Finite Group Databasebeta

← Group #199057

Character table — Group #199057

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12224444224444444444224444444444444444444444444444444444888888888888888824448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-11-1-111-1iiii−i−i−i−i1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ1011111111-1-1-1-11111-1-1-1-11-1-111-1iiii−i−i−i−i1-11111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ1111111111-1-1-1-11111-1-1-1-11-1-111-1iiii−i−i−i−i1-1-1-1-1-11111ii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ1211111111-1-1-1-11111-1-1-1-11-1-111-1iiii−i−i−i−i1-1-1-1-1-11111ii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ1311111111-1-1-1-11111-1-1-1-11-1-111-1−i−i−i−iiiii1-11111-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ1411111111-1-1-1-11111-1-1-1-11-1-111-1−i−i−i−iiiii1-11111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ1511111111-1-1-1-11111-1-1-1-11-1-111-1−i−i−i−iiiii1-1-1-1-1-11111−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ1611111111-1-1-1-11111-1-1-1-11-1-111-1−i−i−i−iiiii1-1-1-1-1-11111−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ171111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-11111-1-111-1-11-11-111-1-111-1-111-1-111-1-111-1-111-1-11-11-11-11-1
χ181111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-11111-1-111-1-11-11-111-1-111-1-1-1-111-1-111-1-111-1-111-11-11-11-11
χ191111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1111-11-1-1-111-1-11111-1-111-1-111-1-111-1-1-11-11-11-11
χ201111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1111-11-1-1-111-1-111-1-111-1-111-1-111-1-1111-11-11-11-1
χ211111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-111-1-1111111-1-111-1-1-11-11-1-111-1-11111-1-111-1-1-1-111-1-1111-11-1-11-11
χ221111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-111-1-1111111-1-111-1-1-11-11-1-111-1-111-1-111-1-11111-1-111-1-1-11-111-11-1
χ231111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-111-1-111-11-1111-1-111-1-111-1-111-1-1-1-111-1-111-11-111-11-1
χ241111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-111-1-111-11-1111-1-111-1-1-1-111-1-11111-1-111-1-11-11-1-11-11
χ251111-1-1-1-1-1-11111-1-111-1-1-11-11-11ii−i−i−i−iii1-111-1-1-1-111i−i−iiii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii1-1-11i−i−ii
χ261111-1-1-1-1-1-11111-1-111-1-1-11-11-11ii−i−i−i−iii1-111-1-1-1-111i−i−iiii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i-111-1−iii−i
χ271111-1-1-1-1-1-11111-1-111-1-1-11-11-11ii−i−i−i−iii1-1-1-11111-1-1i−i−ii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-111-1−iii−i
χ281111-1-1-1-1-1-11111-1-111-1-1-11-11-11ii−i−i−i−iii1-1-1-11111-1-1i−i−ii−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i1-1-11i−i−ii
χ291111-1-1-1-1-1-11111-1-111-1-1-11-11-11−i−iiiii−i−i1-111-1-1-1-111−iii−i−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i1-1-11−iii−i
χ301111-1-1-1-1-1-11111-1-111-1-1-11-11-11−i−iiiii−i−i1-111-1-1-1-111−iii−i−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii-111-1i−i−ii
χ311111-1-1-1-1-1-11111-1-111-1-1-11-11-11−i−iiiii−i−i1-1-1-11111-1-1−iii−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-111-1i−i−ii
χ321111-1-1-1-1-1-11111-1-111-1-1-11-11-11−i−iiiii−i−i1-1-1-11111-1-1−iii−iii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii1-1-11−iii−i
χ3322222222222222222222-2-2-2-2-2-222222222-2-200000000-2-2-2-200000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2222-2-2-2000000002-22-22-22-22-2000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2222-2-2-2000000002-2-22-22-22-22000000000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-222200000000-220000000000002-22-22-22-2000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-222200000000-22000000000000-22-22-22-22000000000000000000000000
χ3922222222-2-2-2-22222-2-2-2-2-222-2-222i2i2i2i−2i−2i−2i−2i-2200000000−2i−2i2i2i00000000000000000000000000000000
χ4022222222-2-2-2-22222-2-2-2-2-222-2-22−2i−2i−2i−2i2i2i2i2i-22000000002i2i−2i−2i00000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-222222-2-2-2-2200000000222-22-2-22-22000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-222222-2-2-2-220000000022-22-222-22-2000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-22222-200000000-2-20000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-22222-200000000-2-2000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ452222-2-2-2-222-2-222-2-2-2-22222-2-22222-2-222-2-2-2-200000000-22-2200000000000000000000000000000000
χ462222-2-2-2-222-2-222-2-2-2-22222-2-222-2-222-2-222-2-2000000002-22-200000000000000000000000000000000
χ472222-2-2-2-222-2-2-2-22222-2-222-22-2-200000000-220000000000002-2-222-2-22000000000000000000000000
χ482222-2-2-2-222-2-2-2-22222-2-222-22-2-200000000-22000000000000-222-2-222-2000000000000000000000000
χ492222-2-2-2-222-2-2-2-22222-2-2-2-22-222000000002-22-2-222-2-22000000000000000000000000000000000000
χ502222-2-2-2-222-2-2-2-22222-2-2-2-22-222000000002-2-222-2-222-2000000000000000000000000000000000000
χ512222-2-2-2-2-2-22222-2-222-2-22-22-22-22i2i−2i−2i−2i−2i2i2i-2200000000−2i2i2i−2i00000000000000000000000000000000
χ522222-2-2-2-2-2-22222-2-222-2-22-22-22-2−2i−2i2i2i2i2i−2i−2i-22000000002i−2i−2i2i00000000000000000000000000000000
χ532222-2-2-2-2-2-222-2-222-2-2222-222-2200000000-2-20000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ542222-2-2-2-2-2-222-2-222-2-2222-222-2200000000-2-2000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ552222-2-2-2-2-2-222-2-222-2-222-22-2-22-200000000222-2-22-222-2000000000000000000000000000000000000
χ562222-2-2-2-2-2-222-2-222-2-222-22-2-22-20000000022-222-22-2-22000000000000000000000000000000000000
χ572-22-22i2i−2i−2i2-22i−2i2-22i−2i2i−2i2-20000002-22i−2i2-22i−2i00000000000000000000002−2i2−i22−2i2−i22−2i2−i22−2i2−i200000000
χ582-22-22i2i−2i−2i2-22i−2i2-22i−2i2i−2i2-20000002-22i−2i2-22i−2i0000000000000000000000−22−i2i2−22−i2i2−22−i2i2−22−i2i200000000
χ592-22-22i2i−2i−2i2-22i−2i2-22i−2i2i−2i2-2000000-22−2i2i-22−2i2i00000000000000000000002−2i2−i22−2i2−i2−22−i2i2−22−i2i200000000
χ602-22-22i2i−2i−2i2-22i−2i2-22i−2i2i−2i2-2000000-22−2i2i-22−2i2i0000000000000000000000−22−i2i2−22−i2i22−2i2−i22−2i2−i200000000
χ612-22-22i2i−2i−2i-22−2i2i2-22i−2i−2i2i-220000002i−2i-22−2i2i2-200000000000000000000002−2i2−i2−22−i2i2i2−i2−22−i2i22−200000000
χ622-22-22i2i−2i−2i-22−2i2i2-22i−2i−2i2i-220000002i−2i-22−2i2i2-20000000000000000000000−22−i2i22−2i2−i2−i2i22−2i2−i2−2200000000
χ632-22-22i2i−2i−2i-22−2i2i2-22i−2i−2i2i-22000000−2i2i2-22i−2i-2200000000000000000000002−2i2−i2−22−i2i2−i2i22−2i2−i2−2200000000
χ642-22-22i2i−2i−2i-22−2i2i2-22i−2i−2i2i-22000000−2i2i2-22i−2i-220000000000000000000000−22−i2i22−2i2−i2i2−i2−22−i2i22−200000000
χ652-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i2i2-20000002-2−2i2i2-2−2i2i00000000000000000000002−2−i2i22−2−i2i22−2−i2i22−2−i2i200000000
χ662-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i2i2-20000002-2−2i2i2-2−2i2i0000000000000000000000−22i2−i2−22i2−i2−22i2−i2−22i2−i200000000
χ672-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i2i2-2000000-222i−2i-222i−2i00000000000000000000002−2−i2i22−2−i2i2−22i2−i2−22i2−i200000000
χ682-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i2i2-2000000-222i−2i-222i−2i0000000000000000000000−22i2−i2−22i2−i22−2−i2i22−2−i2i200000000
χ692-22-2−2i−2i2i2i-222i−2i2-2−2i2i2i−2i-220000002i−2i2-2−2i2i-2200000000000000000000002−2−i2i2−22i2−i2i2−i22−2−i2i2−2200000000
χ702-22-2−2i−2i2i2i-222i−2i2-2−2i2i2i−2i-220000002i−2i2-2−2i2i-220000000000000000000000−22i2−i22−2−i2i2−i2i2−22i2−i22−200000000
χ712-22-2−2i−2i2i2i-222i−2i2-2−2i2i2i−2i-22000000−2i2i-222i−2i2-200000000000000000000002−2−i2i2−22i2−i2−i2i2−22i2−i22−200000000
χ722-22-2−2i−2i2i2i-222i−2i2-2−2i2i2i−2i-22000000−2i2i-222i−2i2-20000000000000000000000−22i2−i22−2−i2i2i2−i22−2−i2i2−2200000000
χ734-44-44i4i−4i−4i4-44i−4i-44−4i4i−4i4i-44000000000000000000000000000000000000000000000000000000000000
χ744-44-44i4i−4i−4i-44−4i4i-44−4i4i4i−4i4-4000000000000000000000000000000000000000000000000000000000000
χ754-44-4−4i−4i4i4i4-4−4i4i-444i−4i4i−4i-44000000000000000000000000000000000000000000000000000000000000
χ764-44-4−4i−4i4i4i-444i−4i-444i−4i−4i4i4-4000000000000000000000000000000000000000000000000000000000000
χ7788-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000
χ798-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000

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