Finite Group Databasebeta

← Group #106947

Character table — Group #106947

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222244444444444444444444444444224444444444444444444444444488888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ511111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i
χ171-1111-1-1-111-1-111-1-1111-1-1-11-111-1-1-111-1-111-1-111-11-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-111-1-1i−ii−i
χ181-1111-1-1-111-1-111-1-1111-1-1-11-111-1-1-111-1-111-1-111-11-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111-1-111-1-111−ii−ii
χ191-1111-1-1-111-1-111-1-1111-1-1-11-111-1-1-111-1-111-1-111-11-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111-1-111-1-111i−ii−i
χ201-1111-1-1-111-1-111-1-1111-1-1-11-111-1-1-111-1-111-1-111-11-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-111-1-1−ii−ii
χ211-1111-1-1-111-1-111-1-1111-1-1-11-111-1-1-1-1-111-1-1111-11-11ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i-1-111-1-11111-1-111-1-1−ii−ii
χ221-1111-1-1-111-1-111-1-1111-1-1-11-111-1-1-1-1-111-1-1111-11-11ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii11-1-111-1-1-1-111-1-111i−ii−i
χ231-1111-1-1-111-1-111-1-1111-1-1-11-111-1-1-1-1-111-1-1111-11-11−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i11-1-111-1-1-1-111-1-111−ii−ii
χ241-1111-1-1-111-1-111-1-1111-1-1-11-111-1-1-1-1-111-1-1111-11-11−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii-1-111-1-11111-1-111-1-1i−ii−i
χ251-1111-1-1-1-1-11111-1-1-1-1-1111-1111-1-1111-1-1-1-111-11-1-11ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ261-1111-1-1-1-1-11111-1-1-1-1-1111-1111-1-1111-1-1-1-111-11-1-11ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii-111-1
χ271-1111-1-1-1-1-11111-1-1-1-1-1111-1111-1-1111-1-1-1-111-11-1-11−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ281-1111-1-1-1-1-11111-1-1-1-1-1111-1111-1-1111-1-1-1-111-11-1-11−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i-111-1
χ291-1111-1-1-1-1-11111-1-1-1-1-1111-1111-1-11-1-11111-1-1-1-111-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i-111-1
χ301-1111-1-1-1-1-11111-1-1-1-1-1111-1111-1-11-1-11111-1-1-1-111-1ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii1-1-11
χ311-1111-1-1-1-1-11111-1-1-1-1-1111-1111-1-11-1-11111-1-1-1-111-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−iii−i−i−i−iii-111-1
χ321-1111-1-1-1-1-11111-1-1-1-1-1111-1111-1-11-1-11111-1-1-1-111-1−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i1-1-11
χ33222222222222222222-22-2-2-22-2-2-2-2-222222222-2-2-2-2-200000000000000000000000000000000000000000000
χ34222222222222222222-22-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-22-2222-22-22-2-200000000-20000000000002-22-22-22-20000000000000000000000000000
χ36222222222222-2-2-2-2-2-22-2222-22-22-2-200000000-2000000000000-22-22-22-220000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22-22200000000200002-22-22-22-2000000000000000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22-2220000000020000-22-22-22-22000000000000000000000000000000000000
χ3922222222-2-2-2-22222-2-22-2222-2-2-2-2-222222-2-2-2-22-2-22200000000000000000000000000000000000000000000
χ4022222222-2-2-2-22222-2-22-2222-2-2-2-2-22-2-2-2-22222222-2-200000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-222222222-22-22-200000000-200002-22-2-22-22000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-222222222-22-22-200000000-20000-22-222-22-2000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-222-22-2-2-222-22-220000000020000000000002-22-2-22-220000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-222-22-2-2-222-22-22000000002000000000000-22-222-22-20000000000000000000000000000
χ45222-2-2-2-222-22-22-22-22-20-20002000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−20000
χ46222-2-2-2-222-22-22-22-22-20-20002000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−220000
χ47222-2-2-2-222-22-22-22-22-20-2000200000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−220000
χ48222-2-2-2-222-22-22-22-22-20-2000200000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−20000
χ49222-2-2-2-22-22-222-22-2-2202000-2000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000
χ50222-2-2-2-22-22-222-22-2-2202000-2000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i20000
χ51222-2-2-2-22-22-222-22-2-2202000-200000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000
χ52222-2-2-2-22-22-222-22-2-2202000-200000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i20000
χ532-2222-2-2-222-2-222-2-222-2-222-2-2-2-222222-2-222-2-2-2-22-2200000000000000000000000000000000000000000000
χ542-2222-2-2-222-2-222-2-222-2-222-2-2-2-2222-2-222-2-222-22-22-200000000000000000000000000000000000000000000
χ552-2222-2-2-222-2-2-2-222-2-222-2-2222-2-22200000000-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ562-2222-2-2-222-2-2-2-222-2-222-2-2222-2-22200000000-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ572-2222-2-2-222-2-2-2-222-2-2-2222-22-222-2-200000000200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ582-2222-2-2-222-2-2-2-222-2-2-2222-22-222-2-20000000020000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ592-2222-2-2-2-2-22222-2-2-2-222-2-222-2-222-222-2-2-2-2222-222-200000000000000000000000000000000000000000000
χ602-2222-2-2-2-2-22222-2-2-2-222-2-222-2-222-2-2-22222-2-222-2-2200000000000000000000000000000000000000000000
χ612-2222-2-2-2-2-222-2-222222-2-2-22-2-222-2200000000-200002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ622-2222-2-2-2-2-222-2-222222-2-2-22-2-222-2200000000-20000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ632-2222-2-2-2-2-222-2-22222-2-222-2-22-2-22-20000000020000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ642-2222-2-2-2-2-222-2-22222-2-222-2-22-2-22-2000000002000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ652-22-2-222-22-2-222-2-222-202000-2000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000i2−i2−i2i2i2−i2−i2i22−2−222−2−220000
χ662-22-2-222-22-2-222-2-222-202000-2000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−222−2−222−20000
χ672-22-2-222-22-2-222-2-222-202000-200000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−222−2−222−20000
χ682-22-2-222-22-2-222-2-222-202000-200000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000−i2i2i2−i2−i2i2i2−i22−2−222−2−220000
χ692-22-2-222-2-222-22-2-22-220-20002000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i20000
χ702-22-2-222-2-222-22-2-22-220-20002000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000−222−22−2−22i2−i2−i2i2−i2i2i2−i20000
χ712-22-2-222-2-222-22-2-22-220-2000200000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i20000
χ722-22-2-222-2-222-22-2-22-220-2000200000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000−222−22−2−22−i2i2i2−i2i2−i2−i2i20000
χ73444-4-4-4-444-44-4-44-44-4404000-400000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-44-44-44-44-444-40-4000400000000000000000000000000000000000000000000000000000000000000
χ7544-44-44-4-40000000000404-4-4000000000000000000000000000000000002-22-22-22-200000000000000000000
χ7644-44-44-4-40000000000404-4-400000000000000000000000000000000000-22-22-22-2200000000000000000000
χ7744-44-44-4-40000000000-40-444000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ7844-44-44-4-40000000000-40-44400000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ794-44-4-444-44-4-44-444-4-440-4000400000000000000000000000000000000000000000000000000000000000000
χ804-44-4-444-4-444-4-444-44-404000-400000000000000000000000000000000000000000000000000000000000000
χ814-4-44-4-444000000000040-44-4000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ824-4-44-4-444000000000040-44-400000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ834-4-44-4-4440000000000-404-44000000000000000000000000000000000002-2-22-222-200000000000000000000
χ844-4-44-4-4440000000000-404-4400000000000000000000000000000000000-222-22-2-2200000000000000000000
χ8588-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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