Finite Group Databasebeta

← Group #210041

Character table — Group #210041

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222224444444444444444448888888888888888888888888888161616161616161616161616
order12222222444444444444444444444444442244444444444444444488888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ171-111-11-1-111-1-111-1-1i−ii−iii−i−i11-1-1ii−i−i1-11-11-1i−i1-1i−i11-1-1i−iii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ181-111-11-1-111-1-111-1-1i−ii−iii−i−i11-1-1ii−i−i1-11-11-1i−i1-1i−i11-1-1i−iii−i−i-1-111−i−iii-11−ii-11−ii-11−ii
χ191-111-11-1-111-1-111-1-1i−ii−iii−i−i11-1-1ii−i−i1-1-111-1i−i-11−ii-1-111−ii−i−iii11-1-1ii−i−i-11−ii1-1i−i-11−ii
χ201-111-11-1-111-1-111-1-1i−ii−iii−i−i11-1-1ii−i−i1-1-111-1i−i-11−ii-1-111−ii−i−iii-1-111−i−iii1-1i−i-11−ii1-1i−i
χ211-111-11-1-111-1-111-1-1i−ii−iii−i−i-1-111−i−iii1-11-1-11−ii1-1i−i-1-111i−i−i−iii11-1-1ii−i−i-11−ii-11−ii1-1i−i
χ221-111-11-1-111-1-111-1-1i−ii−iii−i−i-1-111−i−iii1-11-1-11−ii1-1i−i-1-111i−i−i−iii-1-111−i−iii1-1i−i1-1i−i-11−ii
χ231-111-11-1-111-1-111-1-1i−ii−iii−i−i-1-111−i−iii1-1-11-11−ii-11−ii11-1-1−iiii−i−i11-1-1ii−i−i1-1i−i-11−ii-11−ii
χ241-111-11-1-111-1-111-1-1i−ii−iii−i−i-1-111−i−iii1-1-11-11−ii-11−ii11-1-1−iiii−i−i-1-111−i−iii-11−ii1-1i−i1-1i−i
χ251-111-11-1-111-1-111-1-1−ii−ii−i−iii11-1-1−i−iii1-11-11-1−ii1-1−ii11-1-1−ii−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ261-111-11-1-111-1-111-1-1−ii−ii−i−iii11-1-1−i−iii1-11-11-1−ii1-1−ii11-1-1−ii−i−iii-1-111ii−i−i-11i−i-11i−i-11i−i
χ271-111-11-1-111-1-111-1-1−ii−ii−i−iii11-1-1−i−iii1-1-111-1−ii-11i−i-1-111i−iii−i−i11-1-1−i−iii-11i−i1-1−ii-11i−i
χ281-111-11-1-111-1-111-1-1−ii−ii−i−iii11-1-1−i−iii1-1-111-1−ii-11i−i-1-111i−iii−i−i-1-111ii−i−i1-1−ii-11i−i1-1−ii
χ291-111-11-1-111-1-111-1-1−ii−ii−i−iii-1-111ii−i−i1-11-1-11i−i1-1−ii-1-111−iiii−i−i11-1-1−i−iii-11i−i-11i−i1-1−ii
χ301-111-11-1-111-1-111-1-1−ii−ii−i−iii-1-111ii−i−i1-11-1-11i−i1-1−ii-1-111−iiii−i−i-1-111ii−i−i1-1−ii1-1−ii-11i−i
χ311-111-11-1-111-1-111-1-1−ii−ii−i−iii-1-111ii−i−i1-1-11-11i−i-11i−i11-1-1i−i−i−iii11-1-1−i−iii1-1−ii-11i−i-11i−i
χ321-111-11-1-111-1-111-1-1−ii−ii−i−iii-1-111ii−i−i1-1-11-11i−i-11i−i11-1-1i−i−i−iii-1-111ii−i−i-11i−i1-1−ii1-1−ii
χ33222222222-22-22-22-222-2-22-22-200000000-2-2220000-2-2220000-2-2000000000000000000000000
χ34222222222-22-22-22-222-2-22-22-200000000-2-2-2-2000022-2-2000022000000000000000000000000
χ35222222222-22-22-22-2-2-222-22-2200000000-2-2220000-2-2-2-2000022000000000000000000000000
χ36222222222-22-22-22-2-2-222-22-2200000000-2-2-2-2000022220000-2-2000000000000000000000000
χ3722222222-22-22-22-2222-2-2-22-222222-2-2-2-2-2-200-2-2220000000000000000000000000000000000
χ3822222222-22-22-22-2222-2-2-22-22-2-2-2-22222-2-20022-2-20000000000000000000000000000000000
χ3922222222-22-22-22-22-2-2222-22-222222222-2-200-2-2-2-20000000000000000000000000000000000
χ4022222222-22-22-22-22-2-2222-22-2-2-2-2-2-2-2-2-2-2-20022220000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22222-2-2-2-2000000002200000000002-22-2002-22-200000000000000000000
χ4222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000220000000000-22-2200-22-2200000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-22222000000002200000000002-22-200-22-2200000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000220000000000-22-22002-22-200000000000000000000
χ452-222-22-2-22-2-222-2-222i−2i−2i2i2i−2i−2i2i00000000-222-20000-222i−2i0000−2i2i000000000000000000000000
χ462-222-22-2-22-2-222-2-222i−2i−2i2i2i−2i−2i2i00000000-22-2200002-2−2i2i00002i−2i000000000000000000000000
χ472-222-22-2-22-2-222-2-22−2i2i2i−2i−2i2i2i−2i00000000-222-20000-22−2i2i00002i−2i000000000000000000000000
χ482-222-22-2-22-2-222-2-22−2i2i2i−2i−2i2i2i−2i00000000-22-2200002-22i−2i0000−2i2i000000000000000000000000
χ492-222-22-2-2-222-2-222-22i−2i−2i2i−2i2i2i−2i22-2-2−2i−2i2i2i-2200-222i−2i0000000000000000000000000000000000
χ502-222-22-2-2-222-2-222-22i−2i−2i2i−2i2i2i−2i-2-2222i2i−2i−2i-22002-2−2i2i0000000000000000000000000000000000
χ512-222-22-2-2-222-2-222-2−2i2i2i−2i2i−2i−2i2i22-2-22i2i−2i−2i-2200-22−2i2i0000000000000000000000000000000000
χ522-222-22-2-2-222-2-222-2−2i2i2i−2i2i−2i−2i2i-2-222−2i−2i2i2i-22002-22i−2i0000000000000000000000000000000000
χ532-222-22-2-2-2-222-2-2222i−2i2i−2i−2i−2i2i2i000000002-200000000002-2-22002i−2i−2i2i00000000000000000000
χ542-222-22-2-2-2-222-2-2222i−2i2i−2i−2i−2i2i2i000000002-20000000000-222-200−2i2i2i−2i00000000000000000000
χ552-222-22-2-2-2-222-2-222−2i2i−2i2i2i2i−2i−2i000000002-200000000002-2-2200−2i2i2i−2i00000000000000000000
χ562-222-22-2-2-2-222-2-222−2i2i−2i2i2i2i−2i−2i000000002-20000000000-222-2002i−2i−2i2i00000000000000000000
χ57444-4-4-44-404040-40-40000000000004-44-4000000000000000000000000000000000000000000
χ58444-4-4-44-404040-40-4000000000000-44-44000000000000000000000000000000000000000000
χ59444-4-4-44-40-40-40404000000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ60444-4-4-44-40-40-4040400000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ6144-44-4-4-444040-40-4000000000000000000000000000000000000000000022−2222−22000000000000
χ6244-44-4-4-444040-40-40000000000000000000000000000000000000000000−2222−2222000000000000
χ6344-44-4-4-44-40-404040000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ6444-44-4-4-44-40-40404000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ654-44-44-4-44040-40-4040000000000004i−4i−4i4i000000000000000000000000000000000000000000
χ664-44-44-4-44040-40-404000000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ674-44-44-4-440-404040-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ684-44-44-4-440-404040-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ694-4-444-44-440-40-40400000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ704-4-444-44-440-40-4040000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ714-4-444-44-4-404040-40000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ724-4-444-44-4-404040-4000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ7388-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000

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