Finite Group Databasebeta

← Group #227506

Character table — Group #227506

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444442222444444444488888888888822444444448888888888888888882244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ31111111111111111111111111-1-1-1-11111111111111-1-111-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111-1-1-1-11111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111
χ711111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ811111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111
χ111111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
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
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ171-111-1-11-111-1-111-1-111-1-1ii−i−i-1ii−i−i1ii−i−iii−i−iii−i−i1-11-11-1i−ii−ii−i11-1-111-1-1ii−i−i11-1-11-1i−i1-1i−ii−i
χ181-111-1-11-111-1-111-1-111-1-1ii−i−i-1ii−i−i1−i−iiiii−i−i−i−iii-111-1-11i−ii−ii−i11-1-1-1-111−i−iii-1-111-11−ii1-1i−i−ii
χ191-111-1-11-111-1-111-1-111-1-1ii−i−i-1−i−iii1ii−i−iii−i−iii−i−i-111-1-11i−i−iii−i-1-11111-1-1ii−i−i11-1-1-11−ii-11−ii−ii
χ201-111-1-11-111-1-111-1-111-1-1ii−i−i-1−i−iii1−i−iiiii−i−i−i−iii1-11-11-1i−i−iii−i-1-111-1-111−i−iii-1-1111-1i−i-11−iii−i
χ211-111-1-11-111-1-111-1-111-1-1−i−iii-1ii−i−i1ii−i−i−i−iiiii−i−i1-11-11-1−iii−i−ii-1-111-1-111ii−i−i-1-1111-1−ii-11i−i−ii
χ221-111-1-11-111-1-111-1-111-1-1−i−iii-1ii−i−i1−i−iii−i−iii−i−iii-111-1-11−iii−i−ii-1-11111-1-1−i−iii11-1-1-11i−i-11i−ii−i
χ231-111-1-11-111-1-111-1-111-1-1−i−iii-1−i−iii1ii−i−i−i−iiiii−i−i-111-1-11−ii−ii−ii11-1-1-1-111ii−i−i-1-111-11i−i1-1−iii−i
χ241-111-1-11-111-1-111-1-111-1-1−i−iii-1−i−iii1−i−iii−i−iii−i−iii1-11-11-1−ii−ii−ii11-1-111-1-1−i−iii11-1-11-1−ii1-1−ii−ii
χ251-111-1-11-111-1-111-1-1-1-111ii−i−i-1ii−i−i1ii−i−i−i−iiiii−i−i1-1-111-1i−ii−i−ii-1-11111-1-1−i−iii-1-111-11i−i1-1−ii−ii
χ261-111-1-11-111-1-111-1-1-1-111ii−i−i-1ii−i−i1−i−iii−i−iii−i−iii-11-11-11i−ii−i−ii-1-111-1-111ii−i−i11-1-11-1−ii1-1−iii−i
χ271-111-1-11-111-1-111-1-1-1-111ii−i−i-1−i−iii1ii−i−i−i−iiiii−i−i-11-11-11i−i−ii−ii11-1-111-1-1−i−iii-1-1111-1−ii-11i−ii−i
χ281-111-1-11-111-1-111-1-1-1-111ii−i−i-1−i−iii1−i−iii−i−iii−i−iii1-1-111-1i−i−ii−ii11-1-1-1-111ii−i−i11-1-1-11i−i-11i−i−ii
χ291-111-1-11-111-1-111-1-1-1-111−i−iii-1ii−i−i1ii−i−iii−i−iii−i−i1-1-111-1−iii−ii−i11-1-1-1-111−i−iii11-1-1-11−ii-11−iii−i
χ301-111-1-11-111-1-111-1-1-1-111−i−iii-1ii−i−i1−i−iiiii−i−i−i−iii-11-11-11−iii−ii−i11-1-111-1-1ii−i−i-1-1111-1i−i-11−ii−ii
χ311-111-1-11-111-1-111-1-1-1-111−i−iii-1−i−iii1ii−i−iii−i−iii−i−i-11-11-11−ii−iii−i-1-111-1-111−i−iii11-1-11-1i−i1-1i−i−ii
χ321-111-1-11-111-1-111-1-1-1-111−i−iii-1−i−iii1−i−iiiii−i−i−i−iii1-1-111-1−ii−iii−i-1-11111-1-1ii−i−i-1-111-11−ii1-1i−ii−i
χ33222222222-22-22-22-200000000-22222-222220000-2-2-2-2-2-2002200-2-20000000000000000000000000000
χ34222222222-22-22-22-200000000-22222-2-2-2-2-2000022222200-2-200-2-20000000000000000000000000000
χ35222222222-22-22-22-200000000-2-2-2-2-2-222220000-2-2-2-22200-2-200220000000000000000000000000000
χ36222222222-22-22-22-200000000-2-2-2-2-2-2-2-2-2-200002222-2-2002200220000000000000000000000000000
χ3722222222-22-22-22-2222222222-20000-200002222000000-2-200-2-200-2-200000000000000000000000000
χ3822222222-22-22-22-222222-2-2-2-2-20000-20000-2-2-2-2000000-2-20022002200000000000000000000000000
χ3922222222-22-22-22-22-2-2-2-22222-20000-20000-2-2-2-20000002200-2-2002200000000000000000000000000
χ4022222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-20000222200000022002200-2-200000000000000000000000000
χ41222-22-2-2-2020-20-2022-22-22-22-2000000i2−i2i2−i22-22-2i2−i2i2−i20000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ42222-22-2-2-2020-20-2022-22-22-22-2000000−i2i2−i2i22-22-2−i2i2−i2i20000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ43222-22-2-2-2020-20-2022-22-2-22-22000000i2−i2i2−i2-22-22i2−i2i2−i20000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ44222-22-2-2-2020-20-2022-22-2-22-22000000−i2i2−i2i2-22-22−i2i2−i2i20000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ45222-22-2-2-2020-20-202-22-222-22-2000000i2−i2i2−i2-22-22i2−i2i2−i20000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000
χ46222-22-2-2-2020-20-202-22-222-22-2000000−i2i2−i2i2-22-22−i2i2−i2i20000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000
χ47222-22-2-2-2020-20-202-22-22-22-22000000i2−i2i2−i22-22-2i2−i2i2−i20000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ48222-22-2-2-2020-20-202-22-22-22-22000000−i2i2−i2i22-22-2−i2i2−i2i20000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ492-222-2-22-22-2-222-2-220000000022i2i−2i−2i-22i2i−2i−2i0000−2i−2i2i2i-22002-200−2i2i0000000000000000000000000000
χ502-222-2-22-22-2-222-2-220000000022i2i−2i−2i-2−2i−2i2i2i00002i2i−2i−2i2-200-2200−2i2i0000000000000000000000000000
χ512-222-2-22-22-2-222-2-22000000002−2i−2i2i2i-22i2i−2i−2i0000−2i−2i2i2i2-200-22002i−2i0000000000000000000000000000
χ522-222-2-22-22-2-222-2-22000000002−2i−2i2i2i-2−2i−2i2i2i00002i2i−2i−2i-22002-2002i−2i0000000000000000000000000000
χ532-222-2-22-2-222-2-222-222-2-22i2i−2i−2i20000-200002i2i−2i−2i000000-2200−2i2i00−2i2i00000000000000000000000000
χ542-222-2-22-2-222-2-222-222-2-2−2i−2i2i2i20000-20000−2i−2i2i2i000000-22002i−2i002i−2i00000000000000000000000000
χ552-222-2-22-2-222-2-222-2-2-2222i2i−2i−2i20000-20000−2i−2i2i2i0000002-200−2i2i002i−2i00000000000000000000000000
χ562-222-2-22-2-222-2-222-2-2-222−2i−2i2i2i20000-200002i2i−2i−2i0000002-2002i−2i00−2i2i00000000000000000000000000
χ572-22-2-22-2202020-20-22-2-222i−2i−2i2i0000002−2−222i−2i−2i2i2−2−220000000000000000−i2i2i2−i22−2−22−i2i2i2−i20000000000
χ582-22-2-22-2202020-20-22-2-222i−2i−2i2i000000−222−22i−2i−2i2i−222−20000000000000000i2−i2−i2i2−222−2i2−i2−i2i20000000000
χ592-22-2-22-2202020-20-22-2-22−2i2i2i−2i0000002−2−22−2i2i2i−2i2−2−220000000000000000i2−i2−i2i22−2−22i2−i2−i2i20000000000
χ602-22-2-22-2202020-20-22-2-22−2i2i2i−2i000000−222−2−2i2i2i−2i−222−20000000000000000−i2i2i2−i2−222−2−i2i2i2−i20000000000
χ612-22-2-22-2202020-20-2-222-22i−2i−2i2i0000002−2−22−2i2i2i−2i2−2−220000000000000000−i2i2i2−i2−222−2i2−i2−i2i20000000000
χ622-22-2-22-2202020-20-2-222-22i−2i−2i2i000000−222−2−2i2i2i−2i−222−20000000000000000i2−i2−i2i22−2−22−i2i2i2−i20000000000
χ632-22-2-22-2202020-20-2-222-2−2i2i2i−2i0000002−2−222i−2i−2i2i2−2−220000000000000000i2−i2−i2i2−222−2−i2i2i2−i20000000000
χ642-22-2-22-2202020-20-2-222-2−2i2i2i−2i000000−222−22i−2i−2i2i−222−20000000000000000−i2i2i2−i22−2−22i2−i2−i2i20000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ66444-44-4-4-40-404040-4000000000000002i2−2i22i2−2i20000−2i22i2−2i22i200000000000000000000000000000000000000
χ67444-44-4-4-40-404040-400000000000000−2i22i2−2i22i200002i2−2i22i2−2i200000000000000000000000000000000000000
χ6844-44-44-4-440-40-4040000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ6944-44-44-4-440-40-404000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ7044-44-44-4-4-404040-400000000004i−4i4i−4i000000000000000000000000000000000000000000000000000
χ7144-44-44-4-4-404040-40000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000
χ724-444-4-44-4-4-444-4-44400000000-40000400000000000000000000000000000000000000000000000000
χ734-44-4-44-440-40-404040000000000000022−22−22220000−222222−2200000000000000000000000000000000000000
χ744-44-4-44-440-40-4040400000000000000−222222−22000022−22−222200000000000000000000000000000000000000
χ754-4-444-4-444040-40-40000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ764-4-444-4-444040-40-4000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ774-4-444-4-44-40-4040400000000004-4-44000000000000000000000000000000000000000000000000000
χ784-4-444-4-44-40-404040000000000-444-4000000000000000000000000000000000000000000000000000
χ7988-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000

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