Finite Group Databasebeta

← Group #383813

Character table — Group #383813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222444444444444444444444444888888888888888888888888161616161616161616161616
order12222222222244444444444444448888888888888888224444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ311111111111111111111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1111111-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-11111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1111111
χ171-1-1-111-1111-1-1111-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1ii−i−i1-11-11-1ii−i−i1-11-111-1-1i−i1-1i−ii−ii−i1-1
χ181-1-1-111-1111-1-1111-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1−i−iii1-11-1-11−i−iii1-1-11-1-111−ii-11i−i−iii−i-11
χ191-1-1-111-1111-1-1111-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11ii−i−i-11-111-1−i−iii-111-1-1-111−ii-11−iii−i−ii1-1
χ201-1-1-111-1111-1-1111-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−i−iii-11-11-11ii−i−i-11-1111-1-1i−i1-1−ii−ii−ii-11
χ211-1-1-111-1111-1-1111-1-1-11-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1ii−i−i1-1-11-11−i−iii-11-11-1-111i−i1-1−ii−iii−i1-1
χ221-1-1-111-1111-1-1111-1-1-11-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1−i−iii1-1-111-1ii−i−i-111-111-1-1−ii-11−iii−ii−i-11
χ231-1-1-111-1111-1-1111-1-1-11-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11ii−i−i-111-1-11ii−i−i1-1-1111-1-1−ii-11i−i−ii−ii1-1
χ241-1-1-111-1111-1-1111-1-1-11-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11−i−iii-111-11-1−i−iii1-11-1-1-111i−i1-1i−ii−i−ii-11
χ251-1-1-111-1111-1-1111-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1ii−i−i1-11-1-11ii−i−i1-1-11-1-111i−i-11−iii−i−ii-11
χ261-1-1-111-1111-1-1111-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1−i−iii1-11-11-1−i−iii1-11-111-1-1−ii1-1−ii−ii−ii1-1
χ271-1-1-111-1111-1-1111-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11ii−i−i-11-11-11−i−iii-11-1111-1-1−ii1-1i−ii−ii−i-11
χ281-1-1-111-1111-1-1111-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11−i−iii-11-111-1ii−i−i-111-1-1-111i−i-11i−i−iii−i1-1
χ291-1-1-111-1111-1-1111-1-1-11-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1ii−i−i1-1-111-1−i−iii-111-111-1-1i−i-11i−i−ii−ii-11
χ301-1-1-111-1111-1-1111-1-1-11-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1−i−iii1-1-11-11ii−i−i-11-11-1-111−ii1-1i−ii−i−ii1-1
χ311-1-1-111-1111-1-1111-1-1-11-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11ii−i−i-111-11-1ii−i−i1-11-1-1-111−ii1-1−ii−iii−i-11
χ321-1-1-111-1111-1-1111-1-1-11-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11−i−iii-111-1-11−i−iii1-1-1111-1-1i−i-11−iii−ii−i1-1
χ3322222222-2-2-2-222-2-22-2-22000000000000000022-2-222-2-2002-22-2000022000000-2-20000000000000000
χ3422222222-2-2-2-222-2-22-2-22000000000000000022-2-222-2-200-22-220000-2-2000000220000000000000000
χ3522222222-2-2-2-222-2-22-2-220000000000000000-2-222-2-222002-22-20000-2-2000000220000000000000000
χ3622222222-2-2-2-222-2-22-2-220000000000000000-2-222-2-22200-22-22000022000000-2-20000000000000000
χ3722222222-2-2-2-2-2-222-222-20000000022-2-222-2-200000000220000-2-222000000-2-2000000000000000000
χ3822222222-2-2-2-2-2-222-222-20000000022-2-222-2-200000000-2-2000022-2-200000022000000000000000000
χ3922222222-2-2-2-2-2-222-222-200000000-2-222-2-22200000000220000-2-2-2-200000022000000000000000000
χ4022222222-2-2-2-2-2-222-222-200000000-2-222-2-22200000000-2-200002222000000-2-2000000000000000000
χ4122-2-22-22-22-22-22-2-2-2222-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000002-22-200002i−2i2i−2i000000000000
χ4222-2-22-22-22-22-22-2-2-2222-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000-22-220000−2i2i−2i2i000000000000
χ4322-2-22-22-22-22-22-2-2-2222-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002-22-20000−2i2i−2i2i000000000000
χ4422-2-22-22-22-22-22-2-2-2222-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000-22-2200002i−2i2i−2i000000000000
χ452-2222-2-2-22-2-222-2-22-2-22222-2-2-2-22200000000000000000000000000002i−2i−2i2i0000−2i2i2i−2i000000000000
χ462-2222-2-2-22-2-222-2-22-2-22222-2-2-2-2220000000000000000000000000000−2i2i2i−2i00002i−2i−2i2i000000000000
χ472-2222-2-2-22-2-222-2-22-2-222-2-22222-2-200000000000000000000000000002i−2i−2i2i00002i−2i−2i2i000000000000
χ482-2222-2-2-22-2-222-2-22-2-222-2-22222-2-20000000000000000000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ492-2-2-222-22-2-22222-22-22-2-200000000000000002i2i−2i−2i−2i−2i2i2i002i−2i−2i2i00002-2000000-220000000000000000
χ502-2-2-222-22-2-22222-22-22-2-200000000000000002i2i−2i−2i−2i−2i2i2i00−2i2i2i−2i0000-220000002-20000000000000000
χ512-2-2-222-22-2-22222-22-22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i002i−2i−2i2i0000-220000002-20000000000000000
χ522-2-2-222-22-2-22222-22-22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00−2i2i2i−2i00002-2000000-220000000000000000
χ532-2-2-222-22-2-222-2-22-22-2220000000022-2-2-2-222000000002-20000-222-2000000-22000000000000000000
χ542-2-2-222-22-2-222-2-22-22-2220000000022-2-2-2-22200000000-2200002-2-220000002-2000000000000000000
χ552-2-2-222-22-2-222-2-22-22-22200000000-2-22222-2-2000000002-20000-22-220000002-2000000000000000000
χ562-2-2-222-22-2-222-2-22-22-22200000000-2-22222-2-200000000-2200002-22-2000000-22000000000000000000
χ57444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ58444-4-44-4-40000000000002-22-22-22-222−220022−22000022−220022−22000000000000000000000000000000000000
χ59444-4-44-4-40000000000002-22-22-22-2−222200−22220000−222200−2222000000000000000000000000000000000000
χ60444-4-44-4-4000000000000-22-22-22-2222−220022−220000−222200−2222000000000000000000000000000000000000
χ61444-4-44-4-4000000000000-22-22-22-22−222200−2222000022−220022−22000000000000000000000000000000000000
χ6244-44-4-4-440000000000002i−2i−2i2i2i−2i−2i2i0022−220022−222i2−2i2002i2−2i200000000000000000000000000000000000000
χ6344-44-4-4-440000000000002i−2i−2i2i2i−2i−2i2i00−222200−2222−2i22i200−2i22i200000000000000000000000000000000000000
χ6444-44-4-4-44000000000000−2i2i2i−2i−2i2i2i−2i0022−220022−22−2i22i200−2i22i200000000000000000000000000000000000000
χ6544-44-4-4-44000000000000−2i2i2i−2i−2i2i2i−2i00−222200−22222i2−2i2002i2−2i200000000000000000000000000000000000000
χ6644-4-44-44-44-44-4-4444-4-4-44000000000000000000000000000000000000000000000000000000000000
χ6744-4-44-44-4-44-444-4444-4-4-4000000000000000000000000000000000000000000000000000000000000
χ6844-4-44-44-4-44-44-44-4-4-4444000000000000000000000000000000000000000000000000000000000000
χ694-4444-4-4-44-4-44-444-444-4-4000000000000000000000000000000000000000000000000000000000000
χ704-4444-4-4-4-444-44-44-4-44-44000000000000000000000000000000000000000000000000000000000000
χ714-4444-4-4-4-444-4-44-444-44-4000000000000000000000000000000000000000000000000000000000000
χ724-44-4-4-4440000000000002-2-22-222-20022−2200−222222−2200−222200000000000000000000000000000000000000
χ734-44-4-4-4440000000000002-2-22-222-200−22220022−22−22220022−2200000000000000000000000000000000000000
χ744-44-4-4-444000000000000-222-22-2-220022−2200−2222−22220022−2200000000000000000000000000000000000000
χ754-44-4-4-444000000000000-222-22-2-2200−22220022−2222−2200−222200000000000000000000000000000000000000
χ764-4-44-444-40000000000002i−2i2i−2i−2i2i−2i2i22−2200−222200002i2−2i200−2i22i2000000000000000000000000000000000000
χ774-4-44-444-40000000000002i−2i2i−2i−2i2i−2i2i−22220022−220000−2i22i2002i2−2i2000000000000000000000000000000000000
χ784-4-44-444-4000000000000−2i2i−2i2i2i−2i2i−2i22−2200−22220000−2i22i2002i2−2i2000000000000000000000000000000000000
χ794-4-44-444-4000000000000−2i2i−2i2i2i−2i2i−2i−22220022−2200002i2−2i200−2i22i2000000000000000000000000000000000000
χ804-4-4-444-4444-4-4-4-4-4444-44000000000000000000000000000000000000000000000000000000000000

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