Finite Group Databasebeta

← Group #369178

Character table — Group #369178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12222222222244444444888888888888888822224444444444444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111
χ911111111111111111111-1-1-1-1-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ171-111-1-1-1111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-11-111-1-1ii−i−i1-11-1ii−i−i11-1-1ii−i−iii−i−iii−i−i1-1i−ii−i1-1
χ181-111-1-1-1111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-11-1-1-111−i−iii1-11-1ii−i−i-1-111−i−iiiii−i−iii−i−i-11−ii−ii-11
χ191-111-1-1-1111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−i-11-1111-1-1ii−i−i-11-11ii−i−i11-1-1ii−i−i−i−iii−i−iii-11−ii−ii-11
χ201-111-1-1-1111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−i-11-11-1-111−i−iii-11-11ii−i−i-1-111−i−iii−i−iii−i−iii1-1i−ii−i1-1
χ211-111-1-1-1111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-11-111-1-1−i−iii1-11-1−i−iii11-1-1−i−iii−i−iii−i−iii1-1−ii−ii1-1
χ221-111-1-1-1111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-11-1-1-111ii−i−i1-11-1−i−iii-1-111ii−i−i−i−iii−i−iii-11i−ii−i-11
χ231-111-1-1-1111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii-11-1111-1-1−i−iii-11-11−i−iii11-1-1−i−iiiii−i−iii−i−i-11i−ii−i-11
χ241-111-1-1-1111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii-11-11-1-111ii−i−i-11-11−i−iii-1-111ii−i−iii−i−iii−i−i1-1−ii−ii1-1
χ251-111-1-1-1111-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i1-1-1111-1-1ii−i−i1-1-11−i−iii-1-111−i−iiiii−i−i−i−iii1-1i−i−ii-11
χ261-111-1-1-1111-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i1-1-11-1-111−i−iii1-1-11−i−iii11-1-1ii−i−iii−i−i−i−iii-11−iii−i1-1
χ271-111-1-1-1111-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i-111-111-1-1ii−i−i-111-1−i−iii-1-111−i−iii−i−iiiii−i−i-11−iii−i1-1
χ281-111-1-1-1111-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i-111-1-1-111−i−iii-111-1−i−iii11-1-1ii−i−i−i−iiiii−i−i1-1i−i−ii-11
χ291-111-1-1-1111-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiii1-1-1111-1-1−i−iii1-1-11ii−i−i-1-111ii−i−i−i−iiiii−i−i1-1−iii−i-11
χ301-111-1-1-1111-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiii1-1-11-1-111ii−i−i1-1-11ii−i−i11-1-1−i−iii−i−iiiii−i−i-11i−i−ii1-1
χ311-111-1-1-1111-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiii-111-111-1-1−i−iii-111-1ii−i−i-1-111ii−i−iii−i−i−i−iii-11i−i−ii1-1
χ321-111-1-1-1111-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiii-111-1-1-111ii−i−i-111-1ii−i−i11-1-1−i−iiiii−i−i−i−iii1-1−iii−i-11
χ3322222222-2-2-2-2222-2-2-2-220000000022-2-222-2-200002-22-22-22-200000000000000000000000000000000
χ3422222222-2-2-2-2222-2-2-2-220000000022-2-222-2-20000-22-22-22-2200000000000000000000000000000000
χ3522222222-2-2-2-2222-2-2-2-2200000000-2-222-2-22200002-22-2-22-2200000000000000000000000000000000
χ3622222222-2-2-2-2222-2-2-2-2200000000-2-222-2-2220000-22-222-22-200000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-22222-222-2-222-2-200000000222200000000-2-2-2-20000000000000000000000000000
χ3822222222-2-2-2-2-2-2-22222-222-2-222-2-200000000-2-2-2-20000000022220000000000000000000000000000
χ3922222222-2-2-2-2-2-2-22222-2-2-222-2-2220000000022-2-200000000-2-2220000000000000000000000000000
χ4022222222-2-2-2-2-2-2-22222-2-2-222-2-22200000000-2-2220000000022-2-20000000000000000000000000000
χ4122-2-2-2-2222-22-22-2222-2-2-22-22-22-22-20000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ4222-2-2-2-2222-22-22-2222-2-2-22-22-22-22-2000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ4322-2-2-2-2222-22-22-2222-2-2-2-22-22-22-220000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ4422-2-2-2-2222-22-22-2222-2-2-2-22-22-22-22000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ4522-2-2-2-2222-22-2-22-2-2-2222000000002-22-22-22-2000000000000000000002-22-22-22-20000000000000000
χ4622-2-2-2-2222-22-2-22-2-2-2222000000002-22-22-22-200000000000000000000-22-22-22-220000000000000000
χ4722-2-2-2-2222-22-2-22-2-2-222200000000-22-22-22-22000000000000000000002-22-2-22-220000000000000000
χ4822-2-2-2-2222-22-2-22-2-2-222200000000-22-22-22-2200000000000000000000-22-222-22-20000000000000000
χ4922-2-2-2-222-22-22-22-222-2-222-2-222-2-222-2-222-2-2200000000000000002-22-2000000000000000000000000
χ5022-2-2-2-222-22-22-22-222-2-222-2-222-2-22-222-2-222-20000000000000000-22-22000000000000000000000000
χ5122-2-2-2-222-22-22-22-222-2-22-222-2-222-22-2-222-2-220000000000000000-22-22000000000000000000000000
χ5222-2-2-2-222-22-22-22-222-2-22-222-2-222-2-222-2-222-200000000000000002-22-2000000000000000000000000
χ532-222-2-2-22-2-22222-22-2-22-2000000002i2i−2i−2i−2i−2i2i2i00002-2-222i−2i−2i2i00000000000000000000000000000000
χ542-222-2-2-22-2-22222-22-2-22-2000000002i2i−2i−2i−2i−2i2i2i0000-222-2−2i2i2i−2i00000000000000000000000000000000
χ552-222-2-2-22-2-22222-22-2-22-200000000−2i−2i2i2i2i2i−2i−2i00002-2-22−2i2i2i−2i00000000000000000000000000000000
χ562-222-2-2-22-2-22222-22-2-22-200000000−2i−2i2i2i2i2i−2i−2i0000-222-22i−2i−2i2i00000000000000000000000000000000
χ572-222-2-2-22-2-222-2-22-222-2222-2-2-2-222000000002-22-200000000-22-220000000000000000000000000000
χ582-222-2-2-22-2-222-2-22-222-2222-2-2-2-22200000000-22-22000000002-22-20000000000000000000000000000
χ592-222-2-2-22-2-222-2-22-222-22-2-22222-2-2000000002-2-2200000000-222-20000000000000000000000000000
χ602-222-2-2-22-2-222-2-22-222-22-2-22222-2-200000000-222-2000000002-2-220000000000000000000000000000
χ612-2-2-222-222-2-222-2-2-22-2222-22-2-22-220000000000000000000000000000000000002-2-222-2-2200000000
χ622-2-2-222-222-2-222-2-2-22-2222-22-2-22-22000000000000000000000000000000000000-222-2-222-200000000
χ632-2-2-222-222-2-222-2-2-22-222-22-222-22-20000000000000000000000000000000000002-2-22-222-200000000
χ642-2-2-222-222-2-222-2-2-22-222-22-222-22-2000000000000000000000000000000000000-222-22-2-2200000000
χ652-2-2-222-222-2-22-2222-22-2-2000000002i−2i2i−2i−2i2i−2i2i000000000000000000002-2-222i−2i−2i2i0000000000000000
χ662-2-2-222-222-2-22-2222-22-2-2000000002i−2i2i−2i−2i2i−2i2i00000000000000000000-222-2−2i2i2i−2i0000000000000000
χ672-2-2-222-222-2-22-2222-22-2-200000000−2i2i−2i2i2i−2i2i−2i000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ682-2-2-222-222-2-22-2222-22-2-200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000-222-22i−2i−2i2i0000000000000000
χ692-2-2-222-22-222-2-222-22-22-22-2-22-222-22i−2i−2i2i−2i2i2i−2i00000000000000002i−2i−2i2i000000000000000000000000
χ702-2-2-222-22-222-2-222-22-22-22-2-22-222-2−2i2i2i−2i2i−2i−2i2i0000000000000000−2i2i2i−2i000000000000000000000000
χ712-2-2-222-22-222-2-222-22-22-2-222-22-2-222i−2i−2i2i−2i2i2i−2i0000000000000000−2i2i2i−2i000000000000000000000000
χ722-2-2-222-22-222-2-222-22-22-2-222-22-2-22−2i2i2i−2i2i−2i−2i2i00000000000000002i−2i−2i2i000000000000000000000000
χ73444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ7444-4-4-4-444-44-444-44-4-444-4000000000000000000000000000000000000000000000000000000000000
χ754-444-4-4-4444-4-4-4-444-4-444000000000000000000000000000000000000000000000000000000000000
χ764-4-4-444-44-444-44-4-44-44-44000000000000000000000000000000000000000000000000000000000000
χ77888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ7888-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ798-88-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-888-88-8000000000000000000000000000000000000000000000000000000000000000000000000

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