Finite Group Databasebeta

← Group #370896

Character table — Group #370896

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222244444444444444444444444444224444444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ9111111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ10111111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ11111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ12111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1
χ171-11-111-1-11-11-1ii−i−i11-1-111-1-1i−iii−i−i1111-1-1-1-11-1i−i1-1i−i11-1-1ii−i−i11-1-1i−ii−iii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ181-11-111-1-11-11-1ii−i−i11-1-111-1-1i−iii−i−i1111-1-1-1-11-1i−i1-1i−i11-1-1ii−i−i-1-111i−ii−i−i−iii-1-111−i−iii-1-111−i−iii-11−ii
χ191-11-111-1-11-11-1ii−i−i11-1-111-1-1i−iii−i−i1111-1-1-1-1-11i−i-11−ii-1-111−i−iii11-1-1i−i−iiii−i−i-1-111−i−iii11-1-1ii−i−i-11−ii
χ201-11-111-1-11-11-1ii−i−i11-1-111-1-1i−iii−i−i1111-1-1-1-1-11i−i-11−ii-1-111−i−iii-1-111i−i−ii−i−iii11-1-1ii−i−i-1-111−i−iii1-1i−i
χ211-11-111-1-11-11-1ii−i−i11-1-111-1-1i−iii−i−i-1-1-1-111111-1−ii1-1i−i-1-111−i−iii11-1-1−iii−iii−i−i-1-111−i−iii-1-111−i−iii1-1i−i
χ221-11-111-1-11-11-1ii−i−i11-1-111-1-1i−iii−i−i-1-1-1-111111-1−ii1-1i−i-1-111−i−iii-1-111−iii−i−i−iii11-1-1ii−i−i11-1-1ii−i−i-11−ii
χ231-11-111-1-11-11-1ii−i−i11-1-111-1-1i−iii−i−i-1-1-1-11111-11−ii-11−ii11-1-1ii−i−i11-1-1−ii−iiii−i−i11-1-1ii−i−i-1-111−i−iii-11−ii
χ241-11-111-1-11-11-1ii−i−i11-1-111-1-1i−iii−i−i-1-1-1-11111-11−ii-11−ii11-1-1ii−i−i-1-111−ii−ii−i−iii-1-111−i−iii11-1-1ii−i−i1-1i−i
χ251-11-111-1-11-11-1−i−iii11-1-111-1-1−ii−i−iii1111-1-1-1-11-1−ii1-1−ii11-1-1−i−iii11-1-1−ii−ii−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ261-11-111-1-11-11-1−i−iii11-1-111-1-1−ii−i−iii1111-1-1-1-11-1−ii1-1−ii11-1-1−i−iii-1-111−ii−iiii−i−i-1-111ii−i−i-1-111ii−i−i-11i−i
χ271-11-111-1-11-11-1−i−iii11-1-111-1-1−ii−i−iii1111-1-1-1-1-11−ii-11i−i-1-111ii−i−i11-1-1−iii−i−i−iii-1-111ii−i−i11-1-1−i−iii-11i−i
χ281-11-111-1-11-11-1−i−iii11-1-111-1-1−ii−i−iii1111-1-1-1-1-11−ii-11i−i-1-111ii−i−i-1-111−iii−iii−i−i11-1-1−i−iii-1-111ii−i−i1-1−ii
χ291-11-111-1-11-11-1−i−iii11-1-111-1-1−ii−i−iii-1-1-1-111111-1i−i1-1−ii-1-111ii−i−i11-1-1i−i−ii−i−iii-1-111ii−i−i-1-111ii−i−i1-1−ii
χ301-11-111-1-11-11-1−i−iii11-1-111-1-1−ii−i−iii-1-1-1-111111-1i−i1-1−ii-1-111ii−i−i-1-111i−i−iiii−i−i11-1-1−i−iii11-1-1−i−iii-11i−i
χ311-11-111-1-11-11-1−i−iii11-1-111-1-1−ii−i−iii-1-1-1-11111-11i−i-11i−i11-1-1−i−iii11-1-1i−ii−i−i−iii11-1-1−i−iii-1-111ii−i−i-11i−i
χ321-11-111-1-11-11-1−i−iii11-1-111-1-1−ii−i−iii-1-1-1-11111-11i−i-11i−i11-1-1−i−iii-1-111i−ii−iii−i−i-1-111ii−i−i11-1-1−i−iii1-1−ii
χ332222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002-22-22-22-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-22-22-22-2200000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002-22-2-22-2200000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-22-222-22-200000000000000000000000000000000
χ3722222222-2-2-2-222222-22-22-22-2-2-22-22-2000000002200-2-2-2-20000000000000022000000000000000000000000
χ3822222222-2-2-2-222222-22-22-22-2-2-22-22-200000000-2-200222200000000000000-2-2000000000000000000000000
χ3922222222-2-2-2-22222-22-22-22-22-2-2-22-2222-2-222-2-200220000000000000000-2-200000000000000000000000000
χ4022222222-2-2-2-22222-22-22-22-22-2-2-22-22-2-222-2-22200-2-200000000000000002200000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22-22-22-22-222-22-22000000002200-2-22200000000000000-2-2000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-22-22-22-22-222-22-2200000000-2-20022-2-20000000000000022000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-22-22-22-22222-22-222-2-222-2-200-2-200000000000000002200000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-22-22-22-22222-22-2-2-222-2-22200220000000000000000-2-200000000000000000000000000
χ45222-2-2-22-22-2-220000-2-22-222-220000002i−2i2i−2i2i−2i2i−2i0000000000000000000000002i−2i2i−2i0000000000002-22-20000
χ46222-2-2-22-22-2-220000-2-22-222-220000002i−2i2i−2i2i−2i2i−2i000000000000000000000000−2i2i−2i2i000000000000-22-220000
χ47222-2-2-22-22-2-220000-2-22-222-22000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002i−2i2i−2i000000000000-22-220000
χ48222-2-2-22-22-2-220000-2-22-222-22000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2i2i−2i2i0000000000002-22-20000
χ49222-2-2-22-2-222-200002-2-2-2-22220000002i−2i−2i2i2i−2i−2i2i00000000000000002i−2i2i−2i00000000000000002-22-200000000
χ50222-2-2-22-2-222-200002-2-2-2-22220000002i−2i−2i2i2i−2i−2i2i0000000000000000−2i2i−2i2i0000000000000000-22-2200000000
χ51222-2-2-22-2-222-200002-2-2-2-2222000000−2i2i2i−2i−2i2i2i−2i00000000000000002i−2i2i−2i0000000000000000-22-2200000000
χ52222-2-2-22-2-222-200002-2-2-2-2222000000−2i2i2i−2i−2i2i2i−2i0000000000000000−2i2i−2i2i00000000000000002-22-200000000
χ532-222-2-2-2222-2-20000-2-2-22222-20000002i−2i2i−2i−2i2i−2i2i0000000000000000000000002-2-22000000000000−2i2i2i−2i0000
χ542-222-2-2-2222-2-20000-2-2-22222-20000002i−2i2i−2i−2i2i−2i2i000000000000000000000000-222-20000000000002i−2i−2i2i0000
χ552-222-2-2-2222-2-20000-2-2-22222-2000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000002-2-220000000000002i−2i−2i2i0000
χ562-222-2-2-2222-2-20000-2-2-22222-2000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000-222-2000000000000−2i2i2i−2i0000
χ572-222-2-2-22-2-22200002-222-22-2-20000002i−2i−2i2i−2i2i2i−2i00000000000000002i−2i−2i2i00000000000000002-2-2200000000
χ582-222-2-2-22-2-22200002-222-22-2-20000002i−2i−2i2i−2i2i2i−2i0000000000000000−2i2i2i−2i0000000000000000-222-200000000
χ592-222-2-2-22-2-22200002-222-22-2-2000000−2i2i2i−2i2i−2i−2i2i00000000000000002i−2i−2i2i0000000000000000-222-200000000
χ602-222-2-2-22-2-22200002-222-22-2-2000000−2i2i2i−2i2i−2i−2i2i0000000000000000−2i2i2i−2i00000000000000002-2-2200000000
χ612-22-222-2-22-22-22i2i−2i−2i-2-222-2-2222i−2i−2i−2i2i2i00000000000000002-2-222i−2i−2i2i00000000000000000000000000000000
χ622-22-222-2-22-22-22i2i−2i−2i-2-222-2-2222i−2i−2i−2i2i2i0000000000000000-222-2−2i2i2i−2i00000000000000000000000000000000
χ632-22-222-2-22-22-2−2i−2i2i2i-2-222-2-222−2i2i2i2i−2i−2i00000000000000002-2-22−2i2i2i−2i00000000000000000000000000000000
χ642-22-222-2-22-22-2−2i−2i2i2i-2-222-2-222−2i2i2i2i−2i−2i0000000000000000-222-22i−2i−2i2i00000000000000000000000000000000
χ652-22-222-2-2-22-222i2i−2i−2i2-2-222-2-22−2i2i2i−2i−2i2i000000002-200-22−2i2i000000000000002i−2i000000000000000000000000
χ662-22-222-2-2-22-222i2i−2i−2i2-2-222-2-22−2i2i2i−2i−2i2i00000000-22002-22i−2i00000000000000−2i2i000000000000000000000000
χ672-22-222-2-2-22-222i2i−2i−2i-222-2-222-2−2i2i−2i2i2i−2i22-2-2-2-222002i−2i0000000000000000−2i2i00000000000000000000000000
χ682-22-222-2-2-22-222i2i−2i−2i-222-2-222-2−2i2i−2i2i2i−2i-2-22222-2-200−2i2i00000000000000002i−2i00000000000000000000000000
χ692-22-222-2-2-22-22−2i−2i2i2i2-2-222-2-222i−2i−2i2i2i−2i000000002-200-222i−2i00000000000000−2i2i000000000000000000000000
χ702-22-222-2-2-22-22−2i−2i2i2i2-2-222-2-222i−2i−2i2i2i−2i00000000-22002-2−2i2i000000000000002i−2i000000000000000000000000
χ712-22-222-2-2-22-22−2i−2i2i2i-222-2-222-22i−2i2i−2i−2i2i22-2-2-2-22200−2i2i00000000000000002i−2i00000000000000000000000000
χ722-22-222-2-2-22-22−2i−2i2i2i-222-2-222-22i−2i2i−2i−2i2i-2-22222-2-2002i−2i0000000000000000−2i2i00000000000000000000000000
χ73444-4-4-44-44-4-44000044-44-4-44-400000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-44-4-444-40000-44444-4-4-400000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-4-4400004-44-4000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ7644-4-44-4-4400004-44-400000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ7744-4-44-4-440000-44-44000000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ7844-4-44-4-440000-44-4400000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ794-444-4-4-4444-4-40000444-4-4-4-4400000000000000000000000000000000000000000000000000000000000000
χ804-444-4-4-44-4-4440000-44-4-44-44400000000000000000000000000000000000000000000000000000000000000
χ814-4-444-44-400004i−4i−4i4i000000000000000000000000000000000000000000000000002i−2i−2i2i-222-2000000000000
χ824-4-444-44-400004i−4i−4i4i00000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-22000000000000
χ834-4-444-44-40000−4i4i4i−4i000000000000000000000000000000000000000000000000002i−2i−2i2i2-2-22000000000000
χ844-4-444-44-40000−4i4i4i−4i00000000000000000000000000000000000000000000000000−2i2i2i−2i-222-2000000000000
χ8588-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000000000000000

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