Finite Group Databasebeta

← Group #220771

Character table — Group #220771

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888822444444444488888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ101111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-11111-1-111-1-111-1-111
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-11111-1-1-1-111-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-11111-1-1
χ171-1-111-1-1111-1-11-11-1iiii−i−i−i−i111-1-111-1-1-111-1-111-1-1ii−i−iiiii−i−i−i−i1-11-11-1ii−i−i1-1ii−i−iii−i−i1-1i−ii−i1-1i−i1-1
χ181-1-111-1-1111-1-11-11-1iiii−i−i−i−i111-1-111-1-1-111-1-111-1-1ii−i−iiiii−i−i−i−i-111-11-1−i−iii-11ii−i−iii−i−i-11−ii−ii-11−ii-11
χ191-1-111-1-1111-1-11-11-1iiii−i−i−i−i111-1-1-1-111-1-1-111-1-111ii−i−i−i−i−i−iiiii1-11-1-11ii−i−i1-1ii−i−i−i−iii1-1i−i−ii-11−ii-11
χ201-1-111-1-1111-1-11-11-1iiii−i−i−i−i111-1-1-1-111-1-1-111-1-111ii−i−i−i−i−i−iiiii-111-1-11−i−iii-11ii−i−i−i−iii-11−iii−i1-1i−i1-1
χ211-1-111-1-1111-1-11-11-1iiii−i−i−i−i1-1-11111-1-1-1-1-111-1-111ii−i−i−i−i−i−iiiii1-1-111-1ii−i−i1-1−i−iiiii−i−i-11−iii−i1-1−ii-11
χ221-1-111-1-1111-1-11-11-1iiii−i−i−i−i1-1-11111-1-1-1-1-111-1-111ii−i−i−i−i−i−iiiii-11-111-1−i−iii-11−i−iiiii−i−i1-1i−i−ii-11i−i1-1
χ231-1-111-1-1111-1-11-11-1iiii−i−i−i−i1-1-111-1-111-111-1-111-1-1ii−i−iiiii−i−i−i−i1-1-11-11ii−i−i1-1−i−iii−i−iii-11−ii−ii-11i−i1-1
χ241-1-111-1-1111-1-11-11-1iiii−i−i−i−i1-1-111-1-111-111-1-111-1-1ii−i−iiiii−i−i−i−i-11-11-11−i−iii-11−i−iii−i−iii1-1i−ii−i1-1−ii-11
χ251-1-111-1-1111-1-11-11-1−i−i−i−iiiii111-1-111-1-1-111-1-111-1-1−i−iii−i−i−i−iiiii1-11-11-1−i−iii1-1−i−iii−i−iii1-1−ii−ii1-1−ii1-1
χ261-1-111-1-1111-1-11-11-1−i−i−i−iiiii111-1-111-1-1-111-1-111-1-1−i−iii−i−i−i−iiiii-111-11-1ii−i−i-11−i−iii−i−iii-11i−ii−i-11i−i-11
χ271-1-111-1-1111-1-11-11-1−i−i−i−iiiii111-1-1-1-111-1-1-111-1-111−i−iiiiiii−i−i−i−i1-11-1-11−i−iii1-1−i−iiiii−i−i1-1−iii−i-11i−i-11
χ281-1-111-1-1111-1-11-11-1−i−i−i−iiiii111-1-1-1-111-1-1-111-1-111−i−iiiiiii−i−i−i−i-111-1-11ii−i−i-11−i−iiiii−i−i-11i−i−ii1-1−ii1-1
χ291-1-111-1-1111-1-11-11-1−i−i−i−iiiii1-1-11111-1-1-1-1-111-1-111−i−iiiiiii−i−i−i−i1-1-111-1−i−iii1-1ii−i−i−i−iii-11i−i−ii1-1i−i-11
χ301-1-111-1-1111-1-11-11-1−i−i−i−iiiii1-1-11111-1-1-1-1-111-1-111−i−iiiiiii−i−i−i−i-11-111-1ii−i−i-11ii−i−i−i−iii1-1−iii−i-11−ii1-1
χ311-1-111-1-1111-1-11-11-1−i−i−i−iiiii1-1-111-1-111-111-1-111-1-1−i−iii−i−i−i−iiiii1-1-11-11−i−iii1-1ii−i−iii−i−i-11i−ii−i-11−ii1-1
χ321-1-111-1-1111-1-11-11-1−i−i−i−iiiii1-1-111-1-111-111-1-111-1-1−i−iii−i−i−i−iiiii-11-11-11ii−i−i-11ii−i−iii−i−i1-1−ii−ii1-1i−i-11
χ332222222222-22-2-2-2222222222-200000000-200000000-2-2-2-2000000002200002-22-2-2-200000000000000000000
χ342222222222-22-2-2-2222222222-200000000-200000000-2-2-2-200000000-2-20000-22-222200000000000000000000
χ352222222222-22-2-2-22-2-2-2-2-2-2-2-2-200000000-200000000222200000000220000-22-22-2-200000000000000000000
χ362222222222-22-2-2-22-2-2-2-2-2-2-2-2-200000000-200000000222200000000-2-200002-22-22200000000000000000000
χ3722222222-2-22-2222-200000000-222222222-2-2-2-2-2222200000000000000-2-2-2-200000000000000000000000000
χ3822222222-2-22-2222-200000000-22222-2-2-2-2-22222-2-2-2-200000000000000-2-22200000000000000000000000000
χ3922222222-2-22-2222-200000000-2-2-2-2-22222-22222-2-2-2-20000000000000022-2-200000000000000000000000000
χ4022222222-2-22-2222-200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000222200000000000000000000000000
χ41222-2-2-2-220020-2-220i2i2−i2−i2i2i2−i2−i202-22-22-22-2000002-22-2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ42222-2-2-2-220020-2-220i2i2−i2−i2i2i2−i2−i202-22-2-22-2200000-22-22i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ43222-2-2-2-220020-2-220i2i2−i2−i2i2i2−i2−i20-22-222-22-200000-22-22i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ44222-2-2-2-220020-2-220i2i2−i2−i2i2i2−i2−i20-22-22-22-22000002-22-2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ45222-2-2-2-220020-2-220−i2−i2i2i2−i2−i2i2i202-22-22-22-2000002-22-2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ46222-2-2-2-220020-2-220−i2−i2i2i2−i2−i2i2i202-22-2-22-2200000-22-22−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ47222-2-2-2-220020-2-220−i2−i2i2i2−i2−i2i2i20-22-222-22-200000-22-22−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ48222-2-2-2-220020-2-220−i2−i2i2i2−i2−i2i2i20-22-22-22-22000002-22-2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ492-2-222-2-22222-2-22-2-22i2i2i2i−2i−2i−2i−2i-200000000200000000−2i−2i2i2i000000002-200002i−2i−2i2i-2200000000000000000000
χ502-2-222-2-22222-2-22-2-22i2i2i2i−2i−2i−2i−2i-200000000200000000−2i−2i2i2i00000000-220000−2i2i2i−2i2-200000000000000000000
χ512-2-222-2-22222-2-22-2-2−2i−2i−2i−2i2i2i2i2i-2000000002000000002i2i−2i−2i000000002-20000−2i2i2i−2i-2200000000000000000000
χ522-2-222-2-22222-2-22-2-2−2i−2i−2i−2i2i2i2i2i-2000000002000000002i2i−2i−2i00000000-2200002i−2i−2i2i2-200000000000000000000
χ532-2-222-2-22-2-2-222-22200000000-222-2-222-2-22-2-22222-2-200000000000000-22-2200000000000000000000000000
χ542-2-222-2-22-2-2-222-22200000000-222-2-2-2-222222-2-2-2-22200000000000000-222-200000000000000000000000000
χ552-2-222-2-22-2-2-222-22200000000-2-2-22222-2-2222-2-2-2-222000000000000002-2-2200000000000000000000000000
χ562-2-222-2-22-2-2-222-22200000000-2-2-222-2-2222-2-22222-2-2000000000000002-22-200000000000000000000000000
χ572-2-2-2-222200-20-222022−2−2−2−22202-2-222-2-22000002-2-222−2−2222−2−2−2−2220000000000002−2−222−2−22000000000000
χ582-2-2-2-222200-20-222022−2−2−2−22202-2-22-222-200000-222-22−2−22−2−22222−2−20000000000002−2−22−222−2000000000000
χ592-2-2-2-222200-20-222022−2−2−2−2220-222-22-2-2200000-222-22−2−22−2−22222−2−2000000000000−222−22−2−22000000000000
χ602-2-2-2-222200-20-222022−2−2−2−2220-222-2-222-2000002-2-222−2−2222−2−2−2−222000000000000−222−2−222−2000000000000
χ612-2-2-2-222200-20-2220−2−22222−2−202-2-222-2-22000002-2-22−222−2−2−22222−2−2000000000000−222−2−222−2000000000000
χ622-2-2-2-222200-20-2220−2−22222−2−202-2-22-222-200000-222-2−222−222−2−2−2−222000000000000−222−22−2−22000000000000
χ632-2-2-2-222200-20-2220−2−22222−2−20-222-22-2-2200000-222-2−222−222−2−2−2−2220000000000002−2−22−222−2000000000000
χ642-2-2-2-222200-20-2220−2−22222−2−20-222-2-222-2000002-2-22−222−2−2−22222−2−20000000000002−2−222−2−22000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000000040000000000000000000000000000000000000000000000000000
χ66444-4-4-4-4400-4044-402i22i2−2i2−2i22i22i2−2i2−2i2000000000000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ67444-4-4-4-4400-4044-40−2i2−2i22i22i2−2i2−2i22i22i20000000000000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ6844-44-44-4-44-404000-400000000000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ6944-44-44-4-44-404000-4000000000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000
χ7044-44-44-4-4-440-400044i−4i4i−4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ7144-44-44-4-4-440-40004−4i4i−4i4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7244-4-44-44-40000000022−22−222222−22−222200000000002i2−2i22i2−2i2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ7344-4-44-44-40000000022−22−222222−22−22220000000000−2i22i2−2i22i200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ7444-4-44-44-400000000−222222−22−222222−2200000000002i2−2i22i2−2i200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ7544-4-44-44-400000000−222222−22−222222−220000000000−2i22i2−2i22i2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ764-444-4-44-44-40-400040000000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ774-444-4-44-44-40-40004000000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ784-444-4-44-4-4404000-44-44-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ794-444-4-44-4-4404000-4-44-444-44-400000000000000000000000000000000000000000000000000000000000000
χ804-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000002i2−2i2−2i22i200000000-222-22-2-2200000000000000000000000000000000
χ814-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000−2i22i22i2−2i2000000002-2-22-222-200000000000000000000000000000000
χ824-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000002i2−2i2−2i22i2000000002-2-22-222-200000000000000000000000000000000
χ834-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000−2i22i22i2−2i200000000-222-22-2-2200000000000000000000000000000000
χ844-4-444-4-44-4-444-44-4400000000400000000-40000000000000000000000000000000000000000000000000000
χ854-4-4-4-444400404-4-402222−22−22−22−222222000000000000000000−222222−220000000000000000000000000000000000000000
χ864-4-4-4-444400404-4-40−22−2222222222−22−2200000000000000000022−22−22220000000000000000000000000000000000000000

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