Finite Group Databasebeta

← Group #197749

Character table — Group #197749

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444444444488888888888888882222444488888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ911111111-1-1-1-1111-1-1-1-11111111-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ1011111111-1-1-1-1111-1-1-1-11111111-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1111111111-1-1-1-1111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1211111111-1-1-1-1111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ1311111111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1411111111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ1511111111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ1611111111-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ171-1-1-111-1111-1-111111-1-1-1-1-11-11-111-1-1ii−i−iii−i−iiiii−i−i−i−i1-11-11-11-1i−ii−iii−i−iii−i−i11-1-111-1-1ii−i−i1-1i−ii−i1-1
χ181-1-1-111-1111-1-111111-1-1-1-1-11-11-111-1-1ii−i−iii−i−iiiii−i−i−i−i1-11-11-11-1i−ii−i−i−iii−i−iii-1-111-1-111ii−i−i-11−ii−ii-11
χ191-1-1-111-1111-1-111111-1-1-1-1-11-11-111-1-1ii−i−iii−i−i−i−i−i−iiiii-11-11-11-11i−ii−iii−i−iii−i−i11-1-111-1-1−i−iii-11−ii−ii-11
χ201-1-1-111-1111-1-111111-1-1-1-1-11-11-111-1-1ii−i−iii−i−i−i−i−i−iiiii-11-11-11-11i−ii−i−i−iii−i−iii-1-111-1-111−i−iii1-1i−ii−i1-1
χ211-1-1-111-1111-1-111111-1-1-1-1-11-11-111-1-1−i−iii−i−iiiiiii−i−i−i−i-11-11-11-11−ii−iiii−i−iii−i−i-1-111-1-111ii−i−i1-1−ii−ii1-1
χ221-1-1-111-1111-1-111111-1-1-1-1-11-11-111-1-1−i−iii−i−iiiiiii−i−i−i−i-11-11-11-11−ii−ii−i−iii−i−iii11-1-111-1-1ii−i−i-11i−ii−i-11
χ231-1-1-111-1111-1-111111-1-1-1-1-11-11-111-1-1−i−iii−i−iii−i−i−i−iiiii1-11-11-11-1−ii−iiii−i−iii−i−i-1-111-1-111−i−iii-11i−ii−i-11
χ241-1-1-111-1111-1-111111-1-1-1-1-11-11-111-1-1−i−iii−i−iii−i−i−i−iiiii1-11-11-11-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii1-1−ii−ii1-1
χ251-1-1-111-11-1-111111-1-111-1-1-11-11-1-1-111ii−i−i−i−iiiiiii−i−i−i−i1-1-111-1-11i−i−iiii−i−i−i−iii11-1-1-1-111−i−iii1-1i−i−ii-11
χ261-1-1-111-11-1-111111-1-111-1-1-11-11-1-1-111ii−i−i−i−iiiiiii−i−i−i−i1-1-111-1-11i−i−ii−i−iiiii−i−i-1-11111-1-1−i−iii-11−iii−i1-1
χ271-1-1-111-11-1-111111-1-111-1-1-11-11-1-1-111ii−i−i−i−iii−i−i−i−iiiii-111-1-111-1i−i−iiii−i−i−i−iii11-1-1-1-111ii−i−i-11−iii−i1-1
χ281-1-1-111-11-1-111111-1-111-1-1-11-11-1-1-111ii−i−i−i−iii−i−i−i−iiiii-111-1-111-1i−i−ii−i−iiiii−i−i-1-11111-1-1ii−i−i1-1i−i−ii-11
χ291-1-1-111-11-1-111111-1-111-1-1-11-11-1-1-111−i−iiiii−i−iiiii−i−i−i−i-111-1-111-1−iii−iii−i−i−i−iii-1-11111-1-1−i−iii1-1−iii−i-11
χ301-1-1-111-11-1-111111-1-111-1-1-11-11-1-1-111−i−iiiii−i−iiiii−i−i−i−i-111-1-111-1−iii−i−i−iiiii−i−i11-1-1-1-111−i−iii-11i−i−ii1-1
χ311-1-1-111-11-1-111111-1-111-1-1-11-11-1-1-111−i−iiiii−i−i−i−i−i−iiiii1-1-111-1-11−iii−iii−i−i−i−iii-1-11111-1-1ii−i−i-11i−i−ii1-1
χ321-1-1-111-11-1-111111-1-111-1-1-11-11-1-1-111−i−iiiii−i−i−i−i−i−iiiii1-1-111-1-11−iii−i−i−iiiii−i−i11-1-1-1-111ii−i−i1-1−iii−i-11
χ332222222222222-2-2-2-2-2-222-22-2-2-22-22-2000000000000000022-2-2-2-22200000000000000000000000000000000
χ342222222222222-2-2-2-2-2-222-22-2-2-22-22-20000000000000000-2-22222-2-200000000000000000000000000000000
χ35222222222222-2222222-2-22-22-2-2-2-2-2-2222222220000000000000000-2-2-2-20000000000000000000000000000
χ36222222222222-2222222-2-22-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-222-22-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000002i−2i2i−2i00000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-222-22-2200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2i2i−2i2i00000000
χ3922222222-2-2-2-22-2-2222222-22-2-2-2-22-2200000000000000002222-2-2-2-200000000000000000000000000000000
χ4022222222-2-2-2-22-2-2222222-22-2-2-2-22-220000000000000000-2-2-2-2222200000000000000000000000000000000
χ4122222222-2-2-2-2-222-2-2-2-2-2-22-22-2-222222222-2-2-2-20000000000000000-2-2220000000000000000000000000000
χ4222222222-2-2-2-2-222-2-2-2-2-2-22-22-2-22222-2-2-2-22222000000000000000022-2-20000000000000000000000000000
χ4322222222-2-2-2-2-2-2-22222-2-2-2-2-2222-22-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i−2i2i00000000
χ4422222222-2-2-2-2-2-2-22222-2-2-2-2-2222-22-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002i−2i2i−2i00000000
χ45222-2-2-2-222-22-202-22-22-20020-20000002i−2i2i−2i2i−2i2i−2i00000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ46222-2-2-2-222-22-202-22-22-20020-20000002i−2i2i−2i2i−2i2i−2i00000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ47222-2-2-2-222-22-202-22-22-20020-2000000−2i2i−2i2i−2i2i−2i2i00000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ48222-2-2-2-222-22-202-22-22-20020-2000000−2i2i−2i2i−2i2i−2i2i00000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ49222-2-2-2-22-22-2202-2-22-220020-20000002i−2i2i−2i−2i2i−2i2i00000000000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ50222-2-2-2-22-22-2202-2-22-220020-20000002i−2i2i−2i−2i2i−2i2i00000000000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ51222-2-2-2-22-22-2202-2-22-220020-2000000−2i2i−2i2i2i−2i2i−2i00000000000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ52222-2-2-2-22-22-2202-2-22-220020-2000000−2i2i−2i2i2i−2i2i−2i00000000000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ532-2-22-2-2222-2-2202-22-2-2200-2020000002-2-222-2-22000000000000000000002−2−222−2−222−2−222−2−22000000000000
χ542-2-22-2-2222-2-2202-22-2-2200-2020000002-2-222-2-2200000000000000000000−222−2−222−2−222−2−222−2000000000000
χ552-2-22-2-2222-2-2202-22-2-2200-202000000-222-2-222-2000000000000000000002−2−222−2−22−222−2−222−2000000000000
χ562-2-22-2-2222-2-2202-22-2-2200-202000000-222-2-222-200000000000000000000−222−2−222−22−2−222−2−22000000000000
χ572-2-22-2-222-222-202-2-222-200-2020000002-2-22-222-2000000000000000000002−2−22−222−22−2−22−222−2000000000000
χ582-2-22-2-222-222-202-2-222-200-2020000002-2-22-222-200000000000000000000−222−22−2−22−222−22−2−22000000000000
χ592-2-22-2-222-222-202-2-222-200-202000000-222-22-2-22000000000000000000002−2−22−222−2−222−22−2−22000000000000
χ602-2-22-2-222-222-202-2-222-200-202000000-222-22-2-2200000000000000000000−222−22−2−222−2−22−222−2000000000000
χ612-2-2-222-2222-2-22-2-2-2-222-2-2222-222-2-2200000000000000002-2-22-222-200000000000000000000000000000000
χ622-2-2-222-2222-2-22-2-2-2-222-2-2222-222-2-220000000000000000-222-22-2-2200000000000000000000000000000000
χ632-2-2-222-2222-2-2-22222-2-222-2-2-2-22-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i−2i2i0000000000000000000000000000
χ642-2-2-222-2222-2-2-22222-2-222-2-2-2-22-2-222−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i2i−2i0000000000000000000000000000
χ652-2-2-222-2222-2-2-2-2-2-2-222222-222-2-222-20000000022-2-2-2-22200000000000000000000000000002-2-2200000000
χ662-2-2-222-2222-2-2-2-2-2-2-222222-222-2-222-200000000-2-22222-2-20000000000000000000000000000-222-200000000
χ672-2-2-222-22-2-2222-2-222-2-2-2-2222-22-222-200000000000000002-22-2-22-2200000000000000000000000000000000
χ682-2-2-222-22-2-2222-2-222-2-2-2-2222-22-222-20000000000000000-22-222-22-200000000000000000000000000000000
χ692-2-2-222-22-2-222-222-2-22222-2-2-2-2222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i0000000000000000000000000000
χ702-2-2-222-22-2-222-222-2-22222-2-2-2-2222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i0000000000000000000000000000
χ712-2-2-222-22-2-222-2-2-222-2-2222-222-22-2-220000000022-2-2-2-2220000000000000000000000000000-222-200000000
χ722-2-2-222-22-2-222-2-2-222-2-2222-222-22-2-2200000000-2-22222-2-200000000000000000000000000002-2-2200000000
χ73444-4-4-4-444-44-40-44-44-4400-40400000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-44-44-440-444-44-400-40400000000000000000000000000000000000000000000000000000000000000
χ7544-444-4-4-4000040000004-40-400000000000000022−2222−2222−2222−220000000000000000000000000000000000000000
χ7644-444-4-4-4000040000004-40-4000000000000000−2222−2222−2222−22220000000000000000000000000000000000000000
χ7744-444-4-4-40000-4000000-44040000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ7844-444-4-4-40000-4000000-4404000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ794-44-44-44-400004000000-440-40000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ804-44-44-44-400004000000-440-4000000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ814-44-44-44-40000-40000004-40400000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ824-44-44-44-40000-40000004-404000000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ834-4-44-4-4444-4-440-44-444-40040-400000000000000000000000000000000000000000000000000000000000000
χ844-4-44-4-444-444-40-444-4-440040-400000000000000000000000000000000000000000000000000000000000000
χ8588-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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