2i−2i2-2−2i−2i2i2i000000002-20000−2i2i0000002i−2i0000000000000000000000
χ602-22-22-22-22-2-222-2-22-2-2220000−2i−2i2i2i2-22i2i−2i−2i000000002-200002i−2i000000−2i2i0000000000000000000000
χ612-22-22-22-2-222-2-222-2000022-2-200002-200002i2i−2i−2i−2i−2i2i2i002i−2i-2200−2i2i0000000000000000000000000000
χ622-22-22-22-2-222-2-222-2000022-2-200002-20000−2i−2i2i2i2i2i−2i−2i00−2i2i-22002i−2i0000000000000000000000000000
χ632-22-22-22-2-222-2-222-20000-2-22200002-200002i2i−2i−2i−2i−2i2i2i00−2i2i2-2002i−2i0000000000000000000000000000
χ642-22-22-22-2-222-2-222-20000-2-22200002-20000−2i−2i2i2i2i2i−2i−2i002i−2i2-200−2i2i0000000000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ66444-4-44-4-44040-40-4000000000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ67444-4-44-4-44040-40-40000000000000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ6844-444-4-4-404040-40-400004-44-400000000000000000000000000000000000000000000000000000000
χ6944-444-4-4-404040-40-40000-44-4400000000000000000000000000000000000000000000000000000000
χ7044-444-4-4-40-40-404040000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ7144-444-4-4-40-40-40404000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ724-444-4-4-4440-40-40400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ734-444-4-4-4440-40-4040000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ744-44-44-44-4-4-444-4-444000000000000-4400000000000000000000000000000000000000000000000000
χ754-4-4-444-44040-40-40400004-4-4400000000000000000000000000000000000000000000000000000000
χ764-4-4-444-44040-40-4040000-444-400000000000000000000000000000000000000000000000000000000
χ774-4-4-444-440-404040-400000000000000000000000000000000000000000022−22−2222000000000000000000
χ784-4-4-444-440-404040-4000000000000000000000000000000000000000000−222222−22000000000000000000
χ7988-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000000000

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