Finite Group Databasebeta

← Group #209990

Character table — Group #209990

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222444444444444444444444444444444444444444444444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ911111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ1111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1211111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1311111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ1411111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1511111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1611111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ171-1-1111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i11-1-1ii−i−ii−i1-1i−i1-11-11-111-1-1i−ii−iii−i−i11-1-1ii−i−iii−i−i11-1-111-1-1ii−i−ii−i1-1
χ181-1-1111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i11-1-1ii−i−ii−i1-1i−i1-11-11-111-1-1i−ii−iii−i−i-1-111−i−iii−i−iii-1-111-1-111−i−iii−ii-11
χ191-1-1111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i11-1-1ii−i−ii−i1-1−ii1-1-11-11-1-111i−i−ii−i−iii11-1-1ii−i−i−i−iii-1-11111-1-1ii−i−i−ii-11
χ201-1-1111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i11-1-1ii−i−ii−i1-1−ii1-1-11-11-1-111i−i−ii−i−iii-1-111−i−iiiii−i−i11-1-1-1-111−i−iiii−i1-1
χ211-1-1111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i-1-111−i−iiii−i1-1i−i-111-11-1-1-111−iii−i−i−iii11-1-1ii−i−i−i−iii-1-111-1-111−i−iiii−i1-1
χ221-1-1111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i-1-111−i−iiii−i1-1i−i-111-11-1-1-111−iii−i−i−iii-1-111−i−iiiii−i−i11-1-111-1-1ii−i−i−ii-11
χ231-1-1111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i-1-111−i−iiii−i1-1−ii-11-11-1111-1-1−ii−iiii−i−i11-1-1ii−i−iii−i−i11-1-1-1-111−i−iii−ii-11
χ241-1-1111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i-1-111−i−iiii−i1-1−ii-11-11-1111-1-1−ii−iiii−i−i-1-111−i−iii−i−iii-1-11111-1-1ii−i−ii−i1-1
χ251-1-1111-1-1−i−iii11-1-1−i−iii11-1-1−ii11-1-1−i−iii−ii1-1i−i1-1-11-11-1-111−iii−iii−i−i11-1-1−i−iiiii−i−i-1-11111-1-1−i−iiii−i-11
χ261-1-1111-1-1−i−iii11-1-1−i−iii11-1-1−ii11-1-1−i−iii−ii1-1i−i1-1-11-11-1-111−iii−iii−i−i-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−ii1-1
χ271-1-1111-1-1−i−iii11-1-1−i−iii11-1-1−ii11-1-1−i−iii−ii1-1−ii1-11-11-111-1-1−ii−ii−i−iii11-1-1−i−iii−i−iii11-1-111-1-1−i−iii−ii1-1
χ281-1-1111-1-1−i−iii11-1-1−i−iii11-1-1−ii11-1-1−i−iii−ii1-1−ii1-11-11-111-1-1−ii−ii−i−iii-1-111ii−i−iii−i−i-1-111-1-111ii−i−ii−i-11
χ291-1-1111-1-1−i−iii11-1-1−i−iii11-1-1−ii-1-111ii−i−i−ii1-1i−i-11-11-1111-1-1i−ii−i−i−iii11-1-1−i−iii−i−iii11-1-1-1-111ii−i−ii−i-11
χ301-1-1111-1-1−i−iii11-1-1−i−iii11-1-1−ii-1-111ii−i−i−ii1-1i−i-11-11-1111-1-1i−ii−i−i−iii-1-111ii−i−iii−i−i-1-11111-1-1−i−iii−ii1-1
χ311-1-1111-1-1−i−iii11-1-1−i−iii11-1-1−ii-1-111ii−i−i−ii1-1−ii-111-11-1-1-111i−i−iiii−i−i11-1-1−i−iiiii−i−i-1-111-1-111ii−i−i−ii1-1
χ321-1-1111-1-1−i−iii11-1-1−i−iii11-1-1−ii-1-111ii−i−i−ii1-1−ii-111-11-1-1-111i−i−iiii−i−i-1-111ii−i−i−i−iii11-1-111-1-1−i−iiii−i-11
χ332222222222222-22-222222-22-2-2-222222222-2-2-2-200-2-200000000-2-20000000000000000000000000000000000
χ342222222222222-22-222222-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2002200000000220000000000000000000000000000000000
χ35222222222222-22-22-2-2-2-2-22-222200000000-2-2-2-2220022-2-2000000-2-200000000000000000000000000000000
χ36222222222222-22-22-2-2-2-2-22-222200000000-2-2-2-2-2-200-2-2220000002200000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000002-22-200002-22-20000000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000-22-220000-22-220000000000000000000000000000
χ3922222222-2-2-2-22-22-2-2-2-2-22-22-2222222-2-2-2-222-2-200-2-200000000220000000000000000000000000000000000
χ4022222222-2-2-2-22-22-2-2-2-2-22-22-222-2-2-2-2222222-2-2002200000000-2-20000000000000000000000000000000000
χ4122222222-2-2-2-2-22-222222-22-22-2-20000000022-2-22200-2-222000000-2-200000000000000000000000000000000
χ4222222222-2-2-2-2-22-222222-22-22-2-20000000022-2-2-2-20022-2-20000002200000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-22200000000-2-222000000002-22-20000-22-220000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-22200000000-2-22200000000-22-2200002-22-20000000000000000000000000000
χ4522-2-22-22-22-22-2-20-202-22-22020002-22-22-22-2000000000000000000000000i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i20000
χ4622-2-22-22-22-22-2-20-202-22-22020002-22-22-22-2000000000000000000000000−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i20000
χ4722-2-22-22-22-22-2-20-202-22-2202000-22-22-22-22000000000000000000000000i2−i2i2−i2i2−i2i2−i200000000−i2i2−i2i2−i2i2−i2i20000
χ4822-2-22-22-22-22-2-20-202-22-2202000-22-22-22-22000000000000000000000000−i2i2−i2i2−i2i2−i2i200000000i2−i2i2−i2i2−i2i2−i20000
χ4922-2-22-22-2-22-22-20-20-22-222020002-22-2-22-22000000000000000000000000i2−i2i2−i2−i2i2−i2i200000000i2−i2i2−i2−i2i2−i2i20000
χ5022-2-22-22-2-22-22-20-20-22-222020002-22-2-22-22000000000000000000000000−i2i2−i2i2i2−i2i2−i200000000−i2i2−i2i2i2−i2i2−i20000
χ5122-2-22-22-2-22-22-20-20-22-22202000-22-222-22-2000000000000000000000000i2−i2i2−i2−i2i2−i2i200000000−i2i2−i2i2i2−i2i2−i20000
χ5222-2-22-22-2-22-22-20-20-22-22202000-22-222-22-2000000000000000000000000−i2i2−i2i2i2−i2i2−i200000000i2−i2i2−i2−i2i2−i2i20000
χ532-22-22-2-222i−2i−2i2i-20202i−2i−2i2i20-20002-2-222i−2i−2i2i000000000000000000000000i2−i2−i2i2−222−200000000i2−i2−i2i2−222−20000
χ542-22-22-2-222i−2i−2i2i-20202i−2i−2i2i20-20002-2-222i−2i−2i2i000000000000000000000000−i2i2i2−i22−2−2200000000−i2i2i2−i22−2−220000
χ552-22-22-2-222i−2i−2i2i-20202i−2i−2i2i20-2000-222-2−2i2i2i−2i000000000000000000000000i2−i2−i2i2−222−200000000−i2i2i2−i22−2−220000
χ562-22-22-2-222i−2i−2i2i-20202i−2i−2i2i20-2000-222-2−2i2i2i−2i000000000000000000000000−i2i2i2−i22−2−2200000000i2−i2−i2i2−222−20000
χ572-22-22-2-22−2i2i2i−2i-2020−2i2i2i−2i20-20002-2-22−2i2i2i−2i000000000000000000000000i2−i2−i2i22−2−2200000000i2−i2−i2i22−2−220000
χ582-22-22-2-22−2i2i2i−2i-2020−2i2i2i−2i20-20002-2-22−2i2i2i−2i000000000000000000000000−i2i2i2−i2−222−200000000−i2i2i2−i2−222−20000
χ592-22-22-2-22−2i2i2i−2i-2020−2i2i2i−2i20-2000-222-22i−2i−2i2i000000000000000000000000i2−i2−i2i22−2−2200000000−i2i2i2−i2−222−20000
χ602-22-22-2-22−2i2i2i−2i-2020−2i2i2i−2i20-2000-222-22i−2i−2i2i000000000000000000000000−i2i2i2−i2−222−200000000i2−i2−i2i22−2−220000
χ612-2-2222-2-22i2i−2i−2i2-2-222i2i−2i−2i2-2-22−2i2i22-2-22i2i−2i−2i−2i2i-2200-2200000000−2i2i0000000000000000000000000000000000
χ622-2-2222-2-22i2i−2i−2i2-2-222i2i−2i−2i2-2-22−2i2i-2-222−2i−2i2i2i−2i2i-22002-2000000002i−2i0000000000000000000000000000000000
χ632-2-2222-2-22i2i−2i−2i-222-2−2i−2i2i2i-222-22i−2i00000000−2i2i-222i−2i002-2-22000000−2i2i00000000000000000000000000000000
χ642-2-2222-2-22i2i−2i−2i-222-2−2i−2i2i2i-222-22i−2i00000000−2i2i-22−2i2i00-222-20000002i−2i00000000000000000000000000000000
χ652-2-2222-2-22i2i−2i−2i-2-222−2i−2i2i2i-2-222−2i2i000000002i−2i2-2000000002-2-2200002i−2i−2i2i0000000000000000000000000000
χ662-2-2222-2-22i2i−2i−2i-2-222−2i−2i2i2i-2-222−2i2i000000002i−2i2-200000000-222-20000−2i2i2i−2i0000000000000000000000000000
χ672-2-2222-2-2−2i−2i2i2i2-2-22−2i−2i2i2i2-2-222i−2i22-2-2−2i−2i2i2i2i−2i-2200-22000000002i−2i0000000000000000000000000000000000
χ682-2-2222-2-2−2i−2i2i2i2-2-22−2i−2i2i2i2-2-222i−2i-2-2222i2i−2i−2i2i−2i-22002-200000000−2i2i0000000000000000000000000000000000
χ692-2-2222-2-2−2i−2i2i2i-222-22i2i−2i−2i-222-2−2i2i000000002i−2i-222i−2i00-222-2000000−2i2i00000000000000000000000000000000
χ702-2-2222-2-2−2i−2i2i2i-222-22i2i−2i−2i-222-2−2i2i000000002i−2i-22−2i2i002-2-220000002i−2i00000000000000000000000000000000
χ712-2-2222-2-2−2i−2i2i2i-2-2222i2i−2i−2i-2-2222i−2i00000000−2i2i2-2000000002-2-220000−2i2i2i−2i0000000000000000000000000000
χ722-2-2222-2-2−2i−2i2i2i-2-2222i2i−2i−2i-2-2222i−2i00000000−2i2i2-200000000-222-200002i−2i−2i2i0000000000000000000000000000
χ73444-4-44-4-40000040-400000-40400000000000000000000000000000000000000000022−2222−220000000000000000
χ74444-4-44-4-40000040-400000-404000000000000000000000000000000000000000000−2222−22220000000000000000
χ75444-4-44-4-400000-4040000040-4000000000000000000000000000000000000000000000022−2222−22000000000000
χ76444-4-44-4-400000-4040000040-40000000000000000000000000000000000000000000000−2222−2222000000000000
χ7744-4-44-44-44-44-44040-44-44-40-4000000000000000000000000000000000000000000000000000000000000000
χ7844-4-44-44-4-44-4440404-44-4-40-4000000000000000000000000000000000000000000000000000000000000000
χ794-44-44-4-444i−4i−4i4i40-40−4i4i4i−4i-404000000000000000000000000000000000000000000000000000000000000000
χ804-44-44-4-44−4i4i4i−4i40-404i−4i−4i4i-404000000000000000000000000000000000000000000000000000000000000000
χ814-4-4-4-44440000040400000-40-40000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ824-4-4-4-44440000040400000-40-4000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ834-4-4-4-444400000-40-400000404000000000000000000000000000000000000000000000022−22−2222000000000000
χ844-4-4-4-444400000-40-4000004040000000000000000000000000000000000000000000000−222222−22000000000000
χ8588-88-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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