Finite Group Databasebeta

← Group #227266

Character table — Group #227266

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888822224444448888888888888888888822444444444488888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-111-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-111-1-1
χ171-11-11-11-111-1-111-1-1iiii−i−i−i−i11-1-1-1ii−i−i1ii−i−iii−i−iii−i−i1111-1-1-1-11-1i−i1-1i−i1-1i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ181-11-11-11-111-1-111-1-1iiii−i−i−i−i11-1-1-1ii−i−i1ii−i−iii−i−iii−i−i1111-1-1-1-1-11i−i1-1−ii-11−ii11-1-1ii−i−i-11−ii-11−ii-11−ii
χ191-11-11-11-111-1-111-1-1iiii−i−i−i−i11-1-1-1−i−iii1ii−i−i−i−iii−i−iii-1-1-1-111111-1−ii1-1i−i1-1i−i-1-111ii−i−i1-1−ii-11i−i-11−ii
χ201-11-11-11-111-1-111-1-1iiii−i−i−i−i11-1-1-1−i−iii1ii−i−i−i−iii−i−iii-1-1-1-11111-11−ii1-1−ii-11−ii-1-111ii−i−i-11i−i1-1−ii1-1i−i
χ211-11-11-11-111-1-111-1-1iiii−i−i−i−i-1-111-1ii−i−i1ii−i−i−i−iii−i−iii-1-1-1-111111-1i−i-11i−i1-1i−i11-1-1−i−iii-11i−i1-1−ii-11−ii
χ221-11-11-11-111-1-111-1-1iiii−i−i−i−i-1-111-1ii−i−i1ii−i−i−i−iii−i−iii-1-1-1-11111-11i−i-11−ii-11−ii11-1-1−i−iii1-1−ii-11i−i1-1i−i
χ231-11-11-11-111-1-111-1-1iiii−i−i−i−i-1-111-1−i−iii1ii−i−iii−i−iii−i−i1111-1-1-1-11-1−ii-11i−i1-1i−i-1-111−i−iii-11−ii-11−ii1-1i−i
χ241-11-11-11-111-1-111-1-1iiii−i−i−i−i-1-111-1−i−iii1ii−i−iii−i−iii−i−i1111-1-1-1-1-11−ii-11−ii-11−ii-1-111−i−iii1-1i−i1-1i−i-11−ii
χ251-11-11-11-111-1-111-1-1−i−i−i−iiiii11-1-1-1ii−i−i1−i−iiiii−i−iii−i−i-1-1-1-111111-1i−i1-1−ii1-1−ii-1-111−i−iii1-1i−i-11−ii-11i−i
χ261-11-11-11-111-1-111-1-1−i−i−i−iiiii11-1-1-1ii−i−i1−i−iiiii−i−iii−i−i-1-1-1-11111-11i−i1-1i−i-11i−i-1-111−i−iii-11−ii1-1i−i1-1−ii
χ271-11-11-11-111-1-111-1-1−i−i−i−iiiii11-1-1-1−i−iii1−i−iii−i−iii−i−iii1111-1-1-1-11-1−ii1-1−ii1-1−ii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ281-11-11-11-111-1-111-1-1−i−i−i−iiiii11-1-1-1−i−iii1−i−iii−i−iii−i−iii1111-1-1-1-1-11−ii1-1i−i-11i−i11-1-1−i−iii-11i−i-11i−i-11i−i
χ291-11-11-11-111-1-111-1-1−i−i−i−iiiii-1-111-1ii−i−i1−i−iii−i−iii−i−iii1111-1-1-1-11-1i−i-11−ii1-1−ii-1-111ii−i−i-11i−i-11i−i1-1−ii
χ301-11-11-11-111-1-111-1-1−i−i−i−iiiii-1-111-1ii−i−i1−i−iii−i−iii−i−iii1111-1-1-1-1-11i−i-11i−i-11i−i-1-111ii−i−i1-1−ii1-1−ii-11i−i
χ311-11-11-11-111-1-111-1-1−i−i−i−iiiii-1-111-1−i−iii1−i−iiiii−i−iii−i−i-1-1-1-111111-1−ii-11−ii1-1−ii11-1-1ii−i−i-11−ii1-1i−i-11i−i
χ321-11-11-11-111-1-111-1-1−i−i−i−iiiii-1-111-1−i−iii1−i−iiiii−i−iii−i−i-1-1-1-11111-11−ii-11i−i-11i−i11-1-1ii−i−i1-1i−i-11−ii1-1−ii
χ33222222222-22-22-22-2222222220000-20000-2-2-2-2-20000000000000000220000-2-2-2-22200000000000000000000
χ34222222222-22-22-22-2222222220000-20000-2-2-2-2-20000000000000000-2-200002222-2-200000000000000000000
χ35222222222-22-22-22-2-2-2-2-2-2-2-2-20000-20000-22222000000000000000022000022-2-2-2-200000000000000000000
χ36222222222-22-22-22-2-2-2-2-2-2-2-2-20000-20000-222220000000000000000-2-20000-2-2222200000000000000000000
χ3722222222-22-22-22-22000000002222-22222-20000-2-2-2-222220000000000-2-2-2-200000000000000000000000000
χ3822222222-22-22-22-22000000002222-2-2-2-2-2-200002222-2-2-2-2000000000022-2-200000000000000000000000000
χ3922222222-22-22-22-2200000000-2-2-2-2-22222-200002222-2-2-2-20000000000-2-22200000000000000000000000000
χ4022222222-22-22-22-2200000000-2-2-2-2-2-2-2-2-2-20000-2-2-2-222220000000000222200000000000000000000000000
χ4122-22-2-22-20-202020-2i2i2−i2−i2i2i2−i2−i22-22-202i−2i2i−2i0i2−i2i2−i200002i−2i2i−2i22−2−222−2−20000000000002−22−2i2−i2i2−i2000000000000
χ4222-22-2-22-20-202020-2i2i2−i2−i2i2i2−i2−i22-22-20−2i2i−2i2i0i2−i2i2−i20000−2i2i−2i2i−2−222−2−222000000000000−22−22i2−i2i2−i2000000000000
χ4322-22-2-22-20-202020-2i2i2−i2−i2i2i2−i2−i2-22-2202i−2i2i−2i0i2−i2i2−i20000−2i2i−2i2i−2−222−2−2220000000000002−22−2−i2i2−i2i2000000000000
χ4422-22-2-22-20-202020-2i2i2−i2−i2i2i2−i2−i2-22-220−2i2i−2i2i0i2−i2i2−i200002i−2i2i−2i22−2−222−2−2000000000000−22−22−i2i2−i2i2000000000000
χ4522-22-2-22-20-202020-2−i2−i2i2i2−i2−i2i2i22-22-202i−2i2i−2i0−i2i2−i2i200002i−2i2i−2i−2−222−2−222000000000000−22−22−i2i2−i2i2000000000000
χ4622-22-2-22-20-202020-2−i2−i2i2i2−i2−i2i2i22-22-20−2i2i−2i2i0−i2i2−i2i20000−2i2i−2i2i22−2−222−2−20000000000002−22−2−i2i2−i2i2000000000000
χ4722-22-2-22-20-202020-2−i2−i2i2i2−i2−i2i2i2-22-2202i−2i2i−2i0−i2i2−i2i20000−2i2i−2i2i22−2−222−2−2000000000000−22−22i2−i2i2−i2000000000000
χ4822-22-2-22-20-202020-2−i2−i2i2i2−i2−i2i2i2-22-220−2i2i−2i2i0−i2i2−i2i200002i−2i2i−2i−2−222−2−2220000000000002−22−2i2−i2i2−i2000000000000
χ492-22-22-22-22-2-222-2-222i2i2i2i−2i−2i−2i−2i000020000-2−2i−2i2i2i00000000000000002-20000−2i2i-222i−2i00000000000000000000
χ502-22-22-22-22-2-222-2-222i2i2i2i−2i−2i−2i−2i000020000-2−2i−2i2i2i0000000000000000-2200002i−2i2-2−2i2i00000000000000000000
χ512-22-22-22-22-2-222-2-22−2i−2i−2i−2i2i2i2i2i000020000-22i2i−2i−2i00000000000000002-200002i−2i-22−2i2i00000000000000000000
χ522-22-22-22-22-2-222-2-22−2i−2i−2i−2i2i2i2i2i000020000-22i2i−2i−2i0000000000000000-220000−2i2i2-22i−2i00000000000000000000
χ532-22-22-22-2-222-2-222-20000000022-2-222i2i−2i−2i-20000−2i−2i2i2i2i2i−2i−2i0000000000−2i2i-2200000000000000000000000000
χ542-22-22-22-2-222-2-222-20000000022-2-22−2i−2i2i2i-200002i2i−2i−2i−2i−2i2i2i00000000002i−2i-2200000000000000000000000000
χ552-22-22-22-2-222-2-222-200000000-2-22222i2i−2i−2i-200002i2i−2i−2i−2i−2i2i2i0000000000−2i2i2-200000000000000000000000000
χ562-22-22-22-2-222-2-222-200000000-2-2222−2i−2i2i2i-20000−2i−2i2i2i2i2i−2i−2i00000000002i−2i2-200000000000000000000000000
χ572-2-2-2-22220-20-2020222−2−2−2−2222-2-2202-2-2202−2−2200002-2-2222−2−2−2−2220000000000002−2−222−2−22000000000000
χ582-2-2-2-22220-20-2020222−2−2−2−2222-2-220-222-202−2−220000-222-2−2−22222−2−2000000000000−222−22−2−22000000000000
χ592-2-2-2-22220-20-2020222−2−2−2−222-222-202-2-2202−2−220000-222-2−2−22222−2−20000000000002−2−22−222−2000000000000
χ602-2-2-2-22220-20-2020222−2−2−2−222-222-20-222-202−2−2200002-2-2222−2−2−2−222000000000000−222−2−222−2000000000000
χ612-2-2-2-22220-20-20202−2−22222−2−22-2-2202-2-220−222−200002-2-22−2−22222−2−2000000000000−222−2−222−2000000000000
χ622-2-2-2-22220-20-20202−2−22222−2−22-2-220-222-20−222−20000-222-222−2−2−2−2220000000000002−2−22−222−2000000000000
χ632-2-2-2-22220-20-20202−2−22222−2−2-222-202-2-220−222−20000-222-222−2−2−2−222000000000000−222−22−2−22000000000000
χ642-2-2-2-22220-20-20202−2−22222−2−2-222-20-222-20−222−200002-2-22−2−22222−2−20000000000002−2−222−2−22000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004000040000000000000000000000000000000000000000000000000000
χ66444-4-4-4-440000000022−2222−2222−2222−22000000000000002i2−2i22i2−2i200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ67444-4-4-4-440000000022−2222−2222−2222−2200000000000000−2i22i2−2i22i20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ68444-4-4-4-4400000000−2222−2222−2222−2222000000000000002i2−2i22i2−2i20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ69444-4-4-4-4400000000−2222−2222−2222−222200000000000000−2i22i2−2i22i200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ7044-44-4-44-4040-40-4042i22i2−2i2−2i22i22i2−2i2−2i20000000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ7144-44-4-44-4040-40-404−2i2−2i22i22i2−2i2−2i22i22i200000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ7244-4-444-4-440-40-40400000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ7344-4-444-4-440-40-4040000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ7444-4-444-4-4-404040-404i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-4-404040-40−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ764-444-44-4-4000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000022−22−22220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ774-444-44-4-4000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000−222222−2200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ784-444-44-4-400000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000022−22−222200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ794-444-44-4-400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000−222222−220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ804-44-44-44-4-4-444-4-444000000000000-4000040000000000000000000000000000000000000000000000000000
χ814-4-444-4-444040-40-400000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000
χ824-4-444-4-444040-40-40000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000
χ834-4-444-4-44-40-4040404-4-44-444-400000000000000000000000000000000000000000000000000000000000000
χ844-4-444-4-44-40-404040-444-44-4-4400000000000000000000000000000000000000000000000000000000000000
χ854-4-4-4-444404040-40-42222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000000000000000
χ864-4-4-4-444404040-40-4−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000000000000000

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