Finite Group Databasebeta

← Group #229408

Character table — Group #229408

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888822444444444488888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-111
χ171-111-1-11-11-1-1-11-1111111-1-1-1-111-1-11ii−i−i-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1i−ii−ii−ii−ii−iii−i−i11-1-11-11-1i−ii−i1-11-1
χ181-111-1-11-11-1-1-11-1111111-1-1-1-111-1-11ii−i−i-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1−ii−iii−i−ii−iiii−i−i11-1-1-11-11−ii−ii-11-11
χ191-111-1-11-11-1-1-11-1111111-1-1-1-111-1-11−i−iii-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1i−ii−i−iii−ii−i−i−iii11-1-1-11-11i−ii−i-11-11
χ201-111-1-11-11-1-1-11-1111111-1-1-1-111-1-11−i−iii-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−ii−ii−ii−ii−ii−i−iii11-1-11-11-1−ii−ii1-11-1
χ211-111-1-11-11-1-1-11-1111111-1-1-1-1-1-1111ii−i−i-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11i−ii−ii−ii−ii−iii−i−i-1-1111-11-1−ii−ii-11-11
χ221-111-1-11-11-1-1-11-1111111-1-1-1-1-1-1111ii−i−i-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11−ii−iii−i−ii−iiii−i−i-1-111-11-11i−ii−i1-11-1
χ231-111-1-11-11-1-1-11-1111111-1-1-1-1-1-1111−i−iii-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11i−ii−i−iii−ii−i−i−iii-1-111-11-11−ii−ii1-11-1
χ241-111-1-11-11-1-1-11-1111111-1-1-1-1-1-1111−i−iii-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11−ii−ii−ii−ii−ii−i−iii-1-1111-11-1i−ii−i-11-11
χ251-111-1-11-11-1-1-11-111-1-1-1-1111111-1-11ii−i−i-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1i−i−iii−ii−i−ii−i−iii-1-1111-1-11i−i−ii1-1-11
χ261-111-1-11-11-1-1-11-111-1-1-1-1111111-1-11ii−i−i-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1−iii−ii−i−iii−i−i−iii-1-111-111-1−iii−i-111-1
χ271-111-1-11-11-1-1-11-111-1-1-1-1111111-1-11−i−iii-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1i−i−ii−iii−i−iiii−i−i-1-111-111-1i−i−ii-111-1
χ281-111-1-11-11-1-1-11-111-1-1-1-1111111-1-11−i−iii-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1−iii−i−ii−iii−iii−i−i-1-1111-1-11−iii−i1-1-11
χ291-111-1-11-11-1-1-11-111-1-1-1-11111-1-1111ii−i−i-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11i−i−iii−ii−i−ii−i−iii11-1-11-1-11−iii−i-111-1
χ301-111-1-11-11-1-1-11-111-1-1-1-11111-1-1111ii−i−i-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11−iii−ii−i−iii−i−i−iii11-1-1-111-1i−i−ii1-1-11
χ311-111-1-11-11-1-1-11-111-1-1-1-11111-1-1111−i−iii-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11i−i−ii−iii−i−iiii−i−i11-1-1-111-1−iii−i1-1-11
χ321-111-1-11-11-1-1-11-111-1-1-1-11111-1-1111−i−iii-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11−iii−i−ii−iii−iii−i−i11-1-11-1-11i−i−ii-111-1
χ33222222222-222-2-2-22000000002222-22222-2000022-2-222-2-200000000-2-20000-2-2000000000000000000000000
χ34222222222-222-2-2-22000000002222-2-2-2-2-2-20000-2-222-2-22200000000-2-2000022000000000000000000000000
χ35222222222-222-2-2-2200000000-2-2-2-2-22222-20000-2-222-2-22200000000220000-2-2000000000000000000000000
χ36222222222-222-2-2-2200000000-2-2-2-2-2-2-2-2-2-2000022-2-222-2-20000000022000022000000000000000000000000
χ3722222222-22-2-2222-2222222220000-20000-2-2-2-2-2000000000000000000222200-2-2-2-200000000000000000000
χ3822222222-22-2-2222-2222222220000-20000-2-2-2-2-2000000000000000000-2-2-2-200222200000000000000000000
χ3922222222-22-2-2222-2-2-2-2-2-2-2-2-20000-20000-2222200000000000000000022-2-200-2-22200000000000000000000
χ4022222222-22-2-2222-2-2-2-2-2-2-2-2-20000-20000-22222000000000000000000-2-2220022-2-200000000000000000000
χ41222-2-2-2-22-202-2000222−2−222−2−22i−2i2i−2i02-22-202−22−22i−2i002i−2i00i2i2−i2−i2i2i2−i2−i20000000000002−22−2i2−i2i2−i2000000000000
χ42222-2-2-2-22-202-2000222−2−222−2−22i−2i2i−2i0-22-2202−22−2−2i2i00−2i2i00−i2−i2i2i2−i2−i2i2i2000000000000−22−22i2−i2i2−i2000000000000
χ43222-2-2-2-22-202-2000222−2−222−2−2−2i2i−2i2i02-22-202−22−2−2i2i00−2i2i00−i2−i2i2i2−i2−i2i2i20000000000002−22−2−i2i2−i2i2000000000000
χ44222-2-2-2-22-202-2000222−2−222−2−2−2i2i−2i2i0-22-2202−22−22i−2i002i−2i00i2i2−i2−i2i2i2−i2−i2000000000000−22−22−i2i2−i2i2000000000000
χ45222-2-2-2-22-202-20002−2−222−2−2222i−2i2i−2i02-22-20−22−222i−2i002i−2i00−i2−i2i2i2−i2−i2i2i2000000000000−22−22−i2i2−i2i2000000000000
χ46222-2-2-2-22-202-20002−2−222−2−2222i−2i2i−2i0-22-220−22−22−2i2i00−2i2i00i2i2−i2−i2i2i2−i2−i20000000000002−22−2−i2i2−i2i2000000000000
χ47222-2-2-2-22-202-20002−2−222−2−222−2i2i−2i2i02-22-20−22−22−2i2i00−2i2i00i2i2−i2−i2i2i2−i2−i2000000000000−22−22i2−i2i2−i2000000000000
χ48222-2-2-2-22-202-20002−2−222−2−222−2i2i−2i2i0-22-220−22−222i−2i002i−2i00−i2−i2i2i2−i2−i2i2i20000000000002−22−2i2−i2i2−i2000000000000
χ492-222-2-22-222-2-2-22-220000000022-2-2-22i2i−2i−2i200002i2i−2i−2i−2i−2i2i2i00000000-220000−2i2i000000000000000000000000
χ502-222-2-22-222-2-2-22-220000000022-2-2-2−2i−2i2i2i20000−2i−2i2i2i2i2i−2i−2i00000000-2200002i−2i000000000000000000000000
χ512-222-2-22-222-2-2-22-2200000000-2-222-22i2i−2i−2i20000−2i−2i2i2i2i2i−2i−2i000000002-20000−2i2i000000000000000000000000
χ522-222-2-22-222-2-2-22-2200000000-2-222-2−2i−2i2i2i200002i2i−2i−2i−2i−2i2i2i000000002-200002i−2i000000000000000000000000
χ532-222-2-22-2-2-2222-22-22222-2-2-2-20000-200002-2-2220000000000000000002i−2i2i−2i00−2i2i−2i2i00000000000000000000
χ542-222-2-22-2-2-2222-22-22222-2-2-2-20000-200002-2-222000000000000000000−2i2i−2i2i002i−2i2i−2i00000000000000000000
χ552-222-2-22-2-2-2222-22-2-2-2-2-222220000-20000222-2-20000000000000000002i−2i−2i2i00−2i2i2i−2i00000000000000000000
χ562-222-2-22-2-2-2222-22-2-2-2-2-222220000-20000222-2-2000000000000000000−2i2i2i−2i002i−2i−2i2i00000000000000000000
χ572-22-222-2-2-20-22000222−2−2−2−2222i−2i−2i2i02i−2i−2i2i02−2−22-22002-200−2−22222−2−2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ582-22-222-2-2-20-22000222−2−2−2−2222i−2i−2i2i0−2i2i2i−2i02−2−222-200-220022−2−2−2−222000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ592-22-222-2-2-20-22000222−2−2−2−222−2i2i2i−2i02i−2i−2i2i02−2−222-200-220022−2−2−2−222000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ602-22-222-2-2-20-22000222−2−2−2−222−2i2i2i−2i0−2i2i2i−2i02−2−22-22002-200−2−22222−2−2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ612-22-222-2-2-20-220002−2−22222−2−22i−2i−2i2i02i−2i−2i2i0−222−2-22002-20022−2−2−2−222000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ622-22-222-2-2-20-220002−2−22222−2−22i−2i−2i2i0−2i2i2i−2i0−222−22-200-2200−2−22222−2−2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ632-22-222-2-2-20-220002−2−22222−2−2−2i2i2i−2i02i−2i−2i2i0−222−22-200-2200−2−22222−2−2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ642-22-222-2-2-20-220002−2−22222−2−2−2i2i2i−2i0−2i2i2i−2i0−222−2-22002-20022−2−2−2−222000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004000040000000000000000000000000000000000000000000000000000
χ66444-4-4-4-4440-44000-42222−22−222222−22−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ67444-4-4-4-4440-44000-4−22−222222−22−222222000000000022−2222−22000000000000000000000000000000000000000000000000
χ6844-444-4-4-40400-4-4404-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ6944-444-4-4-40400-4-440-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ7044-444-4-4-40-40044-4000000000000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ7144-444-4-4-40-40044-40000000000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000
χ7244-4-4-444-40000000022−22−222222−22−222200000000000000002i2−2i2002i2−2i22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ7344-4-4-444-40000000022−22−222222−22−22220000000000000000−2i22i200−2i22i2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ7444-4-4-444-400000000−222222−22−222222−2200000000000000002i2−2i2002i2−2i2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ7544-4-4-444-400000000−222222−22−222222−220000000000000000−2i22i200−2i22i22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ764-444-4-44-4-4444-44-4-400000000000040000-40000000000000000000000000000000000000000000000000000
χ774-44-444-4-4404-4000-42222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000000000000000
χ784-44-444-4-4404-4000-4−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000000000000000
χ794-4-44-44-4404004-4-400000000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ804-4-44-44-4404004-4-40000000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ814-4-44-44-440-400-44404-44-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ824-4-44-44-440-400-4440-44-444-44-400000000000000000000000000000000000000000000000000000000000000
χ834-4-4-44-4440000000022−22−2222−222222−22000000000000000022−2200−22222-2-22-222-200000000000000000000000000000000
χ844-4-4-44-4440000000022−22−2222−222222−220000000000000000−22220022−22-222-22-2-2200000000000000000000000000000000
χ854-4-4-44-44400000000−222222−2222−22−2222000000000000000022−2200−2222-222-22-2-2200000000000000000000000000000000
χ864-4-4-44-44400000000−222222−2222−22−22220000000000000000−22220022−222-2-22-222-200000000000000000000000000000000

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