Finite Group Databasebeta

← Group #378116

Character table — Group #378116

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222444444444444444444444444888888888888888888888888888888888888161616161616
order12222222222244444444444444444444444488888888222222224444444444444444888888888888228888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-11111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-1
χ171111-1-1-1-11-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−i11-1-11-11-1ii−i−iii−i−i1-1i−ii−i
χ181111-1-1-1-11-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-11111-1-1-1-11111-1-1ii−i−i−i−iii-1-1111-1-11ii−i−i−i−iii-11−ii−ii
χ191111-1-1-1-11-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1-1-11111-1-111-1-1−i−iiiii−i−i-1-111-111-1−i−iiiii−i−i-11−ii−ii
χ201111-1-1-1-11-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111-1-111-1-11111-1-1−i−iii−i−iii11-1-1-11-11−i−iii−i−iii1-1i−ii−i
χ211111-1-1-1-11-1-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1-1-111-1-111-1-111ii−i−i−i−iii11-1-11-11-1−i−iiiii−i−i-11i−i−ii
χ221111-1-1-1-11-1-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111-1-11111-1-1-1-111ii−i−iii−i−i-1-1111-1-11−i−iii−i−iii1-1−iii−i
χ231111-1-1-1-11-1-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-111-1-1-1-111-1-111−i−iii−i−iii-1-111-111-1ii−i−iii−i−i1-1−iii−i
χ241111-1-1-1-11-1-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-11111-1-111-1-1-1-111−i−iiiii−i−i11-1-1-11-11ii−i−i−i−iii-11i−i−ii
χ251111-1-1-1-11-1-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1-1-111-1-111-1-111−i−iiiii−i−i11-1-11-11-1ii−i−i−i−iii-11−iii−i
χ261111-1-1-1-11-1-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111-1-11111-1-1-1-111−i−iii−i−iii-1-1111-1-11ii−i−iii−i−i1-1i−i−ii
χ271111-1-1-1-11-1-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-111-1-1-1-111-1-111ii−i−iii−i−i-1-111-111-1−i−iii−i−iii1-1i−i−ii
χ281111-1-1-1-11-1-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-11111-1-111-1-1-1-111ii−i−i−i−iii11-1-1-11-11−i−iiiii−i−i-11−iii−i
χ291111-1-1-1-11-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii11-1-11-11-1−i−iii−i−iii1-1−ii−ii
χ301111-1-1-1-11-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-11111-1-1-1-11111-1-1−i−iiiii−i−i-1-1111-1-11−i−iiiii−i−i-11i−ii−i
χ311111-1-1-1-11-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1-1-11111-1-111-1-1ii−i−i−i−iii-1-111-111-1ii−i−i−i−iii-11i−ii−i
χ321111-1-1-1-11-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111-1-111-1-11111-1-1ii−i−iii−i−i11-1-1-11-11ii−i−iii−i−i1-1−ii−ii
χ3322222222-2-2-2-22-22-22-22-20000000022-2-222-2-20000222200000000000000002-22-2000000-2-200000000000000
χ3422222222-2-2-2-22-22-22-22-20000000022-2-222-2-20000-2-2-2-20000000000000000-22-220000002200000000000000
χ3522222222-2-2-2-22-22-22-22-200000000-2-222-2-222000022220000000000000000-22-22000000-2-200000000000000
χ3622222222-2-2-2-22-22-22-22-200000000-2-222-2-2220000-2-2-2-200000000000000002-22-20000002200000000000000
χ3722222222-2-2-2-2-22-22-22-2222-2-222-2-200000000222200000000000000002-22-200000000-2-20000000000000000
χ3822222222-2-2-2-2-22-22-22-2222-2-222-2-200000000-2-2-2-20000000000000000-22-2200000000220000000000000000
χ3922222222-2-2-2-2-22-22-22-22-2-222-2-2220000000022220000000000000000-22-2200000000-2-20000000000000000
χ4022222222-2-2-2-2-22-22-22-22-2-222-2-22200000000-2-2-2-200000000000000002-22-200000000220000000000000000
χ412222-2-2-2-2-222-22-2-222-2-22000000002i2i−2i−2i−2i−2i2i2i000022-2-200000000000000002i−2i−2i2i000000-2200000000000000
χ422222-2-2-2-2-222-22-2-222-2-22000000002i2i−2i−2i−2i−2i2i2i0000-2-2220000000000000000−2i2i2i−2i0000002-200000000000000
χ432222-2-2-2-2-222-22-2-222-2-2200000000−2i−2i2i2i2i2i−2i−2i000022-2-20000000000000000−2i2i2i−2i000000-2200000000000000
χ442222-2-2-2-2-222-22-2-222-2-2200000000−2i−2i2i2i2i2i−2i−2i0000-2-22200000000000000002i−2i−2i2i0000002-200000000000000
χ452222-2-2-2-2-222-2-222-2-222-22i2i−2i−2i−2i−2i2i2i0000000022-2-200000000000000002i−2i−2i2i00000000-220000000000000000
χ462222-2-2-2-2-222-2-222-2-222-22i2i−2i−2i−2i−2i2i2i00000000-2-2220000000000000000−2i2i2i−2i000000002-20000000000000000
χ472222-2-2-2-2-222-2-222-2-222-2−2i−2i2i2i2i2i−2i−2i0000000022-2-20000000000000000−2i2i2i−2i00000000-220000000000000000
χ482222-2-2-2-2-222-2-222-2-222-2−2i−2i2i2i2i2i−2i−2i00000000-2-22200000000000000002i−2i−2i2i000000002-20000000000000000
χ492-22-222-2-222-2-2222-2-2-2-222-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000002i−2i2i−2i000000000000000000000000000000
χ502-22-222-2-222-2-2222-2-2-2-222-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i000000000000000000000000000000
χ512-22-222-2-222-2-2222-2-2-2-22-22-22-22-222i−2i2i−2i2i−2i2i−2i0000000000000000−2i2i−2i2i000000000000000000000000000000
χ522-22-222-2-222-2-2222-2-2-2-22-22-22-22-22−2i2i−2i2i−2i2i−2i2i00000000000000002i−2i2i−2i000000000000000000000000000000
χ532-22-222-2-2-2-2222-222-22-2-2000000002i−2i−2i2i2i−2i−2i2i0000000000002-22-20000000000000000000000002i−2i2i−2i000000
χ542-22-222-2-2-2-2222-222-22-2-2000000002i−2i−2i2i2i−2i−2i2i000000000000-22-22000000000000000000000000−2i2i−2i2i000000
χ552-22-222-2-2-2-2222-222-22-2-200000000−2i2i2i−2i−2i2i2i−2i0000000000002-22-2000000000000000000000000−2i2i−2i2i000000
χ562-22-222-2-2-2-2222-222-22-2-200000000−2i2i2i−2i−2i2i2i−2i000000000000-22-220000000000000000000000002i−2i2i−2i000000
χ572-22-222-2-2-2-222-22-2-22-2222-2-222-2-2200000000000000002-22-20000000000000000000000002-22-20000000000
χ582-22-222-2-2-2-222-22-2-22-2222-2-222-2-220000000000000000-22-22000000000000000000000000-22-220000000000
χ592-22-222-2-2-2-222-22-2-22-222-222-2-222-200000000000000002-22-2000000000000000000000000-22-220000000000
χ602-22-222-2-2-2-222-22-2-22-222-222-2-222-20000000000000000-22-220000000000000000000000002-22-20000000000
χ612-22-2-2-2222-22-222-22-2-22-22i−2i2i−2i−2i2i−2i2i2-22-2-22-220000000000000000−2i2i2i−2i000000000000000000000000000000
χ622-22-2-2-2222-22-222-22-2-22-22i−2i2i−2i−2i2i−2i2i-22-222-22-200000000000000002i−2i−2i2i000000000000000000000000000000
χ632-22-2-2-2222-22-222-22-2-22-2−2i2i−2i2i2i−2i2i−2i2-22-2-22-2200000000000000002i−2i−2i2i000000000000000000000000000000
χ642-22-2-2-2222-22-222-22-2-22-2−2i2i−2i2i2i−2i2i−2i-22-222-22-20000000000000000−2i2i2i−2i000000000000000000000000000000
χ652-22-2-2-222-22-222-2-2-2-2222000000002-2-22-222-20000000000002-2-220000000000000000000000002-2-22000000
χ662-22-2-2-222-22-222-2-2-2-2222000000002-2-22-222-2000000000000-222-2000000000000000000000000-222-2000000
χ672-22-2-2-222-22-222-2-2-2-222200000000-222-22-2-220000000000002-2-22000000000000000000000000-222-2000000
χ682-22-2-2-222-22-222-2-2-2-222200000000-222-22-2-22000000000000-222-20000000000000000000000002-2-22000000
χ692-22-2-2-222-22-22-22222-2-2-22i−2i−2i2i−2i2i2i−2i00000000000000002-2-220000000000000000000000002i−2i−2i2i0000000000
χ702-22-2-2-222-22-22-22222-2-2-22i−2i−2i2i−2i2i2i−2i0000000000000000-222-2000000000000000000000000−2i2i2i−2i0000000000
χ712-22-2-2-222-22-22-22222-2-2-2−2i2i2i−2i2i−2i−2i2i00000000000000002-2-22000000000000000000000000−2i2i2i−2i0000000000
χ722-22-2-2-222-22-22-22222-2-2-2−2i2i2i−2i2i−2i−2i2i0000000000000000-222-20000000000000000000000002i−2i−2i2i0000000000
χ73444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-44-4-44-4-444-4-444000000000000000000000000000000000000000000000000000000000000000000
χ754-44-444-4-444-4-4-4-4-44444-4000000000000000000000000000000000000000000000000000000000000000000
χ764-44-4-4-4444-44-4-4-44-444-44000000000000000000000000000000000000000000000000000000000000000000
χ774-4-444-44-4000000000000000000000000000022−2222−2222−2222−22000000000000000000002-22-2000000000000000000
χ784-4-444-44-4000000000000000000000000000022−2222−22−2222−222200000000000000000000-22-22000000000000000000
χ794-4-444-44-40000000000000000000000000000−2222−222222−2222−2200000000000000000000-22-22000000000000000000
χ804-4-444-44-40000000000000000000000000000−2222−2222−2222−2222000000000000000000002-22-2000000000000000000
χ814-4-44-44-44000000000000000000000000000022−22−222222−22−2222000000000000000000002-2-22000000000000000000
χ824-4-44-44-44000000000000000000000000000022−22−2222−222222−2200000000000000000000-222-2000000000000000000
χ834-4-44-44-440000000000000000000000000000−222222−2222−22−222200000000000000000000-222-2000000000000000000
χ844-4-44-44-440000000000000000000000000000−222222−22−222222−22000000000000000000002-2-22000000000000000000
χ8588-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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