Finite Group Databasebeta

← Group #369186

Character table — Group #369186

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222222222222444444444444448888888888888888888888888888888888881616161616161616
order12222222224444444488888888888888888822224444444444444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1
χ9111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ11111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ12111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1711111-11-1-1-111-1-111-1-1111111-1-1-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i11-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−i1-11-1i−ii−i
χ1811111-11-1-1-111-1-111-1-1111111-1-1-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i-1-111−i−iii-1-111−i−iiiii−i−iii−i−i-11-11−ii−ii
χ1911111-11-1-1-111-1-111-1-1111111-1-1-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i−i−iii−i−iii-11-11−ii−ii
χ2011111-11-1-1-111-1-111-1-1111111-1-1-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i-1-111−i−iii-1-111−i−iii−i−iii−i−iii1-11-1i−ii−i
χ2111111-11-1-1-111-1-111-1-1111111-1-1-1-1−i−i−i−iiiii11-1-1-1-111−i−iii11-1-1−i−iii11-1-1−i−iii−i−iii−i−iii1-11-1−ii−ii
χ2211111-11-1-1-111-1-111-1-1111111-1-1-1-1−i−i−i−iiiii11-1-1-1-111−i−iii-1-111ii−i−i-1-111ii−i−i−i−iii−i−iii-11-11i−ii−i
χ2311111-11-1-1-111-1-111-1-1111111-1-1-1-1−i−i−i−iiiii-1-11111-1-1−i−iii11-1-1−i−iii11-1-1−i−iiiii−i−iii−i−i-11-11i−ii−i
χ2411111-11-1-1-111-1-111-1-1111111-1-1-1-1−i−i−i−iiiii-1-11111-1-1−i−iii-1-111ii−i−i-1-111ii−i−iii−i−iii−i−i1-11-1−ii−ii
χ2511111-11-1-1-111-1-111-1-1-1-1-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−iii11-1-1ii−i−i-1-111−i−iiiii−i−i−i−iii1-1-11i−i−ii
χ2611111-11-1-1-111-1-111-1-1-1-1-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−iii-1-111−i−iii11-1-1ii−i−iii−i−i−i−iii-111-1−iii−i
χ2711111-11-1-1-111-1-111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-1-1-11111−i−iii11-1-1ii−i−i-1-111−i−iii−i−iiiii−i−i-111-1−iii−i
χ2811111-11-1-1-111-1-111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-1-1-11111−i−iii-1-111−i−iii11-1-1ii−i−i−i−iiiii−i−i1-1-11i−i−ii
χ2911111-11-1-1-111-1-111-1-1-1-1-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1ii−i−i11-1-1−i−iii-1-111ii−i−i−i−iiiii−i−i1-1-11−iii−i
χ3011111-11-1-1-111-1-111-1-1-1-1-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111ii−i−i11-1-1−i−iii−i−iiiii−i−i-111-1i−i−ii
χ3111111-11-1-1-111-1-111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-1−i−iii-1-111ii−i−iii−i−i−i−iii-111-1i−i−ii
χ3211111-11-1-1-111-1-111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-1-1-11111ii−i−i-1-111ii−i−i11-1-1−i−iiiii−i−i−i−iii1-1-11−iii−i
χ332222-22-22-2-22-22-22-22-22222-2-222-2-22i2i−2i−2i2i2i−2i−2i000000002i−2i2i−2i00000000000000000000000000000000
χ342222-22-22-2-22-22-22-22-22222-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000−2i2i−2i2i00000000000000000000000000000000
χ352222-22-22-2-22-22-22-22-2-2-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i00000000−2i2i−2i2i00000000000000000000000000000000
χ362222-22-22-2-22-22-22-22-2-2-2-2-222-2-222−2i−2i2i2i−2i−2i2i2i000000002i−2i2i−2i00000000000000000000000000000000
χ372222-2-2-2-2222-2-222-2-222222-2-2-2-22222-2-2-2-222000000002-2-2200000000000000000000000000000000
χ382222-2-2-2-2222-2-222-2-222222-2-2-2-222-2-22222-2-200000000-222-200000000000000000000000000000000
χ392222-2-2-2-2222-2-222-2-22-2-2-2-22222-2-222-2-2-2-22200000000-222-200000000000000000000000000000000
χ402222-2-2-2-2222-2-222-2-22-2-2-2-22222-2-2-2-22222-2-2000000002-2-2200000000000000000000000000000000
χ412-2-2222-2-2-222-2-2-2-222200000000002-22-22-22-2000000000000000000002-22-22-22-20000000000000000
χ422-2-2222-2-2-222-2-2-2-222200000000002-22-22-22-200000000000000000000-22-22-22-220000000000000000
χ432-2-2222-2-2-222-2-2-2-22220000000000-22-22-22-22000000000000000000002-22-2-22-220000000000000000
χ442-2-2222-2-2-222-2-2-2-22220000000000-22-22-22-2200000000000000000000-22-222-22-20000000000000000
χ452-2-2222-2-2-22-22222-2-2-222-2-22-22-22-20000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ462-2-2222-2-2-22-22222-2-2-222-2-22-22-22-2000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ472-2-2222-2-2-22-22222-2-2-2-2-222-22-22-220000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ482-2-2222-2-2-22-22222-2-2-2-2-222-22-22-22000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ492-2-222-2-222-22-222-22-2-200000000002i−2i2i−2i−2i2i−2i2i000000000000000000002-2-222i−2i−2i2i0000000000000000
χ502-2-222-2-222-22-222-22-2-200000000002i−2i2i−2i−2i2i−2i2i00000000000000000000-222-2−2i2i2i−2i0000000000000000
χ512-2-222-2-222-22-222-22-2-20000000000−2i2i−2i2i2i−2i2i−2i000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ522-2-222-2-222-22-222-22-2-20000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000-222-22i−2i−2i2i0000000000000000
χ532-2-222-2-222-2-22-2-22-22222-2-22-2-22-220000000000000000000000000000000000002-2-222-2-2200000000
χ542-2-222-2-222-2-22-2-22-22222-2-22-2-22-22000000000000000000000000000000000000-222-2-222-200000000
χ552-2-222-2-222-2-22-2-22-222-2-222-222-22-20000000000000000000000000000000000002-2-22-222-200000000
χ562-2-222-2-222-2-22-2-22-222-2-222-222-22-2000000000000000000000000000000000000-222-22-2-2200000000
χ572-2-22-222-22-222-22-2-22-200000000002i−2i−2i2i2i−2i−2i2i0000000000002-22-22i−2i2i−2i000000000000000000000000
χ582-2-22-222-22-222-22-2-22-200000000002i−2i−2i2i2i−2i−2i2i000000000000-22-22−2i2i−2i2i000000000000000000000000
χ592-2-22-222-22-222-22-2-22-20000000000−2i2i2i−2i−2i2i2i−2i0000000000002-22-2−2i2i−2i2i000000000000000000000000
χ602-2-22-222-22-222-22-2-22-20000000000−2i2i2i−2i−2i2i2i−2i000000000000-22-222i−2i2i−2i000000000000000000000000
χ612-2-22-222-22-2-2-22-222-2222-2-2-222-2-22000000002-22-22-22-2000000000000000000000000000000000000
χ622-2-22-222-22-2-2-22-222-2222-2-2-222-2-2200000000-22-22-22-22000000000000000000000000000000000000
χ632-2-22-222-22-2-2-22-222-22-2-2222-2-222-2000000002-2-222-2-22000000000000000000000000000000000000
χ642-2-22-222-22-2-2-22-222-22-2-2222-2-222-200000000-222-2-222-2000000000000000000000000000000000000
χ652-2-22-2-222-22222-2-2-2-2200000000002-2-22-222-20000000000002-2-222-2-22000000000000000000000000
χ662-2-22-2-222-22222-2-2-2-2200000000002-2-22-222-2000000000000-222-2-222-2000000000000000000000000
χ672-2-22-2-222-22222-2-2-2-220000000000-222-22-2-220000000000002-2-22-222-2000000000000000000000000
χ682-2-22-2-222-22222-2-2-2-220000000000-222-22-2-22000000000000-222-22-2-22000000000000000000000000
χ692-2-22-2-222-22-2-2-22222-222-2-2-22-222-2000000002-2-22-222-2000000000000000000000000000000000000
χ702-2-22-2-222-22-2-2-22222-222-2-2-22-222-200000000-222-22-2-22000000000000000000000000000000000000
χ712-2-22-2-222-22-2-2-22222-2-2-2222-22-2-22000000002-22-2-22-22000000000000000000000000000000000000
χ722-2-22-2-222-22-2-2-22222-2-2-2222-22-2-2200000000-22-222-22-2000000000000000000000000000000000000
χ734444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000000000
χ7444444-44-4-4-4-4-444-4-44400000000000000000000000000000000000000000000000000000000000000
χ754444-44-44-4-4-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ764444-4-4-4-444-444-4-444-400000000000000000000000000000000000000000000000000000000000000
χ7788-8-8000000000000004i2−4i24i2−4i20000000000000000000000000000000000000000000000000000000000
χ7888-8-800000000000000−4i24i2−4i24i20000000000000000000000000000000000000000000000000000000000
χ798-88-8000000000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000000000000
χ808-88-800000000000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000000000000

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