Finite Group Databasebeta

← Group #107992

Character table — Group #107992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111111111112222222244444444444444448888888888888888888888888888888888888888888888888888
order12222222444444442222444444444444444444442244444444444444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ171-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-11-1ii−i−iii−i−i1-11-1i−ii−i1-111-1-1i−ii−ii−ii−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1
χ181-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-11-1ii−i−iii−i−i1-11-1i−ii−i1-111-1-1i−ii−ii−ii−i−i−iii−i−iii-1-111-1-111−i−iii−i−iii-1-111-1-111
χ191-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-11-1ii−i−iii−i−i1-1-11−ii−ii-11-1-111i−ii−i−ii−iiii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-1-111-1-111
χ201-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-11-1ii−i−iii−i−i1-1-11−ii−ii-11-1-111i−ii−i−ii−ii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i11-1-111-1-1
χ211-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-11-1−i−iii−i−iii1-11-1−ii−ii1-111-1-1−ii−ii−ii−iiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i-1-111-1-111
χ221-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-11-1−i−iii−i−iii1-11-1−ii−ii1-111-1-1−ii−ii−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1
χ231-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-11-1−i−iii−i−iii1-1-11i−ii−i-11-1-111−ii−iii−ii−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1
χ241-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-11-1−i−iii−i−iii1-1-11i−ii−i-11-1-111−ii−iii−ii−i−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-1-111-1-111
χ251-1-1111-1-1-1-1-1-1111111-1-111-1-111-1-1-11ii−i−i−i−iii-111-1i−i−ii1-1-1-111i−i−iii−i−ii11-1-1-1-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i
χ261-1-1111-1-1-1-1-1-1111111-1-111-1-111-1-1-11ii−i−i−i−iii-111-1i−i−ii1-1-1-111i−i−iii−i−ii-1-11111-1-1ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii
χ271-1-1111-1-1-1-1-1-1111111-1-111-1-111-1-1-11ii−i−i−i−iii-11-11−iii−i-1111-1-1i−i−ii−iii−i11-1-1-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii
χ281-1-1111-1-1-1-1-1-1111111-1-111-1-111-1-1-11ii−i−i−i−iii-11-11−iii−i-1111-1-1i−i−ii−iii−i-1-11111-1-1ii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i
χ291-1-1111-1-1-1-1-1-1111111-1-111-1-111-1-1-11−i−iiiii−i−i-111-1−iii−i1-1-1-111−iii−i−iii−i11-1-1-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii
χ301-1-1111-1-1-1-1-1-1111111-1-111-1-111-1-1-11−i−iiiii−i−i-111-1−iii−i1-1-1-111−iii−i−iii−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i
χ311-1-1111-1-1-1-1-1-1111111-1-111-1-111-1-1-11−i−iiiii−i−i-11-11i−i−ii-1111-1-1−iii−ii−i−ii11-1-1-1-111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i
χ321-1-1111-1-1-1-1-1-1111111-1-111-1-111-1-1-11−i−iiiii−i−i-11-11i−i−ii-1111-1-1−iii−ii−i−ii-1-11111-1-1−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii
χ33222222222222222222222222-2-2-2-2-2-222222222-2-2000000000000-2-2-2-2000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000002222000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-22-22-22-200000000-22220000-2-22-22-20000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-22-22-22-200000000-22-2-2000022-22-220000000000000000000000000000000000000000
χ372222222222222222-2-2-2-2-2-2-2-2-22-22-22000000002-20022220000000000-2-2-2-200000000000000000000000000000000
χ382222222222222222-2-2-2-2-2-2-2-2-22-22-22000000002-200-2-2-2-20000000000222200000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-222000000000000-2-222000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-222222200000000000022-2-2000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-2-2-2-222222-22-2-22000000002-2220000-2-2-22-220000000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2-2-2-2-222222-22-2-22000000002-2-2-20000222-22-20000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-22222-22-222-200000000-220022-2-20000000000-2-22200000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-22222-22-222-200000000-2200-2-222000000000022-2-200000000000000000000000000000000
χ4522-22-2-22-22i2i−2i−2i2i−2i2i−2i2-22-22i−2i2i−2i0000002-22-22i−2i2i−2i000000000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ4622-22-2-22-22i2i−2i−2i2i−2i2i−2i2-22-22i−2i2i−2i0000002-22-22i−2i2i−2i00000000000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ4722-22-2-22-22i2i−2i−2i2i−2i2i−2i2-22-22i−2i2i−2i000000-22-22−2i2i−2i2i000000000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ4822-22-2-22-22i2i−2i−2i2i−2i2i−2i2-22-22i−2i2i−2i000000-22-22−2i2i−2i2i00000000000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ4922-22-2-22-2−2i−2i2i2i−2i2i−2i2i2-22-2−2i2i−2i2i0000002-22-2−2i2i−2i2i000000000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ5022-22-2-22-2−2i−2i2i2i−2i2i−2i2i2-22-2−2i2i−2i2i0000002-22-2−2i2i−2i2i00000000000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ5122-22-2-22-2−2i−2i2i2i−2i2i−2i2i2-22-2−2i2i−2i2i000000-22-222i−2i2i−2i000000000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ5222-22-2-22-2−2i−2i2i2i−2i2i−2i2i2-22-2−2i2i−2i2i000000-22-222i−2i2i−2i00000000000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ532-222-2-2-222i2i−2i−2i−2i2i−2i2i2-2-22−2i2i2i−2i0000002i−2i−2i2i-222-2000000000000000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ542-222-2-2-222i2i−2i−2i−2i2i−2i2i2-2-22−2i2i2i−2i0000002i−2i−2i2i-222-200000000000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ552-222-2-2-222i2i−2i−2i−2i2i−2i2i2-2-22−2i2i2i−2i000000−2i2i2i−2i2-2-22000000000000000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ562-222-2-2-222i2i−2i−2i−2i2i−2i2i2-2-22−2i2i2i−2i000000−2i2i2i−2i2-2-2200000000000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ572-222-2-2-22−2i−2i2i2i2i−2i2i−2i2-2-222i−2i−2i2i0000002i−2i−2i2i2-2-22000000000000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ582-222-2-2-22−2i−2i2i2i2i−2i2i−2i2-2-222i−2i−2i2i0000002i−2i−2i2i2-2-2200000000000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ592-222-2-2-22−2i−2i2i2i2i−2i2i−2i2-2-222i−2i−2i2i000000−2i2i2i−2i-222-2000000000000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ602-222-2-2-22−2i−2i2i2i2i−2i2i−2i2-2-222i−2i−2i2i000000−2i2i2i−2i-222-200000000000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ612-2-2222-2-22222-2-2-2-222-2-2-2-222-2-222-222i2i−2i−2i2i2i−2i−2i-22000000000000−2i2i−2i2i000000000000000000000000000000000000
χ622-2-2222-2-22222-2-2-2-222-2-2-2-222-2-222-22−2i−2i2i2i−2i−2i2i2i-220000000000002i−2i2i−2i000000000000000000000000000000000000
χ632-2-2222-2-22222-2-2-2-2-2-22222-2-22-2-222200000000-2-22-20000-222-2-220000000000000000000000000000000000000000
χ642-2-2222-2-22222-2-2-2-2-2-22222-2-22-2-222200000000-2-2-2200002-2-222-20000000000000000000000000000000000000000
χ652-2-2222-2-22222-2-2-2-2-2-22222-2-2-222-2-2-20000000022002i−2i2i−2i0000000000−2i2i−2i2i00000000000000000000000000000000
χ662-2-2222-2-22222-2-2-2-2-2-22222-2-2-222-2-2-2000000002200−2i2i−2i2i00000000002i−2i2i−2i00000000000000000000000000000000
χ672-2-2222-2-2-2-2-2-2222222-2-222-2-2-2-2222-22i2i−2i−2i−2i−2i2i2i2-2000000000000−2i2i2i−2i000000000000000000000000000000000000
χ682-2-2222-2-2-2-2-2-2222222-2-222-2-2-2-2222-2−2i−2i2i2i2i2i−2i−2i2-20000000000002i−2i−2i2i000000000000000000000000000000000000
χ692-2-2222-2-2-2-2-2-22222-2-222-2-2222-2-22-2-200000000222-20000-22-222-20000000000000000000000000000000000000000
χ702-2-2222-2-2-2-2-2-22222-2-222-2-2222-2-22-2-20000000022-2200002-22-2-220000000000000000000000000000000000000000
χ712-2-2222-2-2-2-2-2-22222-2-222-2-222-222-22200000000-2-2002i−2i−2i2i0000000000−2i2i2i−2i00000000000000000000000000000000
χ722-2-2222-2-2-2-2-2-22222-2-222-2-222-222-22200000000-2-200−2i2i2i−2i00000000002i−2i−2i2i00000000000000000000000000000000
χ73444-44-4-4-44-44-444-4-400000000000000000000000000000000000000000000000000002-22-22-22-20000000000000000
χ74444-44-4-4-44-44-444-4-40000000000000000000000000000000000000000000000000000-22-22-22-220000000000000000
χ75444-44-4-4-4-44-44-4-44400000000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ76444-44-4-4-4-44-44-4-4440000000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ7744-44-4-44-44i4i−4i−4i4i−4i4i−4i-44-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ7844-44-4-44-4−4i−4i4i4i−4i4i−4i4i-44-444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ7944-4-4-44-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ8044-4-4-44-444i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ8144-4-4-44-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ8244-4-4-44-44−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ834-444-4-4-444i4i−4i−4i−4i4i−4i4i-444-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ844-444-4-4-44−4i−4i4i4i4i−4i4i−4i-444-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ854-44-4-444-44i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ864-44-4-444-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ874-44-4-444-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ884-44-4-444-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ894-4-4-44-4444-44-4-4-44400000000000000000000000000000000000000000000000000002-2-222-2-220000000000000000
χ904-4-4-44-4444-44-4-4-4440000000000000000000000000000000000000000000000000000-222-2-222-20000000000000000
χ914-4-4-44-444-44-4444-4-400000000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ924-4-4-44-444-44-4444-4-40000000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.