Finite Group Databasebeta

← Group #227264

Character table — Group #227264

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888822224444444488888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-11111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-1
χ171-1-111-11-111-1-111-1-1iiii−i−i−i−i11-1-1-1ii−i−i1ii−i−iii−i−iii−i−i1111-1-1-1-11-11-1i−i1-1i−ii−i11-1-1ii−i−i1-11-1i−ii−i1-1i−i
χ181-1-111-11-111-1-111-1-1iiii−i−i−i−i11-1-1-1ii−i−i1ii−i−iii−i−iii−i−i1111-1-1-1-11-1-11−ii-11i−i−ii11-1-1ii−i−i-11-11−ii−ii-11−ii
χ191-1-111-11-111-1-111-1-1iiii−i−i−i−i11-1-1-1−i−iii1ii−i−i−i−iii−i−iii-1-1-1-111111-11-1i−i1-1−iii−i-1-111ii−i−i1-1-11i−i−ii-11−ii
χ201-1-111-11-111-1-111-1-1iiii−i−i−i−i11-1-1-1−i−iii1ii−i−i−i−iii−i−iii-1-1-1-111111-1-11−ii-11−ii−ii-1-111ii−i−i-111-1−iii−i1-1i−i
χ211-1-111-11-111-1-111-1-1iiii−i−i−i−i-1-111-1ii−i−i1ii−i−i−i−iii−i−iii-1-1-1-11111-111-1i−i1-1i−ii−i11-1-1−i−iii-111-1−iii−i-11−ii
χ221-1-111-11-111-1-111-1-1iiii−i−i−i−i-1-111-1ii−i−i1ii−i−i−i−iii−i−iii-1-1-1-11111-11-11−ii-11i−i−ii11-1-1−i−iii1-1-11i−i−ii1-1i−i
χ231-1-111-11-111-1-111-1-1iiii−i−i−i−i-1-111-1−i−iii1ii−i−iii−i−iii−i−i1111-1-1-1-1-111-1i−i1-1−iii−i-1-111−i−iii-11-11−ii−ii1-1i−i
χ241-1-111-11-111-1-111-1-1iiii−i−i−i−i-1-111-1−i−iii1ii−i−iii−i−iii−i−i1111-1-1-1-1-11-11−ii-11−ii−ii-1-111−i−iii1-11-1i−ii−i-11−ii
χ251-1-111-11-111-1-111-1-1−i−i−i−iiiii11-1-1-1ii−i−i1−i−iiiii−i−iii−i−i-1-1-1-111111-11-1−ii1-1i−i−ii-1-111−i−iii1-1-11−iii−i-11i−i
χ261-1-111-11-111-1-111-1-1−i−i−i−iiiii11-1-1-1ii−i−i1−i−iiiii−i−iii−i−i-1-1-1-111111-1-11i−i-11i−ii−i-1-111−i−iii-111-1i−i−ii1-1−ii
χ271-1-111-11-111-1-111-1-1−i−i−i−iiiii11-1-1-1−i−iii1−i−iii−i−iii−i−iii1111-1-1-1-11-11-1−ii1-1−ii−ii11-1-1−i−iii1-11-1−ii−ii1-1−ii
χ281-1-111-11-111-1-111-1-1−i−i−i−iiiii11-1-1-1−i−iii1−i−iii−i−iii−i−iii1111-1-1-1-11-1-11i−i-11−iii−i11-1-1−i−iii-11-11i−ii−i-11i−i
χ291-1-111-11-111-1-111-1-1−i−i−i−iiiii-1-111-1ii−i−i1−i−iii−i−iii−i−iii1111-1-1-1-1-111-1−ii1-1i−i−ii-1-111ii−i−i-11-11i−ii−i1-1−ii
χ301-1-111-11-111-1-111-1-1−i−i−i−iiiii-1-111-1ii−i−i1−i−iii−i−iii−i−iii1111-1-1-1-1-11-11i−i-11i−ii−i-1-111ii−i−i1-11-1−ii−ii-11i−i
χ311-1-111-11-111-1-111-1-1−i−i−i−iiiii-1-111-1−i−iii1−i−iiiii−i−iii−i−i-1-1-1-11111-111-1−ii1-1−ii−ii11-1-1ii−i−i-111-1i−i−ii-11i−i
χ321-1-111-11-111-1-111-1-1−i−i−i−iiiii-1-111-1−i−iii1−i−iiiii−i−iii−i−i-1-1-1-11111-11-11i−i-11−iii−i11-1-1ii−i−i1-1-11−iii−i1-1−ii
χ33222222222-22-22-22-2000000002222-22222-20000-2-2-2-2222200000000-2-2000000-2-20000000000000000000000
χ34222222222-22-22-22-2000000002222-2-2-2-2-2-200002222-2-2-2-200000000-2-2000000220000000000000000000000
χ35222222222-22-22-22-200000000-2-2-2-2-22222-200002222-2-2-2-20000000022000000-2-20000000000000000000000
χ36222222222-22-22-22-200000000-2-2-2-2-2-2-2-2-2-20000-2-2-2-222220000000022000000220000000000000000000000
χ3722222222-22-22-22-22222222220000-20000-2-2-2-2-20000000000000000002222-2-200-2-200000000000000000000
χ3822222222-22-22-22-22222222220000-20000-2-2-2-2-2000000000000000000-2-2-2-222002200000000000000000000
χ3922222222-22-22-22-22-2-2-2-2-2-2-2-20000-20000-2222200000000000000000022-2-2-2-2002200000000000000000000
χ4022222222-22-22-22-22-2-2-2-2-2-2-2-20000-20000-22222000000000000000000-2-2222200-2-200000000000000000000
χ4122-22-2-2-22-202020-20i2i2−i2−i2i2i2−i2−i22i−2i2i−2i02-22-20i2−i2i2−i200002i−2i2i−2i22−2−222−2−2000000000000i2−i2i2−i22−22−2000000000000
χ4222-22-2-2-22-202020-20i2i2−i2−i2i2i2−i2−i22i−2i2i−2i0-22-220i2−i2i2−i20000−2i2i−2i2i−2−222−2−222000000000000−i2i2−i2i22−22−2000000000000
χ4322-22-2-2-22-202020-20i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i02-22-20i2−i2i2−i20000−2i2i−2i2i−2−222−2−222000000000000i2−i2i2−i2−22−22000000000000
χ4422-22-2-2-22-202020-20i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i0-22-220i2−i2i2−i200002i−2i2i−2i22−2−222−2−2000000000000−i2i2−i2i2−22−22000000000000
χ4522-22-2-2-22-202020-20−i2−i2i2i2−i2−i2i2i22i−2i2i−2i02-22-20−i2i2−i2i200002i−2i2i−2i−2−222−2−222000000000000−i2i2−i2i2−22−22000000000000
χ4622-22-2-2-22-202020-20−i2−i2i2i2−i2−i2i2i22i−2i2i−2i0-22-220−i2i2−i2i20000−2i2i−2i2i22−2−222−2−2000000000000i2−i2i2−i2−22−22000000000000
χ4722-22-2-2-22-202020-20−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i02-22-20−i2i2−i2i20000−2i2i−2i2i22−2−222−2−2000000000000−i2i2−i2i22−22−2000000000000
χ4822-22-2-2-22-202020-20−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i0-22-220−i2i2−i2i200002i−2i2i−2i−2−222−2−222000000000000i2−i2i2−i22−22−2000000000000
χ492-222-22-2-2-20-20202022−2−2−2−2222i−2i−2i2i02i−2i−2i2i02−2−220000-222-2−2−22222−2−2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ502-222-22-2-2-20-20202022−2−2−2−2222i−2i−2i2i0−2i2i2i−2i02−2−2200002-2-2222−2−2−2−222000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ512-222-22-2-2-20-20202022−2−2−2−222−2i2i2i−2i02i−2i−2i2i02−2−2200002-2-2222−2−2−2−222000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ522-222-22-2-2-20-20202022−2−2−2−222−2i2i2i−2i0−2i2i2i−2i02−2−220000-222-2−2−22222−2−2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ532-222-22-2-2-20-202020−2−22222−2−22i−2i−2i2i02i−2i−2i2i0−222−20000-222-222−2−2−2−222000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ542-222-22-2-2-20-202020−2−22222−2−22i−2i−2i2i0−2i2i2i−2i0−222−200002-2-22−2−22222−2−2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ552-222-22-2-2-20-202020−2−22222−2−2−2i2i2i−2i02i−2i−2i2i0−222−200002-2-22−2−22222−2−2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ562-222-22-2-2-20-202020−2−22222−2−2−2i2i2i−2i0−2i2i2i−2i0−222−20000-222-222−2−2−2−222000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ572-2-222-22-22-2-222-2-220000000022-2-222i2i−2i−2i-20000−2i−2i2i2i2i2i−2i−2i00000000-22000000−2i2i0000000000000000000000
χ582-2-222-22-22-2-222-2-220000000022-2-22−2i−2i2i2i-200002i2i−2i−2i−2i−2i2i2i00000000-220000002i−2i0000000000000000000000
χ592-2-222-22-22-2-222-2-2200000000-2-22222i2i−2i−2i-200002i2i−2i−2i−2i−2i2i2i000000002-2000000−2i2i0000000000000000000000
χ602-2-222-22-22-2-222-2-2200000000-2-2222−2i−2i2i2i-20000−2i−2i2i2i2i2i−2i−2i000000002-20000002i−2i0000000000000000000000
χ612-2-222-22-2-222-2-222-22i2i2i2i−2i−2i−2i−2i000020000-2−2i−2i2i2i0000000000000000002-22i−2i-2200−2i2i00000000000000000000
χ622-2-222-22-2-222-2-222-22i2i2i2i−2i−2i−2i−2i000020000-2−2i−2i2i2i000000000000000000-22−2i2i2-2002i−2i00000000000000000000
χ632-2-222-22-2-222-2-222-2−2i−2i−2i−2i2i2i2i2i000020000-22i2i−2i−2i0000000000000000002-2−2i2i-22002i−2i00000000000000000000
χ642-2-222-22-2-222-2-222-2−2i−2i−2i−2i2i2i2i2i000020000-22i2i−2i−2i000000000000000000-222i−2i2-200−2i2i00000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004000040000000000000000000000000000000000000000000000000000
χ66444-44-4-4-4040-40-4044-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ67444-44-4-4-4040-40-404-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ68444-44-4-4-40-404040-400000000000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ69444-44-4-4-40-404040-4000000000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000
χ7044-44-4-4-4440-40-40402i22i2−2i2−2i22i22i2−2i2−2i20000000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ7144-44-4-4-4440-40-4040−2i2−2i22i22i2−2i2−2i22i22i200000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ7244-4-4-444-4000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000002i2−2i22i2−2i200002-2-222-2-2200000000000000000000000000000000
χ7344-4-4-444-4000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000−2i22i2−2i22i20000-222-2-222-200000000000000000000000000000000
χ7444-4-4-444-400000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000002i2−2i22i2−2i20000-222-2-222-200000000000000000000000000000000
χ7544-4-4-444-400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000−2i22i2−2i22i200002-2-222-2-2200000000000000000000000000000000
χ764-444-44-4-44040-40-402222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000000000000000
χ774-444-44-4-44040-40-40−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000000000000000
χ784-44-4-4-4440000000022−22−2222−222222−220000000000000022−22−222200002-2-22-222-200000000000000000000000000000000
χ794-44-4-4-4440000000022−22−2222−222222−2200000000000000−222222−220000-222-22-2-2200000000000000000000000000000000
χ804-44-4-4-44400000000−222222−2222−22−22220000000000000022−22−22220000-222-22-2-2200000000000000000000000000000000
χ814-44-4-4-44400000000−222222−2222−22−222200000000000000−222222−2200002-2-22-222-200000000000000000000000000000000
χ824-4-444-44-4-4-444-4-444000000000000-4000040000000000000000000000000000000000000000000000000000
χ834-4-4-444-4404040-40-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ844-4-4-444-4404040-40-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ854-4-4-444-440-40-4040400000000000000000000000000000022−2222−22−2222−222200000000000000000000000000000000
χ864-4-4-444-440-40-40404000000000000000000000000000000−2222−222222−2222−2200000000000000000000000000000000

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