Finite Group Databasebeta

← Group #209088

Character table — Group #209088

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12224444224488888888444444448888888822244444448888888888888888888888888824448888
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
χ31111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ711111111111111111111-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ811111111111111111111-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ9111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ12111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-11111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ171111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-111-1-1-11-1ii−i−ii−iii−i−i11-1-1ii−i−i11-1-1ii−i−i1-11-1i−ii−i
χ181111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-111-1-1-11-1ii−i−ii−iii−i−i-1-111−i−iii-1-111−i−iii-11-11−ii−ii
χ191111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i1-11-1-111-1-11−i−iiii−i−i−iii11-1-1ii−i−i11-1-1ii−i−i-11-11−ii−ii
χ201111-1-1-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i1-11-1-111-1-11−i−iiii−i−i−iii-1-111−i−iii-1-111−i−iii1-11-1i−ii−i
χ211111-1-1-1-111-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-11-1-1-11111-1−i−iii−iiii−i−i11-1-1ii−i−i-1-111−i−iii1-1-11i−i−ii
χ221111-1-1-1-111-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-11-1-1-11111-1−i−iii−iiii−i−i-1-111−i−iii11-1-1ii−i−i-111-1−iii−i
χ231111-1-1-1-111-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-1-1111-1-11-11ii−i−i−ii−i−iii11-1-1ii−i−i-1-111−i−iii-111-1−iii−i
χ241111-1-1-1-111-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-1-1111-1-11-11ii−i−i−ii−i−iii-1-111−i−iii11-1-1ii−i−i1-1-11i−i−ii
χ251111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-111-1-1-11-1−i−iii−ii−i−iii11-1-1−i−iii11-1-1−i−iii1-11-1−ii−ii
χ261111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-111-1-1-11-1−i−iii−ii−i−iii-1-111ii−i−i-1-111ii−i−i-11-11i−ii−i
χ271111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii1-11-1-111-1-11ii−i−i−iiii−i−i11-1-1−i−iii11-1-1−i−iii-11-11i−ii−i
χ281111-1-1-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii1-11-1-111-1-11ii−i−i−iiii−i−i-1-111ii−i−i-1-111ii−i−i1-11-1−ii−ii
χ291111-1-1-1-111-1-1−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-11-1-1-11111-1ii−i−ii−i−i−iii11-1-1−i−iii-1-111ii−i−i1-1-11−iii−i
χ301111-1-1-1-111-1-1−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-11-1-1-11111-1ii−i−ii−i−i−iii-1-111ii−i−i11-1-1−i−iii-111-1i−i−ii
χ311111-1-1-1-111-1-1−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-1-1111-1-11-11−i−iiii−iii−i−i11-1-1−i−iii-1-111ii−i−i-111-1i−i−ii
χ321111-1-1-1-111-1-1−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-1-1111-1-11-11−i−iiii−iii−i−i-1-111ii−i−i11-1-1−i−iii1-1-11−iii−i
χ33222222222222222222222222-2-2-2-2-2-2-2-22222-2000000-2000000-2-20000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-220000002000000220000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2000000-2000000220000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222220000002000000-2-20000000000000000000000000000
χ3722222222-2-2-2-222-2-222-2-200002-22-22-22-200000002-22-20002-22-2000000000000000000000000000000
χ3822222222-2-2-2-222-2-222-2-200002-22-22-22-20000000-22-22000-22-22000000000000000000000000000000
χ3922222222-2-2-2-222-2-222-2-20000-22-22-22-22000002-200000-220000002-22-2000000000000000000000000
χ4022222222-2-2-2-222-2-222-2-20000-22-22-22-2200000-22000002-2000000-22-22000000000000000000000000
χ4122222222-2-2-2-2-2-222-2-22200002-22-2-22-2200000002-22-2000-22-22000000000000000000000000000000
χ4222222222-2-2-2-2-2-222-2-22200002-22-2-22-220000000-22-220002-22-2000000000000000000000000000000
χ4322222222-2-2-2-2-2-222-2-2220000-22-222-22-2000002-200000-22000000-22-22000000000000000000000000
χ4422222222-2-2-2-2-2-222-2-2220000-22-222-22-200000-22000002-20000002-22-2000000000000000000000000
χ452222-2-2-2-222-2-22i2i2i2i−2i−2i−2i−2i22-2-2-2-222−2i−2i2i2i2i2i−2i−2i-20000002000000−2i2i0000000000000000000000000000
χ462222-2-2-2-222-2-22i2i2i2i−2i−2i−2i−2i-2-222-2-222−2i−2i2i2i−2i−2i2i2i2000000-20000002i−2i0000000000000000000000000000
χ472222-2-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i22-2-2-2-2222i2i−2i−2i−2i−2i2i2i-200000020000002i−2i0000000000000000000000000000
χ482222-2-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i-2-222-2-2222i2i−2i−2i2i2i−2i−2i2000000-2000000−2i2i0000000000000000000000000000
χ492222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i00002-2-222i−2i−2i2i00000002-2-220002i−2i−2i2i000000000000000000000000000000
χ502222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i00002-2-222i−2i−2i2i0000000-222-2000−2i2i2i−2i000000000000000000000000000000
χ512222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i0000-222-2−2i2i2i−2i000002200000-2-20000002i−2i−2i2i000000000000000000000000
χ522222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i0000-222-2−2i2i2i−2i00000-2-20000022000000−2i2i2i−2i000000000000000000000000
χ532222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i00002-2-22−2i2i2i−2i00000002-2-22000−2i2i2i−2i000000000000000000000000000000
χ542222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i00002-2-22−2i2i2i−2i0000000-222-20002i−2i−2i2i000000000000000000000000000000
χ552222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000-222-22i−2i−2i2i000002200000-2-2000000−2i2i2i−2i000000000000000000000000
χ562222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000-222-22i−2i−2i2i00000-2-200000220000002i−2i−2i2i000000000000000000000000
χ572-2-2222-2-22-2-222i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000002-22-2000000000000000000002−22−2i2−i2i2−i2i2−i2i2−i22−22−200000000
χ582-2-2222-2-22-2-222i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000002-22-200000000000000000000−22−22−i2i2−i2i2−i2i2−i2i2−22−2200000000
χ592-2-2222-2-22-2-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000-22-22000000000000000000002−22−2i2−i2i2−i2−i2i2−i2i2−22−2200000000
χ602-2-2222-2-22-2-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000-22-2200000000000000000000−22−22−i2i2−i2i2i2−i2i2−i22−22−200000000
χ612-2-2222-2-22-2-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000-22-22000000000000000000002−22−2−i2i2−i2i2i2−i2i2−i2−22−2200000000
χ622-2-2222-2-22-2-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000-22-2200000000000000000000−22−22i2−i2i2−i2−i2i2−i2i22−22−200000000
χ632-2-2222-2-22-2-22−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000002-22-2000000000000000000002−22−2−i2i2−i2i2−i2i2−i2i22−22−200000000
χ642-2-2222-2-22-2-22−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000002-22-200000000000000000000−22−22i2−i2i2−i2i2−i2i2−i2−22−2200000000
χ652-2-22-2-2222-22-22-22-2-22-222i−2i−2i2i00000000−2i2i2i−2i000000000000000000002−2−222−2−22i2−i2−i2i2−i2i2i2−i200000000
χ662-2-22-2-2222-22-22-22-2-22-222i−2i−2i2i00000000−2i2i2i−2i00000000000000000000−222−2−222−2−i2i2i2−i2i2−i2−i2i200000000
χ672-2-22-2-2222-22-22-22-2-22-22−2i2i2i−2i000000002i−2i−2i2i000000000000000000002−2−222−2−22−i2i2i2−i2i2−i2−i2i200000000
χ682-2-22-2-2222-22-22-22-2-22-22−2i2i2i−2i000000002i−2i−2i2i00000000000000000000−222−2−222−2i2−i2−i2i2−i2i2i2−i200000000
χ692-2-22-2-2222-22-2-22-222-22-22i−2i−2i2i000000002i−2i−2i2i000000000000000000002−2−22−222−2i2−i2−i2i2i2−i2−i2i200000000
χ702-2-22-2-2222-22-2-22-222-22-22i−2i−2i2i000000002i−2i−2i2i00000000000000000000−222−22−2−22−i2i2i2−i2−i2i2i2−i200000000
χ712-2-22-2-2222-22-2-22-222-22-2−2i2i2i−2i00000000−2i2i2i−2i000000000000000000002−2−22−222−2−i2i2i2−i2−i2i2i2−i200000000
χ722-2-22-2-2222-22-2-22-222-22-2−2i2i2i−2i00000000−2i2i2i−2i00000000000000000000−222−22−2−22i2−i2−i2i2i2−i2−i2i200000000
χ734-4-4444-4-4-444-44i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ744-4-4444-4-4-444-4−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ754-4-44-4-444-44-444-4-44-444-4000000000000000000000000000000000000000000000000000000000000
χ764-4-44-4-444-44-44-444-44-4-44000000000000000000000000000000000000000000000000000000000000
χ7788-8-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000
χ7888-8-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000
χ798-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000

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