Finite Group Databasebeta

← Group #194754

Character table — Group #194754

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222222222222444422224444444444444444444444444444444444444488888888888888884444
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
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ911111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ1111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ1211111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1311111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1411111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ1511111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1611111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ171-1-111-1-111-1-11111-1-1-1-1111-1-111-1-111-1-1111-1-1-11-1ii−i−iii−i−iii−i−iii−i−i1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ181-1-111-1-111-1-11111-1-1-1-1111-1-111-1-111-1-1111-1-1-11-1ii−i−iii−i−iii−i−iii−i−i1-1-1-111-1-111−i−iii−i−iii−i−iii−i−iii-11-11
χ191-1-111-1-111-1-11111-1-1-1-1111-1-111-1-111-1-1111-1-1-11-1−i−iii−i−iii−i−iii−i−iii1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ201-1-111-1-111-1-11111-1-1-1-1111-1-111-1-111-1-1111-1-1-11-1−i−iii−i−iii−i−iii−i−iii1-1-1-111-1-111ii−i−iii−i−iii−i−iii−i−i-11-11
χ211-1-111-1-111-1-11111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11ii−i−iii−i−i−i−iii−i−iii-1111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ221-1-111-1-111-1-11111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11ii−i−iii−i−i−i−iii−i−iii-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i1-11-1
χ231-1-111-1-111-1-11111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11−i−iii−i−iiiii−i−iii−i−i-1111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ241-1-111-1-111-1-11111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11−i−iii−i−iiiii−i−iii−i−i-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii1-11-1
χ251-1-111-1-111-1-1-1-1-1-111111-1-11111-1-1-1-11111-11-1-11-1ii−i−i−i−iiiii−i−i−i−iii-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ261-1-111-1-111-1-1-1-1-1-111111-1-11111-1-1-1-11111-11-1-11-1ii−i−i−i−iiiii−i−i−i−iii-11-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i-111-1
χ271-1-111-1-111-1-1-1-1-1-111111-1-11111-1-1-1-11111-11-1-11-1−i−iiiii−i−i−i−iiiii−i−i-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ281-1-111-1-111-1-1-1-1-1-111111-1-11111-1-1-1-11111-11-1-11-1−i−iiiii−i−i−i−iiiii−i−i-11-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii-111-1
χ291-1-111-1-111-1-1-1-1-1-111111-1-111-1-11111-1-111-11-1-1-11ii−i−i−i−iii−i−iiiii−i−i1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i-111-1
χ301-1-111-1-111-1-1-1-1-1-111111-1-111-1-11111-1-111-11-1-1-11ii−i−i−i−iii−i−iiiii−i−i1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii1-1-11
χ311-1-111-1-111-1-1-1-1-1-111111-1-111-1-11111-1-111-11-1-1-11−i−iiiii−i−iii−i−i−i−iii1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii-111-1
χ321-1-111-1-111-1-1-1-1-1-111111-1-111-1-11111-1-111-11-1-1-11−i−iiiii−i−iii−i−i−i−iii1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i1-1-11
χ3322222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000-2-20000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000000000000000220000000000000000000000000000
χ3522222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-222-2-2-2-20000000000000000220000000000000000000000000000
χ3622222222222-2-2-2-2-2-2-2-222222-2-2-2-22222-2-222-2-2220000000000000000-2-20000000000000000000000000000
χ3722222222-2-2-222-2-222-2-2-22222000000002-2-2-22-200000000002-22-22-22-2000000000000000000000000000000
χ3822222222-2-2-222-2-222-2-2-22222000000002-2-2-22-20000000000-22-22-22-22000000000000000000000000000000
χ3922222222-2-2-222-2-222-2-2-2-2-2-2-200000000-2222-22002-22-22-22-200000000000000000000000000000000000000
χ4022222222-2-2-222-2-222-2-2-2-2-2-2-200000000-2222-2200-22-22-22-2200000000000000000000000000000000000000
χ4122222222-2-2-2-2-222-2-222-2222200000000-22-2-2-22002-22-2-22-2200000000000000000000000000000000000000
χ4222222222-2-2-2-2-222-2-222-2222200000000-22-2-2-2200-22-222-22-200000000000000000000000000000000000000
χ4322222222-2-2-2-2-222-2-222-2-2-2-2-2000000002-2222-200000000002-22-2-22-22000000000000000000000000000000
χ4422222222-2-2-2-2-222-2-222-2-2-2-2-2000000002-2222-20000000000-22-222-22-2000000000000000000000000000000
χ452222-2-2-2-222-22-22-22-22-2-200002-22-22-22-200000000000000000000000000000000002−22−22−22−22−22−22−22−20000
χ462222-2-2-2-222-22-22-22-22-2-200002-22-22-22-20000000000000000000000000000000000−22−22−22−22−22−22−22−220000
χ472222-2-2-2-222-22-22-22-22-2-20000-22-22-22-2200000000000000000000000000000000002−22−22−22−2−22−22−22−220000
χ482222-2-2-2-222-22-22-22-22-2-20000-22-22-22-220000000000000000000000000000000000−22−22−22−222−22−22−22−20000
χ492222-2-2-2-222-2-22-22-22-22-200002-22-2-22-2200000000000000000000000000000000002−22−2−22−222−22−2−22−220000
χ502222-2-2-2-222-2-22-22-22-22-200002-22-2-22-220000000000000000000000000000000000−22−222−22−2−22−222−22−20000
χ512222-2-2-2-222-2-22-22-22-22-20000-22-222-22-200000000000000000000000000000000002−22−2−22−22−22−222−22−20000
χ522222-2-2-2-222-2-22-22-22-22-20000-22-222-22-20000000000000000000000000000000000−22−222−22−22−22−2−22−220000
χ532-2-222-2-222-2-22222-2-2-2-22-2-22222-2-222-2-2-2-2-2222-220000000000000000-220000000000000000000000000000
χ542-2-222-2-222-2-22222-2-2-2-22-2-222-2-222-2-222-2-2-22222-200000000000000002-20000000000000000000000000000
χ552-2-222-2-222-2-2-2-2-2-22222222-2-222-2-2-2-222-2-22-222-2200000000000000002-20000000000000000000000000000
χ562-2-222-2-222-2-2-2-2-2-22222222-2-2-2-22222-2-2-2-22-2222-20000000000000000-220000000000000000000000000000
χ572-2-222-2-22-22222-2-2-2-222-222-2-2000000002-2-22-2200000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ582-2-222-2-22-22222-2-2-2-222-222-2-2000000002-2-22-220000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ592-2-222-2-22-22222-2-2-2-222-2-2-22200000000-222-22-2002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000000000
χ602-2-222-2-22-22222-2-2-2-222-2-2-22200000000-222-22-200−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000000000
χ612-2-222-2-22-222-2-22222-2-2-222-2-200000000-22-222-2002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000
χ622-2-222-2-22-222-2-22222-2-2-222-2-200000000-22-222-200−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000
χ632-2-222-2-22-222-2-22222-2-2-2-2-222000000002-22-2-2200000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ642-2-222-2-22-222-2-22222-2-2-2-2-222000000002-22-2-220000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ652-2-22-222-22-222-22-2-22-22-200002-2-222-2-220000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000
χ662-2-22-222-22-222-22-2-22-22-200002-2-222-2-220000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000
χ672-2-22-222-22-222-22-2-22-22-20000-222-2-222-20000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000
χ682-2-22-222-22-222-22-2-22-22-20000-222-2-222-20000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000
χ692-2-22-222-22-22-22-222-22-2-200002-2-22-222-20000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000
χ702-2-22-222-22-22-22-222-22-2-200002-2-22-222-20000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000
χ712-2-22-222-22-22-22-222-22-2-20000-222-22-2-220000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000
χ722-2-22-222-22-22-22-222-22-2-20000-222-22-2-220000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000
χ734444-4-4-4-4-4-444-4-444-4-444000000000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4-4-44-444-4-444-44000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-440000000000004-44-400000000000000000000000000000000002-22-22-22-200000000000000000000
χ7644-4-4-44-440000000000004-44-40000000000000000000000000000000000-22-22-22-2200000000000000000000
χ7744-4-4-44-44000000000000-44-4400000000000000000000000000000000002-22-2-22-2200000000000000000000
χ7844-4-4-44-44000000000000-44-440000000000000000000000000000000000-22-222-22-200000000000000000000
χ794-44-4-4-4440000000000004-4-4400000000000000000000000000000000002-2-222-2-2200000000000000000000
χ804-44-4-4-4440000000000004-4-440000000000000000000000000000000000-222-2-222-200000000000000000000
χ814-44-4-4-444000000000000-444-400000000000000000000000000000000002-2-22-222-200000000000000000000
χ824-44-4-4-444000000000000-444-40000000000000000000000000000000000-222-22-2-2200000000000000000000
χ834-4-44-444-4-44-44-4-44-444-44000000000000000000000000000000000000000000000000000000000000000000
χ844-4-44-444-4-44-4-444-44-4-444000000000000000000000000000000000000000000000000000000000000000000
χ8588-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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