Finite Group Databasebeta

← Group #370820

Character table — Group #370820

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444444444488888888888888884444444444444444888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ1011111111111111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-111
χ1211111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1
χ1311111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-111
χ1411111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1
χ1511111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ1611111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111111111-1-1-1-111-1-1-1-111
χ171-111-1-1-1111-1-11-1ii−i−i11-1-11-1ii−i−ii−i1111-1-1-1-111-1-1ii−i−i1-1i−iii−i−ii−i1-111-1-11-1ii−i−iii−i−ii−i11-1-1i−i1-1i−i1-1
χ181-111-1-1-1111-1-11-1ii−i−i11-1-11-1ii−i−ii−i1111-1-1-1-111-1-1ii−i−i1-1i−i−i−iiii−i1-1-1-1111-1−i−iiiii−i−ii−i-1-111−ii-11−ii-11
χ191-111-1-1-1111-1-11-1ii−i−i11-1-11-1ii−i−ii−i1111-1-1-1-1-1-111−i−iii-11−iiii−i−i−ii-1111-1-1-11ii−i−iii−i−i−ii11-1-1−ii-11−ii-11
χ201-111-1-1-1111-1-11-1ii−i−i11-1-11-1ii−i−ii−i1111-1-1-1-1-1-111−i−iii-11−ii−i−iii−ii-11-1-111-11−i−iiiii−i−i−ii-1-111i−i1-1i−i1-1
χ211-111-1-1-1111-1-11-1ii−i−i11-1-11-1ii−i−ii−i-1-1-1-1111111-1-1ii−i−i-11−iiii−i−i−ii-1111-1-11-1−i−iii−i−iiii−i-1-111i−i1-1−ii-11
χ221-111-1-1-1111-1-11-1ii−i−i11-1-11-1ii−i−ii−i-1-1-1-1111111-1-1ii−i−i-11−ii−i−iii−ii-11-1-1111-1ii−i−i−i−iiii−i11-1-1−ii-11i−i1-1
χ231-111-1-1-1111-1-11-1ii−i−i11-1-11-1ii−i−ii−i-1-1-1-11111-1-111−i−iii1-1i−iii−i−ii−i1-111-1-1-11−i−iii−i−iii−ii-1-111−ii-11i−i1-1
χ241-111-1-1-1111-1-11-1ii−i−i11-1-11-1ii−i−ii−i-1-1-1-11111-1-111−i−iii1-1i−i−i−iiii−i1-1-1-111-11ii−i−i−i−iii−ii11-1-1i−i1-1−ii-11
χ251-111-1-1-1111-1-11-1−i−iii11-1-11-1−i−iii−ii1111-1-1-1-111-1-1−i−iii1-1−iiii−i−i−ii1-1-1-1111-1ii−i−i−i−iii−ii-1-111i−i-11i−i-11
χ261-111-1-1-1111-1-11-1−i−iii11-1-11-1−i−iii−ii1111-1-1-1-111-1-1−i−iii1-1−ii−i−iii−ii1-111-1-11-1−i−iii−i−iii−ii11-1-1−ii1-1−ii1-1
χ271-111-1-1-1111-1-11-1−i−iii11-1-11-1−i−iii−ii1111-1-1-1-1-1-111ii−i−i-11i−iii−i−ii−i-11-1-111-11ii−i−i−i−iiii−i-1-111−ii1-1−ii1-1
χ281-111-1-1-1111-1-11-1−i−iii11-1-11-1−i−iii−ii1111-1-1-1-1-1-111ii−i−i-11i−i−i−iiii−i-1111-1-1-11−i−iii−i−iiii−i11-1-1i−i-11i−i-11
χ291-111-1-1-1111-1-11-1−i−iii11-1-11-1−i−iii−ii-1-1-1-1111111-1-1−i−iii-11i−iii−i−ii−i-11-1-1111-1−i−iiiii−i−i−ii11-1-1i−i-11−ii1-1
χ301-111-1-1-1111-1-11-1−i−iii11-1-11-1−i−iii−ii-1-1-1-1111111-1-1−i−iii-11i−i−i−iiii−i-1111-1-11-1ii−i−iii−i−i−ii-1-111−ii1-1i−i-11
χ311-111-1-1-1111-1-11-1−i−iii11-1-11-1−i−iii−ii-1-1-1-11111-1-111ii−i−i1-1−iiii−i−i−ii1-1-1-111-11−i−iiiii−i−ii−i11-1-1−ii1-1i−i-11
χ321-111-1-1-1111-1-11-1−i−iii11-1-11-1−i−iii−ii-1-1-1-11111-1-111ii−i−i1-1−ii−i−iii−ii1-111-1-1-11ii−i−iii−i−ii−i-1-111i−i-11−ii1-1
χ33222222222222-2-22222-2-2-2-2-2-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000002i−2i2i−2i00000000000000
χ34222222222222-2-22222-2-2-2-2-2-2-2-2-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000−2i2i−2i2i00000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000−2i2i−2i2i00000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000002i−2i2i−2i00000000000000
χ3722222222-2-2-2-22-22222-2-2222-22-22-2-2-2000000000000000022220000-2-2-2-20000000000000000000000000000
χ3822222222-2-2-2-22-22222-2-2222-22-22-2-2-20000000000000000-2-2-2-2000022220000000000000000000000000000
χ3922222222-2-2-2-22-2-2-2-2-2-2-2222-2-22-2222000000000000000022-2-2000022-2-20000000000000000000000000000
χ4022222222-2-2-2-22-2-2-2-2-2-2-2222-2-22-22220000000000000000-2-2220000-2-2220000000000000000000000000000
χ4122222222-2-2-2-2-22222222-2-2-22-22-22-2-200000000222222220000000000000000-2-200000000-2-2000000000000
χ4222222222-2-2-2-2-22222222-2-2-22-22-22-2-200000000-2-2-2-2-2-2-2-20000000000000000220000000022000000000000
χ4322222222-2-2-2-2-22-2-2-2-222-2-2-222-22-222000000002222-2-2-2-20000000000000000-2-20000000022000000000000
χ4422222222-2-2-2-2-22-2-2-2-222-2-2-222-22-22200000000-2-2-2-2222200000000000000002200000000-2-2000000000000
χ45222-22-2-2-22-22-22200002-22-2-2-20000002-22-22-22-20000000000002-22-200000000002-22-2000000000000000000
χ46222-22-2-2-22-22-22200002-22-2-2-20000002-22-22-22-2000000000000-22-220000000000-22-22000000000000000000
χ47222-22-2-2-22-22-22200002-22-2-2-2000000-22-22-22-220000000000002-22-20000000000-22-22000000000000000000
χ48222-22-2-2-22-22-22200002-22-2-2-2000000-22-22-22-22000000000000-22-2200000000002-22-2000000000000000000
χ49222-22-2-2-22-22-2-2-20000-22-22220000002i−2i−2i2i2i−2i−2i2i000000000000000000002i−2i2i−2i0000000000002-22-200000000
χ50222-22-2-2-22-22-2-2-20000-22-22220000002i−2i−2i2i2i−2i−2i2i00000000000000000000−2i2i−2i2i000000000000-22-2200000000
χ51222-22-2-2-22-22-2-2-20000-22-2222000000−2i2i2i−2i−2i2i2i−2i000000000000000000002i−2i2i−2i000000000000-22-2200000000
χ52222-22-2-2-22-22-2-2-20000-22-2222000000−2i2i2i−2i−2i2i2i−2i00000000000000000000−2i2i−2i2i0000000000002-22-200000000
χ532-222-2-2-2222-2-2-222i2i−2i−2i-2-222-22−2i−2i2i2i2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000-222-200000000000000
χ542-222-2-2-2222-2-2-222i2i−2i−2i-2-222-22−2i−2i2i2i2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000002-2-2200000000000000
χ552-222-2-2-2222-2-2-22−2i−2i2i2i-2-222-222i2i−2i−2i−2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000002-2-2200000000000000
χ562-222-2-2-2222-2-2-22−2i−2i2i2i-2-222-222i2i−2i−2i−2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000-222-200000000000000
χ572-222-2-2-22-2-222222i2i−2i−2i-2-2-2-2222i−2i−2i2i−2i2i00000000000000002-22i−2i0000−2i2i-220000000000000000000000000000
χ582-222-2-2-22-2-222222i2i−2i−2i-2-2-2-2222i−2i−2i2i−2i2i0000000000000000-22−2i2i00002i−2i2-20000000000000000000000000000
χ592-222-2-2-22-2-22222−2i−2i2i2i-2-2-2-222−2i2i2i−2i2i−2i00000000000000002-2−2i2i00002i−2i-220000000000000000000000000000
χ602-222-2-2-22-2-22222−2i−2i2i2i-2-2-2-222−2i2i2i−2i2i−2i0000000000000000-222i−2i0000−2i2i2-20000000000000000000000000000
χ612-222-2-2-22-2-222-2-22i2i−2i−2i2222-2-2−2i2i2i−2i−2i2i0000000022-2-22i2i−2i−2i0000000000000000-2200000000−2i2i000000000000
χ622-222-2-2-22-2-222-2-22i2i−2i−2i2222-2-2−2i2i2i−2i−2i2i00000000-2-222−2i−2i2i2i00000000000000002-2000000002i−2i000000000000
χ632-222-2-2-22-2-222-2-2−2i−2i2i2i2222-2-22i−2i−2i2i2i−2i0000000022-2-2−2i−2i2i2i0000000000000000-22000000002i−2i000000000000
χ642-222-2-2-22-2-222-2-2−2i−2i2i2i2222-2-22i−2i−2i2i2i−2i00000000-2-2222i2i−2i−2i00000000000000002-200000000−2i2i000000000000
χ652-22-2-222-22-2-222-200002-2-22-220000002-22-2-22-220000000000002i−2i−2i2i00000000002i−2i−2i2i000000000000000000
χ662-22-2-222-22-2-222-200002-2-22-220000002-22-2-22-22000000000000−2i2i2i−2i0000000000−2i2i2i−2i000000000000000000
χ672-22-2-222-22-2-222-200002-2-22-22000000-22-222-22-20000000000002i−2i−2i2i0000000000−2i2i2i−2i000000000000000000
χ682-22-2-222-22-2-222-200002-2-22-22000000-22-222-22-2000000000000−2i2i2i−2i00000000002i−2i−2i2i000000000000000000
χ692-22-2-222-22-2-22-220000-222-22-20000002i−2i−2i2i−2i2i2i−2i000000000000000000002i−2i−2i2i0000000000002-2-2200000000
χ702-22-2-222-22-2-22-220000-222-22-20000002i−2i−2i2i−2i2i2i−2i00000000000000000000−2i2i2i−2i000000000000-222-200000000
χ712-22-2-222-22-2-22-220000-222-22-2000000−2i2i2i−2i2i−2i−2i2i000000000000000000002i−2i−2i2i000000000000-222-200000000
χ722-22-2-222-22-2-22-220000-222-22-2000000−2i2i2i−2i2i−2i−2i2i00000000000000000000−2i2i2i−2i0000000000002-2-2200000000
χ73444-44-4-4-4-44-444-40000-444-4-4400000000000000000000000000000000000000000000000000000000000000
χ74444-44-4-4-4-44-44-4400004-4-444-400000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-440000004i−4i4i−4i0000000000000000000022−2222−222i2−2i22i2−2i20000000000000000000000000000000000000000
χ7644-4-4-44-440000004i−4i4i−4i00000000000000000000−2222−2222−2i22i2−2i22i20000000000000000000000000000000000000000
χ7744-4-4-44-44000000−4i4i−4i4i0000000000000000000022−2222−22−2i22i2−2i22i20000000000000000000000000000000000000000
χ7844-4-4-44-44000000−4i4i−4i4i00000000000000000000−2222−22222i2−2i22i2−2i20000000000000000000000000000000000000000
χ794-44-4-444-4-444-4440000-44-44-4-400000000000000000000000000000000000000000000000000000000000000
χ804-44-4-444-4-444-4-4-400004-44-44400000000000000000000000000000000000000000000000000000000000000
χ814-4-4-44-4440000004-4-440000000000000000000022−22−222222−22−22220000000000000000000000000000000000000000
χ824-4-4-44-4440000004-4-4400000000000000000000−222222−22−222222−220000000000000000000000000000000000000000
χ834-4-4-44-444000000-444-40000000000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ844-4-4-44-444000000-444-400000000000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ8588-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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