Finite Group Databasebeta

← Group #378098

Character table — Group #378098

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444444444488888888888888884444444444444444888888888888888822448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-11111-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
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
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ1011111111111111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1
χ1211111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111
χ1311111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-11111-1-1
χ1411111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-111
χ1511111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ1611111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-11111-1-1
χ171-111-1-11-111-1-111ii−i−i-1-1-1-111iii−i−i−iiiii−i−i−i−iii−i−i11-1-11-1ii−i−i1-111-1-1ii−i−ii−iii−i−i11-1-11-111-1-11-1i−ii−i1-1
χ181-111-1-11-111-1-111ii−i−i-1-1-1-111iii−i−i−iiiii−i−i−i−iii−i−i11-1-11-1ii−i−i1-1-1-111−i−iiii−i−i−iii11-1-11-1-1-111-11−ii−ii-11
χ191-111-1-11-111-1-111ii−i−i-1-1-1-111iii−i−i−iiiii−i−i−i−i−i−iii-1-111-11−i−iii-1111-1-1ii−i−i−iiii−i−i11-1-1-1111-1-1-11−ii−ii-11
χ201-111-1-11-111-1-111ii−i−i-1-1-1-111iii−i−i−iiiii−i−i−i−i−i−iii-1-111-11−i−iii-11-1-111−i−iii−ii−i−iii11-1-1-11-1-1111-1i−ii−i1-1
χ211-111-1-11-111-1-111ii−i−i-1-1-1-111iii−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11−i−iii-1111-1-1ii−i−ii−i−i−iii-1-1111-1-1-1111-1i−i−ii-11
χ221-111-1-11-111-1-111ii−i−i-1-1-1-111iii−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11−i−iii-11-1-111−i−iiii−iii−i−i-1-1111-111-1-1-11−iii−i1-1
χ231-111-1-11-111-1-111ii−i−i-1-1-1-111iii−i−i−i−i−i−i−iiiii−i−iii-1-1111-1ii−i−i1-111-1-1ii−i−i−ii−i−iii-1-111-11-1-111-11−iii−i1-1
χ241-111-1-11-111-1-111ii−i−i-1-1-1-111iii−i−i−i−i−i−i−iiiii−i−iii-1-1111-1ii−i−i1-1-1-111−i−iii−iiii−i−i-1-111-1111-1-11-1i−i−ii-11
χ251-111-1-11-111-1-111−i−iii-1-1-1-111−i−i−iiiiiiii−i−i−i−iii−i−i-1-1111-1−i−iii1-111-1-1−i−iiii−iii−i−i-1-111-11-1-111-11i−i−ii1-1
χ261-111-1-11-111-1-111−i−iii-1-1-1-111−i−i−iiiiiiii−i−i−i−iii−i−i-1-1111-1−i−iii1-1-1-111ii−i−ii−i−i−iii-1-111-1111-1-11-1−iii−i-11
χ271-111-1-11-111-1-111−i−iii-1-1-1-111−i−i−iiiiiiii−i−i−i−i−i−iii11-1-1-11ii−i−i-1111-1-1−i−iii−iiii−i−i-1-1111-1-1-1111-1−iii−i-11
χ281-111-1-11-111-1-111−i−iii-1-1-1-111−i−i−iiiiiiii−i−i−i−i−i−iii11-1-1-11ii−i−i-11-1-111ii−i−i−ii−i−iii-1-1111-111-1-1-11i−i−ii1-1
χ291-111-1-11-111-1-111−i−iii-1-1-1-111−i−i−iiii−i−i−i−iiiiiii−i−i-1-111-11ii−i−i-1111-1-1−i−iiii−i−i−iii11-1-1-1111-1-1-11i−ii−i-11
χ301-111-1-11-111-1-111−i−iii-1-1-1-111−i−i−iiii−i−i−i−iiiiiii−i−i-1-111-11ii−i−i-11-1-111ii−i−ii−iii−i−i11-1-1-11-1-1111-1−ii−ii1-1
χ311-111-1-11-111-1-111−i−iii-1-1-1-111−i−i−iiii−i−i−i−iiiii−i−iii11-1-11-1−i−iii1-111-1-1−i−iii−ii−i−iii11-1-11-111-1-11-1−ii−ii1-1
χ321-111-1-11-111-1-111−i−iii-1-1-1-111−i−i−iiii−i−i−i−iiiii−i−iii11-1-11-1−i−iii1-1-1-111ii−i−i−iiii−i−i11-1-11-1-1-111-11i−ii−i-11
χ33222222222222-2-22222-2-2-2-2-2-22-2-22-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000002i−2i2i−2i00000000000000
χ34222222222222-2-22222-2-2-2-2-2-22-2-22-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000−2i2i−2i2i00000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000−2i2i−2i2i00000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000002i−2i2i−2i00000000000000
χ3722222222-2-2-2-22-2222222-2-22-2-22-2-22-200000000222222220000000000000000-2-200000000-2-2000000000000
χ3822222222-2-2-2-22-2222222-2-22-2-22-2-22-200000000-2-2-2-2-2-2-2-20000000000000000220000000022000000000000
χ3922222222-2-2-2-22-2-2-2-2-222-2-22-22-222-22000000002222-2-2-2-20000000000000000-2-20000000022000000000000
χ4022222222-2-2-2-22-2-2-2-2-222-2-22-22-222-2200000000-2-2-2-2222200000000000000002200000000-2-2000000000000
χ4122222222-2-2-2-2-222222-2-222-22-2-22-2-220000000000000000222-22-2-2-200000000000000000000000000000000
χ4222222222-2-2-2-2-222222-2-222-22-2-22-2-220000000000000000-2-2-22-222200000000000000000000000000000000
χ4322222222-2-2-2-2-22-2-2-2-2-2-222-2222-222-2000000000000000022-22-22-2-200000000000000000000000000000000
χ4422222222-2-2-2-2-22-2-2-2-2-2-222-2222-222-20000000000000000-2-22-22-22200000000000000000000000000000000
χ45222-2-2-2-222-22-22-200002-22-2-220000002-22-22-22-200000000000000002i−2i2i−2i0000002i−2i2i−2i000000000000000000
χ46222-2-2-2-222-22-22-200002-22-2-220000002-22-22-22-20000000000000000−2i2i−2i2i000000−2i2i−2i2i000000000000000000
χ47222-2-2-2-222-22-22-200002-22-2-22000000-22-22-22-2200000000000000002i−2i2i−2i000000−2i2i−2i2i000000000000000000
χ48222-2-2-2-222-22-22-200002-22-2-22000000-22-22-22-220000000000000000−2i2i−2i2i0000002i−2i2i−2i000000000000000000
χ49222-2-2-2-222-22-2-220000-22-222-20000002i−2i−2i2i2i−2i−2i2i000000000000000000002-22-20000000000002i−2i2i−2i00000000
χ50222-2-2-2-222-22-2-220000-22-222-20000002i−2i−2i2i2i−2i−2i2i00000000000000000000-22-22000000000000−2i2i−2i2i00000000
χ51222-2-2-2-222-22-2-220000-22-222-2000000−2i2i2i−2i−2i2i2i−2i000000000000000000002-22-2000000000000−2i2i−2i2i00000000
χ52222-2-2-2-222-22-2-220000-22-222-2000000−2i2i2i−2i−2i2i2i−2i00000000000000000000-22-220000000000002i−2i2i−2i00000000
χ532-222-2-22-222-2-2-2-22i2i−2i−2i2222-2-22i−2i−2i−2i2i2i22-2-2-2-222000000000000000000000000000000−2i2i2i−2i00000000000000
χ542-222-2-22-222-2-2-2-22i2i−2i−2i2222-2-22i−2i−2i−2i2i2i-2-22222-2-20000000000000000000000000000002i−2i−2i2i00000000000000
χ552-222-2-22-222-2-2-2-2−2i−2i2i2i2222-2-2−2i2i2i2i−2i−2i22-2-2-2-2220000000000000000000000000000002i−2i−2i2i00000000000000
χ562-222-2-22-222-2-2-2-2−2i−2i2i2i2222-2-2−2i2i2i2i−2i−2i-2-22222-2-2000000000000000000000000000000−2i2i2i−2i00000000000000
χ572-222-2-22-2-2-2222-22i2i−2i−2i-2-2222-2−2i2i−2i2i−2i2i000000002i2i−2i−2i22-2-20000000000000000−2i2i00000000-22000000000000
χ582-222-2-22-2-2-2222-22i2i−2i−2i-2-2222-2−2i2i−2i2i−2i2i00000000−2i−2i2i2i-2-22200000000000000002i−2i000000002-2000000000000
χ592-222-2-22-2-2-2222-2−2i−2i2i2i-2-2222-22i−2i2i−2i2i−2i000000002i2i−2i−2i-2-2220000000000000000−2i2i000000002-2000000000000
χ602-222-2-22-2-2-2222-2−2i−2i2i2i-2-2222-22i−2i2i−2i2i−2i00000000−2i−2i2i2i22-2-200000000000000002i−2i00000000-22000000000000
χ612-222-2-22-2-2-222-222i2i−2i−2i22-2-2-22−2i−2i2i2i2i−2i00000000000000002-22i−2i−2i2i-2200000000000000000000000000000000
χ622-222-2-22-2-2-222-222i2i−2i−2i22-2-2-22−2i−2i2i2i2i−2i0000000000000000-22−2i2i2i−2i2-200000000000000000000000000000000
χ632-222-2-22-2-2-222-22−2i−2i2i2i22-2-2-222i2i−2i−2i−2i2i00000000000000002-2−2i2i2i−2i-2200000000000000000000000000000000
χ642-222-2-22-2-2-222-22−2i−2i2i2i22-2-2-222i2i−2i−2i−2i2i0000000000000000-222i−2i−2i2i2-200000000000000000000000000000000
χ652-22-222-2-22-2-222-20000-22-22-220000002i−2i2i−2i−2i2i−2i2i00000000000000002i−2i−2i2i000000-222-2000000000000000000
χ662-22-222-2-22-2-222-20000-22-22-220000002i−2i2i−2i−2i2i−2i2i0000000000000000−2i2i2i−2i0000002-2-22000000000000000000
χ672-22-222-2-22-2-222-20000-22-22-22000000−2i2i−2i2i2i−2i2i−2i00000000000000002i−2i−2i2i0000002-2-22000000000000000000
χ682-22-222-2-22-2-222-20000-22-22-22000000−2i2i−2i2i2i−2i2i−2i0000000000000000−2i2i2i−2i000000-222-2000000000000000000
χ692-22-222-2-22-2-22-2200002-22-22-20000002-2-22-222-2000000000000000000002i−2i−2i2i000000000000−2i2i2i−2i00000000
χ702-22-222-2-22-2-22-2200002-22-22-20000002-2-22-222-200000000000000000000−2i2i2i−2i0000000000002i−2i−2i2i00000000
χ712-22-222-2-22-2-22-2200002-22-22-2000000-222-22-2-22000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i00000000
χ722-22-222-2-22-2-22-2200002-22-22-2000000-222-22-2-2200000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i00000000
χ73444-4-4-4-44-44-444400004-4-44-4-400000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-44-44-44-4-40000-444-44400000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-44-40000004i−4i4i−4i000000000000000000002i2−2i22i2−2i222−2222−220000000000000000000000000000000000000000
χ7644-4-44-44-40000004i−4i4i−4i00000000000000000000−2i22i2−2i22i2−2222−22220000000000000000000000000000000000000000
χ7744-4-44-44-4000000−4i4i−4i4i000000000000000000002i2−2i22i2−2i2−2222−22220000000000000000000000000000000000000000
χ7844-4-44-44-4000000−4i4i−4i4i00000000000000000000−2i22i2−2i22i222−2222−220000000000000000000000000000000000000000
χ794-44-444-4-4-444-4440000-444-4-4-400000000000000000000000000000000000000000000000000000000000000
χ804-44-444-4-4-444-4-4-400004-4-444400000000000000000000000000000000000000000000000000000000000000
χ814-4-4-4-44440000004-4-440000000000000000000022−22−222222−22−22220000000000000000000000000000000000000000
χ824-4-4-4-44440000004-4-4400000000000000000000−222222−22−222222−220000000000000000000000000000000000000000
χ834-4-4-4-4444000000-444-40000000000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ844-4-4-4-4444000000-444-400000000000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ8588-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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