Finite Group Databasebeta

← Group #378681

Character table — Group #378681

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12222222222244444444444444448888888844444444444444444444444488888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ911111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1011111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111
χ171-11-1-111-11-1-1111-111-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i1-1i−i1-111-1-11-1i−i1-111-1-111-1-1ii−i−iii−i−i1-1i−i1-1i−i
χ181-11-1-111-11-1-1111-111-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i1-1i−i-1111-1-11-1i−i-11-1-11111-1-1−i−iii−i−iii-11−ii-11−ii
χ191-11-1-111-11-1-1111-111-1-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iii-11−ii1-1-1-111-11−ii1-111-1-111-1-1ii−i−iii−i−i-11−ii-11−ii
χ201-11-1-111-11-1-1111-111-1-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iii-11−ii-11-1-111-11−ii-11-1-11111-1-1−i−iii−i−iii1-1i−i1-1i−i
χ211-11-1-111-11-1-1111-111-1-1-1ii−i−iii−i−i−i−i−i−iiiiiii−i−i1-1−ii1-1-1-1111-1−ii1-1-1-111-1-111−i−iiiii−i−i1-1−ii-11i−i
χ221-11-1-111-11-1-1111-111-1-1-1ii−i−iii−i−i−i−i−i−iiiiiii−i−i1-1−ii-11-1-1111-1−ii-1111-1-1-1-111ii−i−i−i−iii-11i−i1-1−ii
χ231-11-1-111-11-1-1111-111-1-1-1ii−i−iii−i−i−i−i−i−iiiii−i−iii-11i−i1-111-1-1-11i−i1-1-1-111-1-111−i−iiiii−i−i-11i−i1-1−ii
χ241-11-1-111-11-1-1111-111-1-1-1ii−i−iii−i−i−i−i−i−iiiii−i−iii-11i−i-1111-1-1-11i−i-1111-1-1-1-111ii−i−i−i−iii1-1−ii-11i−i
χ251-11-1-111-11-1-1111-111-1-1-1−i−iii−i−iiiiiii−i−i−i−iii−i−i-11−ii1-111-1-1-11−ii1-1-1-111-1-111ii−i−i−i−iii-11−ii1-1i−i
χ261-11-1-111-11-1-1111-111-1-1-1−i−iii−i−iiiiiii−i−i−i−iii−i−i-11−ii-1111-1-1-11−ii-1111-1-1-1-111−i−iiiii−i−i1-1i−i-11−ii
χ271-11-1-111-11-1-1111-111-1-1-1−i−iii−i−iiiiiii−i−i−i−i−i−iii1-1i−i1-1-1-1111-1i−i1-1-1-111-1-111ii−i−i−i−iii1-1i−i-11−ii
χ281-11-1-111-11-1-1111-111-1-1-1−i−iii−i−iiiiiii−i−i−i−i−i−iii1-1i−i-11-1-1111-1i−i-1111-1-1-1-111−i−iiiii−i−i-11−ii1-1i−i
χ291-11-1-111-11-1-1111-111-1-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−i-11i−i1-1-1-111-11i−i1-111-1-111-1-1−i−iii−i−iii-11i−i-11i−i
χ301-11-1-111-11-1-1111-111-1-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−i-11i−i-11-1-111-11i−i-11-1-11111-1-1ii−i−iii−i−i1-1−ii1-1−ii
χ311-11-1-111-11-1-1111-111-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii1-1−ii1-111-1-11-1−ii1-111-1-111-1-1−i−iii−i−iii1-1−ii1-1−ii
χ321-11-1-111-11-1-1111-111-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii1-1−ii-1111-1-11-1−ii-11-1-11111-1-1ii−i−iii−i−i-11i−i-11i−i
χ3322222222-2-2-2-22-222-2-2-222222-2-2-2-200000000000000002200000000-2-20000000000002-22-200000000
χ3422222222-2-2-2-22-222-2-2-222222-2-2-2-20000000000000000-2-20000000022000000000000-22-2200000000
χ3522222222-2-2-2-22-222-2-2-22-2-2-2-2222200000000000000002200000000-2-2000000000000-22-2200000000
χ3622222222-2-2-2-22-222-2-2-22-2-2-2-222220000000000000000-2-200000000220000000000002-22-200000000
χ3722222222-2-2-2-2-22-2-2222-20000000022-2-222-2-200002222000000-2-2-2-200000000000000000000000000
χ3822222222-2-2-2-2-22-2-2222-20000000022-2-222-2-20000-2-2-2-2000000222200000000000000000000000000
χ3922222222-2-2-2-2-22-2-2222-200000000-2-222-2-222000022-2-2000000-2-22200000000000000000000000000
χ4022222222-2-2-2-2-22-2-2222-200000000-2-222-2-2220000-2-22200000022-2-200000000000000000000000000
χ4122-22-22-2-222-2-2222-2-22-2-2000000002-22-22-22-22-22-20000002-22-2000000000000000000000000000000
χ4222-22-22-2-222-2-2222-2-22-2-2000000002-22-22-22-2-22-22000000-22-22000000000000000000000000000000
χ4322-22-22-2-222-2-2222-2-22-2-200000000-22-22-22-222-22-2000000-22-22000000000000000000000000000000
χ4422-22-22-2-222-2-2222-2-22-2-200000000-22-22-22-22-22-220000002-22-2000000000000000000000000000000
χ4522-22-22-2-222-2-2-2-2-222-2222i−2i2i−2i2i−2i2i−2i00000000000000000000000000002i−2i2i−2i00002-22-2000000000000
χ4622-22-22-2-222-2-2-2-2-222-2222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000−2i2i−2i2i0000-22-22000000000000
χ4722-22-22-2-222-2-2-2-2-222-222−2i2i−2i2i−2i2i−2i2i00000000000000000000000000002i−2i2i−2i0000-22-22000000000000
χ4822-22-22-2-222-2-2-2-2-222-222−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000−2i2i−2i2i00002-22-2000000000000
χ4922-22-22-2-2-2-222-22-22-22-222i−2i2i−2i−2i2i−2i2i2-2-222-2-220000000000000000000000002i−2i2i−2i0000000000000000
χ5022-22-22-2-2-2-222-22-22-22-222i−2i2i−2i−2i2i−2i2i-222-2-222-2000000000000000000000000−2i2i−2i2i0000000000000000
χ5122-22-22-2-2-2-222-22-22-22-22−2i2i−2i2i2i−2i2i−2i2-2-222-2-22000000000000000000000000−2i2i−2i2i0000000000000000
χ5222-22-22-2-2-2-222-22-22-22-22−2i2i−2i2i2i−2i2i−2i-222-2-222-20000000000000000000000002i−2i2i−2i0000000000000000
χ532-22-2-222-2-222-22-2-22-222-22i2i−2i−2i−2i−2i2i2i00000000000000002-200000000-220000000000002i−2i−2i2i00000000
χ542-22-2-222-2-222-22-2-22-222-22i2i−2i−2i−2i−2i2i2i0000000000000000-22000000002-2000000000000−2i2i2i−2i00000000
χ552-22-2-222-2-222-22-2-22-222-2−2i−2i2i2i2i2i−2i−2i00000000000000002-200000000-22000000000000−2i2i2i−2i00000000
χ562-22-2-222-2-222-22-2-22-222-2−2i−2i2i2i2i2i−2i−2i0000000000000000-22000000002-20000000000002i−2i−2i2i00000000
χ572-22-2-222-2-222-2-222-22-2-22000000002i2i−2i−2i−2i−2i2i2i00002-22i−2i000000-22−2i2i00000000000000000000000000
χ582-22-2-222-2-222-2-222-22-2-22000000002i2i−2i−2i−2i−2i2i2i0000-22−2i2i0000002-22i−2i00000000000000000000000000
χ592-22-2-222-2-222-2-222-22-2-2200000000−2i−2i2i2i2i2i−2i−2i00002-2−2i2i000000-222i−2i00000000000000000000000000
χ602-22-2-222-2-222-2-222-22-2-2200000000−2i−2i2i2i2i2i−2i−2i0000-222i−2i0000002-2−2i2i00000000000000000000000000
χ612-2-2-222-222-22-222-2-2-2-222000000002i−2i2i−2i−2i2i−2i2i2i−2i−2i2i0000002-2-22000000000000000000000000000000
χ622-2-2-222-222-22-222-2-2-2-222000000002i−2i2i−2i−2i2i−2i2i−2i2i2i−2i000000-222-2000000000000000000000000000000
χ632-2-2-222-222-22-222-2-2-2-22200000000−2i2i−2i2i2i−2i2i−2i2i−2i−2i2i000000-222-2000000000000000000000000000000
χ642-2-2-222-222-22-222-2-2-2-22200000000−2i2i−2i2i2i−2i2i−2i−2i2i2i−2i0000002-2-22000000000000000000000000000000
χ652-2-2-222-222-22-2-2-22222-2-22-2-222-2-2200000000000000000000000000002i−2i−2i2i0000−2i2i2i−2i000000000000
χ662-2-2-222-222-22-2-2-22222-2-22-2-222-2-220000000000000000000000000000−2i2i2i−2i00002i−2i−2i2i000000000000
χ672-2-2-222-222-22-2-2-22222-2-2-222-2-222-200000000000000000000000000002i−2i−2i2i00002i−2i−2i2i000000000000
χ682-2-2-222-222-22-2-2-22222-2-2-222-2-222-20000000000000000000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ692-2-2-222-22-22-22-2222-2-22-22-2-22-222-22i−2i−2i2i−2i2i2i−2i000000000000000000000000−2i2i2i−2i0000000000000000
χ702-2-2-222-22-22-22-2222-2-22-22-2-22-222-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000002i−2i−2i2i0000000000000000
χ712-2-2-222-22-22-22-2222-2-22-2-222-22-2-222i−2i−2i2i−2i2i2i−2i0000000000000000000000002i−2i−2i2i0000000000000000
χ722-2-2-222-22-22-22-2222-2-22-2-222-22-2-22−2i2i2i−2i2i−2i−2i2i000000000000000000000000−2i2i2i−2i0000000000000000
χ73444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ7444-44-44-4-4-4-4444-44-44-44-4000000000000000000000000000000000000000000000000000000000000
χ754-44-4-444-44-4-44-4-44-4-4444000000000000000000000000000000000000000000000000000000000000
χ764-4-4-444-44-44-444-4-4-444-44000000000000000000000000000000000000000000000000000000000000
χ77888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000
χ7888-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000
χ798-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000

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