Finite Group Databasebeta

← Group #209840

Character table — Group #209840

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444422444444444444444444888888888888888822448888
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
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ12111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ171-11-111-1-111-1-1ii−i−i11-1-1i−ii−i11-1-1i−iii−i−i1-11-11-1i−i1-111-1-1i−iii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i
χ181-11-111-1-111-1-1ii−i−i11-1-1i−ii−i11-1-1i−iii−i−i1-11-11-1i−i1-111-1-1i−iii−i−ii−i-1-111−i−iii-1-111−i−iii-11−ii-11−ii
χ191-11-111-1-111-1-1ii−i−i11-1-1i−ii−i11-1-1i−iii−i−i1-11-1-11−ii-11-1-111i−i−i−iii−ii11-1-1ii−i−i-1-111−i−iii1-1i−i-11−ii
χ201-11-111-1-111-1-1ii−i−i11-1-1i−ii−i11-1-1i−iii−i−i1-11-1-11−ii-11-1-111i−i−i−iii−ii-1-111−i−iii11-1-1ii−i−i-11−ii1-1i−i
χ211-11-111-1-111-1-1ii−i−i11-1-1i−ii−i-1-111i−i−i−iii1-1-111-1i−i1-1-1-111−ii−i−iiii−i11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii
χ221-11-111-1-111-1-1ii−i−i11-1-1i−ii−i-1-111i−i−i−iii1-1-111-1i−i1-1-1-111−ii−i−iiii−i-1-111−i−iii-1-111−i−iii1-1i−i1-1i−i
χ231-11-111-1-111-1-1ii−i−i11-1-1i−ii−i-1-111i−i−i−iii1-1-11-11−ii-1111-1-1−iiii−i−i−ii11-1-1ii−i−i-1-111−i−iii-11−ii1-1i−i
χ241-11-111-1-111-1-1ii−i−i11-1-1i−ii−i-1-111i−i−i−iii1-1-11-11−ii-1111-1-1−iiii−i−i−ii-1-111−i−iii11-1-1ii−i−i1-1i−i-11−ii
χ251-11-111-1-111-1-1−i−iii11-1-1−ii−ii11-1-1−ii−i−iii1-11-11-1−ii1-111-1-1−ii−i−iii−ii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii
χ261-11-111-1-111-1-1−i−iii11-1-1−ii−ii11-1-1−ii−i−iii1-11-11-1−ii1-111-1-1−ii−i−iii−ii-1-111ii−i−i-1-111ii−i−i-11i−i-11i−i
χ271-11-111-1-111-1-1−i−iii11-1-1−ii−ii11-1-1−ii−i−iii1-11-1-11i−i-11-1-111−iiii−i−ii−i11-1-1−i−iii-1-111ii−i−i1-1−ii-11i−i
χ281-11-111-1-111-1-1−i−iii11-1-1−ii−ii11-1-1−ii−i−iii1-11-1-11i−i-11-1-111−iiii−i−ii−i-1-111ii−i−i11-1-1−i−iii-11i−i1-1−ii
χ291-11-111-1-111-1-1−i−iii11-1-1−ii−ii-1-111−iiii−i−i1-1-111-1−ii1-1-1-111i−iii−i−i−ii11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i
χ301-11-111-1-111-1-1−i−iii11-1-1−ii−ii-1-111−iiii−i−i1-1-111-1−ii1-1-1-111i−iii−i−i−ii-1-111ii−i−i-1-111ii−i−i1-1−ii1-1−ii
χ311-11-111-1-111-1-1−i−iii11-1-1−ii−ii-1-111−iiii−i−i1-1-11-11i−i-1111-1-1i−i−i−iiii−i11-1-1−i−iii-1-111ii−i−i-11i−i1-1−ii
χ321-11-111-1-111-1-1−i−iii11-1-1−ii−ii-1-111−iiii−i−i1-1-11-11i−i-1111-1-1i−i−i−iiii−i-1-111ii−i−i11-1-1−i−iii1-1−ii-11i−i
χ33222222222-22-222222-22-2-2-2222222-2-2-2-2-2-2-2-2-2-2000000000022000000000000000000000000000000
χ34222222222-22-222222-22-2-2-222-2-2-2-2-2-22222-2-2220000000000-2-2000000000000000000000000000000
χ35222222222-22-2-2-2-2-22-22-222-2-22222222222-2-2-2-20000000000-2-2000000000000000000000000000000
χ36222222222-22-2-2-2-2-22-22-222-2-2-2-2-2-222-2-2-2-2-2-222000000000022000000000000000000000000000000
χ3722222222-22-222222-22-22-2-2-2-20000220000-2-20022-2-2-2-2000000000022000000000000000000000000
χ3822222222-22-222222-22-22-2-2-2-20000220000-2-200-2-222220000000000-2-2000000000000000000000000
χ3922222222-22-22-2-2-2-2-22-2222220000-2-20000-2-2002222-2-20000000000-2-2000000000000000000000000
χ4022222222-22-22-2-2-2-2-22-2222220000-2-20000-2-200-2-2-2-222000000000022000000000000000000000000
χ4122222222-2-2-2-22222-2-2-2-222-2-20000-2-2000022000000002-22-2002-22-200000000000000000000000000
χ4222222222-2-2-2-22222-2-2-2-222-2-20000-2-200002200000000-22-2200-22-2200000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222000022000022000000002-22-200-22-2200000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22200002200002200000000-22-22002-22-200000000000000000000000000
χ452-22-222-2-22-2-222i2i−2i−2i2-2-22−2i2i2i−2i22-2-2−2i2i−2i−2i2i2i-22-2200000000002i−2i000000000000000000000000000000
χ462-22-222-2-22-2-222i2i−2i−2i2-2-22−2i2i2i−2i-2-222−2i2i2i2i−2i−2i-222-20000000000−2i2i000000000000000000000000000000
χ472-22-222-2-22-2-22−2i−2i2i2i2-2-222i−2i−2i2i22-2-22i−2i2i2i−2i−2i-22-220000000000−2i2i000000000000000000000000000000
χ482-22-222-2-22-2-22−2i−2i2i2i2-2-222i−2i−2i2i-2-2222i−2i−2i−2i2i2i-222-200000000002i−2i000000000000000000000000000000
χ492-22-222-2-2-222-22i2i−2i−2i-222-2−2i2i−2i2i00002i−2i0000-22002-2−2i2i-2200000000002i−2i000000000000000000000000
χ502-22-222-2-2-222-22i2i−2i−2i-222-2−2i2i−2i2i00002i−2i0000-2200-222i−2i2-20000000000−2i2i000000000000000000000000
χ512-22-222-2-2-222-2−2i−2i2i2i-222-22i−2i2i−2i0000−2i2i0000-22002-22i−2i-220000000000−2i2i000000000000000000000000
χ522-22-222-2-2-222-2−2i−2i2i2i-222-22i−2i2i−2i0000−2i2i0000-2200-22−2i2i2-200000000002i−2i000000000000000000000000
χ532-22-222-2-2-2-2222i2i−2i−2i-2-2222i−2i−2i2i0000−2i2i00002-2000000002-2-22002i−2i−2i2i00000000000000000000000000
χ542-22-222-2-2-2-2222i2i−2i−2i-2-2222i−2i−2i2i0000−2i2i00002-200000000-222-200−2i2i2i−2i00000000000000000000000000
χ552-22-222-2-2-2-222−2i−2i2i2i-2-222−2i2i2i−2i00002i−2i00002-2000000002-2-2200−2i2i2i−2i00000000000000000000000000
χ562-22-222-2-2-2-222−2i−2i2i2i-2-222−2i2i2i−2i00002i−2i00002-200000000-222-2002i−2i−2i2i00000000000000000000000000
χ57444-4-4-4-4400004-44-40000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ58444-4-4-4-4400004-44-4000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ59444-4-4-4-440000-44-440000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ60444-4-4-4-440000-44-44000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ6144-444-4-4-4040400000-40-400000000000000000000000000000000000022−2222−2200000000000000000000
χ6244-444-4-4-4040400000-40-4000000000000000000000000000000000000−2222−222200000000000000000000
χ6344-444-4-4-40-40-40000040400000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ6444-444-4-4-40-40-4000004040000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ6544-4-4-444-440-400000-404000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ6644-4-4-444-440-400000-40400000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ6744-4-4-444-4-4040000040-4000000000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ6844-4-4-444-4-4040000040-400000000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ694-444-4-44-400004i−4i−4i4i0000000000000000000000000000000000000000000000002i−2i−2i2i-222-200000000
χ704-444-4-44-400004i−4i−4i4i000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000
χ714-444-4-44-40000−4i4i4i−4i0000000000000000000000000000000000000000000000002i−2i−2i2i2-2-2200000000
χ724-444-4-44-40000−4i4i4i−4i000000000000000000000000000000000000000000000000−2i2i2i−2i-222-200000000
χ734-4-44-44-4440400000-40-4000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ744-4-44-44-4440400000-40-400000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ754-4-44-44-44-40-400000404000000000004-4-440000000000000000000000000000000000000000000000
χ764-4-44-44-44-40-40000040400000000000-444-40000000000000000000000000000000000000000000000
χ774-4-4-44-444040-400000-40400000000000000000000000000000000000022−22−222200000000000000000000
χ784-4-4-44-444040-400000-404000000000000000000000000000000000000−222222−2200000000000000000000
χ794-4-4-44-4440-4040000040-4000000000000000000000000000000000000000022−22−22220000000000000000
χ804-4-4-44-4440-4040000040-40000000000000000000000000000000000000000−222222−220000000000000000

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