Finite Group Databasebeta

← Group #227210

Character table — Group #227210

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444442222444444444488888888888844444444448888888888888888884444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ5111111111111111111111-1-1-1-11111111111111111111-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1111111-1-1-1-111-1-1
χ91111111111111111-1-1-1-11111111111-1-1-1-1111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ111111111111111111-1-1-1-111111-1-1-1-11111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-111-1-111-1-1
χ131111111111111111-1-1-1-11-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111111111-1-11111-1-1-1-1
χ151111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-111
χ171-1-1-1111-111-1-111-1-111-1-1-111-1-1ii−i−i1ii−i−iii−i−iii−i−ii−ii−i1-11-1i−i11-1-1i−iii−i−iii−i−i11-1-1i−i1-11-1i−i1-1
χ181-1-1-1111-111-1-111-1-111-1-1-111-1-1ii−i−i1ii−i−i−i−iii−i−iiii−i−ii1-11-1−ii-1-111i−iii−i−i−i−iii-1-111i−i-111-1−ii-11
χ191-1-1-1111-111-1-111-1-111-1-1-111-1-1−i−iii1−i−iiiii−i−iii−i−i−iii−i1-11-1i−i-1-111−ii−i−iiiii−i−i-1-111−ii-111-1i−i-11
χ201-1-1-1111-111-1-111-1-111-1-1-111-1-1−i−iii1−i−iii−i−iii−i−iii−ii−ii1-11-1−ii11-1-1−ii−i−iii−i−iii11-1-1−ii1-11-1−ii1-1
χ211-1-1-1111-111-1-111-1-111-1-1-1-1-111ii−i−i1ii−i−iii−i−iii−i−ii−i−ii1-1-11−ii11-1-1i−i−i−iiiii−i−i11-1-1−ii-11-11−ii-11
χ221-1-1-1111-111-1-111-1-111-1-1-1-1-111ii−i−i1ii−i−i−i−iii−i−iiii−ii−i1-1-11i−i-1-111i−i−i−iii−i−iii-1-111−ii1-1-11i−i1-1
χ231-1-1-1111-111-1-111-1-111-1-1-1-1-111−i−iii1−i−iiiii−i−iii−i−i−ii−ii1-1-11−ii-1-111−iiii−i−iii−i−i-1-111i−i1-1-11−ii1-1
χ241-1-1-1111-111-1-111-1-111-1-1-1-1-111−i−iii1−i−iii−i−iii−i−iii−iii−i1-1-11i−i11-1-1−iiii−i−i−i−iii11-1-1i−i-11-11i−i-11
χ251-1-1-1111-111-1-111-1-1-1-111-111-1-1ii−i−i1−i−iiiii−i−iii−i−ii−ii−i-111-1i−i11-1-1−ii−i−iii−i−iii-1-111i−i1-1-11−ii-11
χ261-1-1-1111-111-1-111-1-1-1-111-111-1-1ii−i−i1−i−iii−i−iii−i−iiii−i−ii-111-1−ii-1-111−ii−i−iiiii−i−i11-1-1i−i-11-11i−i1-1
χ271-1-1-1111-111-1-111-1-1-1-111-111-1-1−i−iii1ii−i−iii−i−iii−i−i−iii−i-111-1i−i-1-111i−iii−i−i−i−iii11-1-1−ii-11-11−ii1-1
χ281-1-1-1111-111-1-111-1-1-1-111-111-1-1−i−iii1ii−i−i−i−iii−i−iii−ii−ii-111-1−ii11-1-1i−iii−i−iii−i−i-1-111−ii1-1-11i−i-11
χ291-1-1-1111-111-1-111-1-1-1-111-1-1-111ii−i−i1−i−iiiii−i−iii−i−ii−i−ii-11-11−ii11-1-1−iiii−i−i−i−iii-1-111−ii-111-1i−i1-1
χ301-1-1-1111-111-1-111-1-1-1-111-1-1-111ii−i−i1−i−iii−i−iii−i−iiii−ii−i-11-11i−i-1-111−iiii−i−iii−i−i11-1-1−ii1-11-1−ii-11
χ311-1-1-1111-111-1-111-1-1-1-111-1-1-111−i−iii1ii−i−iii−i−iii−i−i−ii−ii-11-11−ii-1-111i−i−i−iii−i−iii11-1-1i−i1-11-1i−i-11
χ321-1-1-1111-111-1-111-1-1-1-111-1-1-111−i−iii1ii−i−i−i−iii−i−iii−iii−i-11-11i−i11-1-1i−i−i−iiiii−i−i-1-111i−i-111-1−ii1-1
χ33222222222-22-22-22-20000-222220000-200002222-2-2-2-2002200-2-2-2-20000000000000000000000000000
χ34222222222-22-22-22-20000-222220000-20000-2-2-2-2222200-2-200-2-2220000000000000000000000000000
χ35222222222-22-22-22-20000-2-2-2-2-20000-200002222-2-2-2-200-2-20022220000000000000000000000000000
χ36222222222-22-22-22-20000-2-2-2-2-20000-20000-2-2-2-2222200220022-2-20000000000000000000000000000
χ3722222222-22-22-22-222222-200002222-2222200000000-2-200-2-200000000-2-20000000000000000000000
χ3822222222-22-22-22-222222-20000-2-2-2-2-2-2-2-2-2000000002200-2-200000000220000000000000000000000
χ3922222222-22-22-22-22-2-2-2-2-200002222-2-2-2-2-200000000-2-2002200000000220000000000000000000000
χ4022222222-22-22-22-22-2-2-2-2-20000-2-2-2-2-222220000000022002200000000-2-20000000000000000000000
χ4122-222-2-2-20-20-202022-22-2000002i−2i2i−2i02i−2i2i−2i2−22−22−22−20000000000i2−i2i2−i20000002−22−2i2−i2i2−i20000000000
χ4222-222-2-2-20-20-202022-22-2000002i−2i2i−2i02i−2i2i−2i−22−22−22−220000000000−i2i2−i2i2000000−22−22−i2i2−i2i20000000000
χ4322-222-2-2-20-20-202022-22-200000−2i2i−2i2i0−2i2i−2i2i2−22−22−22−20000000000−i2i2−i2i20000002−22−2−i2i2−i2i20000000000
χ4422-222-2-2-20-20-202022-22-200000−2i2i−2i2i0−2i2i−2i2i−22−22−22−220000000000i2−i2i2−i2000000−22−22i2−i2i2−i20000000000
χ4522-222-2-2-20-20-20202-22-22000002i−2i2i−2i0−2i2i−2i2i2−22−22−22−20000000000i2−i2i2−i2000000−22−22−i2i2−i2i20000000000
χ4622-222-2-2-20-20-20202-22-22000002i−2i2i−2i0−2i2i−2i2i−22−22−22−220000000000−i2i2−i2i20000002−22−2i2−i2i2−i20000000000
χ4722-222-2-2-20-20-20202-22-2200000−2i2i−2i2i02i−2i2i−2i2−22−22−22−20000000000−i2i2−i2i2000000−22−22i2−i2i2−i20000000000
χ4822-222-2-2-20-20-20202-22-2200000−2i2i−2i2i02i−2i2i−2i−22−22−22−220000000000i2−i2i2−i20000002−22−2−i2i2−i2i20000000000
χ492-22-22-2-220-202020-22-2-22000002-2-2202-2-22i2−i2−i2i2i2−i2−i2i20000000000−i2i2i2−i2000000i2−i2−i2i2−i2i2i2−i20000000000
χ502-22-22-2-220-202020-22-2-22000002-2-2202-2-22−i2i2i2−i2−i2i2i2−i20000000000i2−i2−i2i2000000−i2i2i2−i2i2−i2−i2i20000000000
χ512-22-22-2-220-202020-22-2-2200000-222-20-222-2i2−i2−i2i2i2−i2−i2i20000000000i2−i2−i2i2000000i2−i2−i2i2i2−i2−i2i20000000000
χ522-22-22-2-220-202020-22-2-2200000-222-20-222-2−i2i2i2−i2−i2i2i2−i20000000000−i2i2i2−i2000000−i2i2i2−i2−i2i2i2−i20000000000
χ532-22-22-2-220-202020-2-222-2000002-2-220-222-2i2−i2−i2i2i2−i2−i2i20000000000−i2i2i2−i2000000−i2i2i2−i2i2−i2−i2i20000000000
χ542-22-22-2-220-202020-2-222-2000002-2-220-222-2−i2i2i2−i2−i2i2i2−i20000000000i2−i2−i2i2000000i2−i2−i2i2−i2i2i2−i20000000000
χ552-22-22-2-220-202020-2-222-200000-222-202-2-22i2−i2−i2i2i2−i2−i2i20000000000i2−i2−i2i2000000−i2i2i2−i2−i2i2i2−i20000000000
χ562-22-22-2-220-202020-2-222-200000-222-202-2-22−i2i2i2−i2−i2i2i2−i20000000000−i2i2i2−i2000000i2−i2−i2i2i2−i2−i2i20000000000
χ572-2-2-2222-22-2-222-2-220000222-2-20000-200002i2i−2i−2i−2i−2i2i2i002i−2i00-22−2i2i0000000000000000000000000000
χ582-2-2-2222-22-2-222-2-220000222-2-20000-20000−2i−2i2i2i2i2i−2i−2i00−2i2i00-222i−2i0000000000000000000000000000
χ592-2-2-2222-22-2-222-2-2200002-2-2220000-200002i2i−2i−2i−2i−2i2i2i00−2i2i002-22i−2i0000000000000000000000000000
χ602-2-2-2222-22-2-222-2-2200002-2-2220000-20000−2i−2i2i2i2i2i−2i−2i002i−2i002-2−2i2i0000000000000000000000000000
χ612-2-2-2222-2-222-2-222-222-2-2200002i2i−2i−2i-22i2i−2i−2i00000000−2i2i00-2200000000−2i2i0000000000000000000000
χ622-2-2-2222-2-222-2-222-222-2-220000−2i−2i2i2i-2−2i−2i2i2i000000002i−2i00-22000000002i−2i0000000000000000000000
χ632-2-2-2222-2-222-2-222-2-2-222200002i2i−2i−2i-2−2i−2i2i2i00000000−2i2i002-2000000002i−2i0000000000000000000000
χ642-2-2-2222-2-222-2-222-2-2-22220000−2i−2i2i2i-22i2i−2i−2i000000002i−2i002-200000000−2i2i0000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000400000000400000000000000000000000000000000000000000000000000
χ6644-444-4-4-404040-40-400000000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ6744-444-4-4-404040-40-4000000000000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ6844-4-4-44-4440-40-40400000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ6944-4-4-44-4440-40-4040000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ7044-4-4-44-44-404040-40000004i−4i4i−4i0000000000000000000000000000000000000000000000000000000
χ7144-4-4-44-44-404040-4000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000000
χ724-444-44-4-44040-40-4000000000000000000000000000000000000000000022−22−2222000000000000000000
χ734-444-44-4-44040-40-40000000000000000000000000000000000000000000−222222−22000000000000000000
χ744-444-44-4-4-40-404040000004i−4i−4i4i0000000000000000000000000000000000000000000000000000000
χ754-444-44-4-4-40-40404000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000
χ764-44-44-4-44040-40-4040000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ774-44-44-4-44040-40-404000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ784-4-4-4444-4-4-444-4-4440000-400000000400000000000000000000000000000000000000000000000000
χ79888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000

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