Finite Group Databasebeta

← Group #72341747

Character table — Group #72341747

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size11112222226666666612121212121212121212121212121212161616163232323232323232484848484848484848484848484848484848484848484848484848484848484848484848646464646464646464646464
order1222444444224444442222444444444444224436661212121222444444444444444444444444448888888866661212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ31111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ51111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1
χ61111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1
χ71111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-11111
χ81111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-111-1-11111
χ911-1-1i−ii−i1-11-1i−ii−i1-111-1-111-1-1ii−i−iii−i−i1-1i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i11-1-11-1i−iii−i−i
χ1011-1-1i−ii−i1-11-1i−ii−i1-111-1-111-1-1ii−i−iii−i−i1-1i−i11-1-1ii−i−i-11−ii1-1i−i-11−ii-1-111−i−iii-1-111−i−iii-11−ii-11−ii11-1-11-1i−iii−i−i
χ1111-1-1i−ii−i1-11-1i−ii−i1-111-1-111-1-1ii−i−iii−i−i-11−ii11-1-1ii−i−i1-1i−i-11−ii1-1i−i11-1-1ii−i−i-1-111−i−iii-11−ii-11−ii-1-1111-1i−i−i−iii
χ1211-1-1i−ii−i1-11-1i−ii−i1-111-1-111-1-1ii−i−iii−i−i-11−ii11-1-1ii−i−i-11−ii-11−ii-11−ii-1-111−i−iii11-1-1ii−i−i1-1i−i1-1i−i-1-1111-1i−i−i−iii
χ1311-1-1−ii−ii1-11-1−ii−ii1-111-1-111-1-1−i−iii−i−iii1-1−ii11-1-1−i−iii1-1−ii1-1−ii1-1−ii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii11-1-11-1−ii−i−iii
χ1411-1-1−ii−ii1-11-1−ii−ii1-111-1-111-1-1−i−iii−i−iii1-1−ii11-1-1−i−iii-11i−i1-1−ii-11i−i-1-111ii−i−i-1-111ii−i−i-11i−i-11i−i11-1-11-1−ii−i−iii
χ1511-1-1−ii−ii1-11-1−ii−ii1-111-1-111-1-1−i−iii−i−iii-11i−i11-1-1−i−iii1-1−ii-11i−i1-1−ii11-1-1−i−iii-1-111ii−i−i-11i−i-11i−i-1-1111-1−iiii−i−i
χ1611-1-1−ii−ii1-11-1−ii−ii1-111-1-111-1-1−i−iii−i−iii-11i−i11-1-1−i−iii-11i−i-11i−i-11i−i-1-111ii−i−i11-1-1−i−iii1-1−ii1-1−ii-1-1111-1−iiii−i−i
χ1722222222222222222222222222222222222222-1-1-1-1-1-1-1-1000022220000000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1
χ182222222222222222222222222222222222-2-2-2-2-1-1-1-1-1-1-1-10000-2-2-2-200000000000000000000000000001111-1-1-1-11111
χ19222222-2-2-2-22222-2-2-2-22-22-22-22-22-22-22-22-20000222222220000000000000000000000000000000000000000-2-2-2-20000
χ20222222-2-2-2-22222-2-2-2-22-22-22-22-22-22-22-22-20000-1-1-1-1-1-1-1-1000000000000000000000000000000000000−i3i3−i3i31111−i3i3−i3i3
χ21222222-2-2-2-22222-2-2-2-22-22-22-22-22-22-22-22-20000-1-1-1-1-1-1-1-1000000000000000000000000000000000000i3−i3i3−i31111i3−i3i3−i3
χ222222-2-222-2-222-2-222-2-22-22-22-22-2-22-22-22-2200002222-2-2-2-20000000000000000000000000000000000000000-2-2220000
χ232222-2-222-2-222-2-222-2-22-22-22-22-2-22-22-22-220000-1-1-1-11111000000000000000000000000000000000000−i3i3−i3i311-1-1i3−i3i3−i3
χ242222-2-222-2-222-2-222-2-22-22-22-22-2-22-22-22-220000-1-1-1-11111000000000000000000000000000000000000i3−i3i3−i311-1-1−i3i3−i3i3
χ252222-2-2-2-22222-2-2-2-22222222222-2-2-2-2-2-2-2-222-2-2-1-1-1-11111000022-2-20000000000000000000000000000-1-1-1-1-1-1111111
χ262222-2-2-2-22222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-1-1-1-111110000-2-22200000000000000000000000000001111-1-111-1-1-1-1
χ2722-2-22i−2i2i−2i2-22-22i−2i2i−2i2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i2-22i−2i-1-111−i−iii00002-22i−2i0000000000000000000000000000-1-111-11−ii−i−iii
χ2822-2-22i−2i2i−2i2-22-22i−2i2i−2i2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i-22−2i2i-1-111−i−iii0000-22−2i2i000000000000000000000000000011-1-1-11−iiii−i−i
χ2922-2-22i−2i−2i2i-222-22i−2i−2i2i-222-2-222-2-222i−2i−2i2i2i−2i−2i2i000022-2-22i2i−2i−2i0000000000000000000000000000000000000000-22−2i2i0000
χ3022-2-22i−2i−2i2i-222-22i−2i−2i2i-222-2-222-2-222i−2i−2i2i2i−2i−2i2i0000-1-111−i−iii000000000000000000000000000000000000−i3i3i3−i31-1i−i3−3−33
χ3122-2-22i−2i−2i2i-222-22i−2i−2i2i-222-2-222-2-222i−2i−2i2i2i−2i−2i2i0000-1-111−i−iii000000000000000000000000000000000000i3−i3−i3i31-1i−i−333−3
χ3222-2-2−2i2i2i−2i-222-2−2i2i2i−2i-222-2-222-2-22−2i2i2i−2i−2i2i2i−2i000022-2-2−2i−2i2i2i0000000000000000000000000000000000000000-222i−2i0000
χ3322-2-2−2i2i2i−2i-222-2−2i2i2i−2i-222-2-222-2-22−2i2i2i−2i−2i2i2i−2i0000-1-111ii−i−i000000000000000000000000000000000000−i3i3i3−i31-1−ii−333−3
χ3422-2-2−2i2i2i−2i-222-2−2i2i2i−2i-222-2-222-2-22−2i2i2i−2i−2i2i2i−2i0000-1-111ii−i−i000000000000000000000000000000000000i3−i3−i3i31-1−ii3−3−33
χ3522-2-2−2i2i−2i2i2-22-2−2i2i−2i2i2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i2-2−2i2i-1-111ii−i−i00002-2−2i2i0000000000000000000000000000-1-111-11i−iii−i−i
χ3622-2-2−2i2i−2i2i2-22-2−2i2i−2i2i2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i-222i−2i-1-111ii−i−i0000-222i−2i000000000000000000000000000011-1-1-11i−i−i−iii
χ37333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333000000001111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000
χ38333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333300000000-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000
χ39333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-300000000111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ40333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-300000000-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000
χ413333-3-3-3-33333-3-3-3-333-1-1-1-1-1-1-1-11111111133-3-30000000011-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1000000000000
χ423333-3-3-3-33333-3-3-3-333-1-1-1-1-1-1-1-11111111133-3-300000000-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111000000000000
χ433333-3-3-3-33333-3-3-3-333-1-1-1-1-1-1-1-111111111-3-3330000000011-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111000000000000
χ443333-3-3-3-33333-3-3-3-333-1-1-1-1-1-1-1-111111111-3-33300000000-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1000000000000
χ4533-3-33i−3i3i−3i3-33-33i−3i3i−3i3-3-1-111-1-111−i−iii−i−iii3-33i−3i000000001-1i−i-11−ii1-1i−i-1-111−i−iii-1-111−i−iii1-1i−i1-1i−i000000000000
χ4633-3-33i−3i3i−3i3-33-33i−3i3i−3i3-3-1-111-1-111−i−iii−i−iii3-33i−3i00000000-11−ii-11−ii-11−ii11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii000000000000
χ4733-3-33i−3i3i−3i3-33-33i−3i3i−3i3-3-1-111-1-111−i−iii−i−iii-33−3i3i000000001-1i−i1-1i−i1-1i−i-1-111−i−iii11-1-1ii−i−i-11−ii-11−ii000000000000
χ4833-3-33i−3i3i−3i3-33-33i−3i3i−3i3-3-1-111-1-111−i−iii−i−iii-33−3i3i00000000-11−ii1-1i−i-11−ii11-1-1ii−i−i-1-111−i−iii1-1i−i1-1i−i000000000000
χ4933-3-3−3i3i−3i3i3-33-3−3i3i−3i3i3-3-1-111-1-111ii−i−iii−i−i3-3−3i3i000000001-1−ii-11i−i1-1−ii-1-111ii−i−i-1-111ii−i−i1-1−ii1-1−ii000000000000
χ5033-3-3−3i3i−3i3i3-33-3−3i3i−3i3i3-3-1-111-1-111ii−i−iii−i−i3-3−3i3i00000000-11i−i-11i−i-11i−i11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i000000000000
χ5133-3-3−3i3i−3i3i3-33-3−3i3i−3i3i3-3-1-111-1-111ii−i−iii−i−i-333i−3i000000001-1−ii1-1−ii1-1−ii-1-111ii−i−i11-1-1−i−iii-11i−i-11i−i000000000000
χ5233-3-3−3i3i−3i3i3-33-3−3i3i−3i3i3-3-1-111-1-111ii−i−iii−i−i-333i−3i00000000-11i−i1-1−ii-11i−i11-1-1−i−iii-1-111ii−i−i1-1−ii1-1−ii000000000000
χ536666666666-2-2-2-2-2-2-2-22-22-2-22-222-22-2-22-2200000000000022220000-2-2-2-2000000000000000000000000000000000000
χ546666666666-2-2-2-2-2-2-2-22-22-2-22-222-22-2-22-22000000000000-2-2-2-200002222000000000000000000000000000000000000
χ556666666666-2-2-2-2-2-2-2-2-22-222-22-2-22-222-22-200000000000000000000000000000000000000002222-2-2-2-2000000000000
χ566666666666-2-2-2-2-2-2-2-2-22-222-22-2-22-222-22-20000000000000000000000000000000000000000-2-2-2-22222000000000000
χ57666666-6-6-6-66666-6-6-6-6-22-22-22-22-22-22-22-22000000000000000000000000000000000000000000000000000000000000
χ58666666-6-6-6-6-2-2-2-222222222-2-2-2-22222-2-2-2-20000000000000000000000002-22-22-22-20000000000000000000000000000
χ59666666-6-6-6-6-2-2-2-222222222-2-2-2-22222-2-2-2-2000000000000000000000000-22-22-22-220000000000000000000000000000
χ60666666-6-6-6-6-2-2-2-22222-2-2-2-22222-2-2-2-22222000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ61666666-6-6-6-6-2-2-2-22222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ626666-6-666-6-666-6-666-6-6-22-22-22-222-22-22-22-2000000000000000000000000000000000000000000000000000000000000
χ636666-6-666-6-6-2-222-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000002-22-2-22-220000000000000000000000000000
χ646666-6-666-6-6-2-222-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000-22-222-22-20000000000000000000000000000
χ656666-6-666-6-6-2-222-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ666666-6-666-6-6-2-222-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ676666-6-6-6-666-2-22222-2-22-22-2-22-22-22-222-22-200000000000022-2-20000-2-222000000000000000000000000000000000000
χ686666-6-6-6-666-2-22222-2-22-22-2-22-22-22-222-22-2000000000000-2-222000022-2-2000000000000000000000000000000000000
χ696666-6-6-6-666-2-22222-2-2-22-222-22-22-22-2-22-22000000000000000000000000000000000000000022-2-2-2-222000000000000
χ706666-6-6-6-666-2-22222-2-2-22-222-22-22-22-2-22-220000000000000000000000000000000000000000-2-22222-2-2000000000000
χ7166-6-66i−6i6i−6i6-6-22−2i2i−2i2i-222-2-22-222-22i−2i−2i2i−2i2i2i−2i0000000000002-22i−2i0000-22−2i2i000000000000000000000000000000000000
χ7266-6-66i−6i6i−6i6-6-22−2i2i−2i2i-222-2-22-222-22i−2i−2i2i−2i2i2i−2i000000000000-22−2i2i00002-22i−2i000000000000000000000000000000000000
χ7366-6-66i−6i6i−6i6-6-22−2i2i−2i2i-22-222-22-2-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000002-22i−2i-22−2i2i000000000000
χ7466-6-66i−6i6i−6i6-6-22−2i2i−2i2i-22-222-22-2-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000-22−2i2i2-22i−2i000000000000
χ7566-6-66i−6i−6i6i-666-66i−6i−6i6i-66-222-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000000000000000
χ7666-6-66i−6i−6i6i-66-22−2i2i2i−2i2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000002-2-222i−2i−2i2i0000000000000000000000000000
χ7766-6-66i−6i−6i6i-66-22−2i2i2i−2i2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000-222-2−2i2i2i−2i0000000000000000000000000000
χ7866-6-66i−6i−6i6i-66-22−2i2i2i−2i2-2-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000002i−2i−2i2i-222-200000000000000000000
χ7966-6-66i−6i−6i6i-66-22−2i2i2i−2i2-2-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000000000
χ8066-6-6−6i6i6i−6i-666-6−6i6i6i−6i-66-222-2-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000000000000000
χ8166-6-6−6i6i6i−6i-66-222i−2i−2i2i2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000002-2-22−2i2i2i−2i0000000000000000000000000000
χ8266-6-6−6i6i6i−6i-66-222i−2i−2i2i2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000-222-22i−2i−2i2i0000000000000000000000000000
χ8366-6-6−6i6i6i−6i-66-222i−2i−2i2i2-2-2-22222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000002i−2i−2i2i2-2-2200000000000000000000
χ8466-6-6−6i6i6i−6i-66-222i−2i−2i2i2-2-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000−2i2i2i−2i-222-200000000000000000000
χ8566-6-6−6i6i−6i6i6-6-222i−2i2i−2i-222-2-22-222-2−2i2i2i−2i2i−2i−2i2i0000000000002-2−2i2i0000-222i−2i000000000000000000000000000000000000
χ8666-6-6−6i6i−6i6i6-6-222i−2i2i−2i-222-2-22-222-2−2i2i2i−2i2i−2i−2i2i000000000000-222i−2i00002-2−2i2i000000000000000000000000000000000000
χ8766-6-6−6i6i−6i6i6-6-222i−2i2i−2i-22-222-22-2-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000002-2−2i2i-222i−2i000000000000
χ8866-6-6−6i6i−6i6i6-6-222i−2i2i−2i-22-222-22-2-222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000-222i−2i2-2−2i2i000000000000
χ8916-1616-1600000000000000000000000000000000004-4-440000000000000000000000000000000000000000000000000000
χ9016-1616-160000000000000000000000000000000000-222-2−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ9116-1616-160000000000000000000000000000000000-222-22i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ9216-16-161600000000000000000000000000000000004-44-40000000000000000000000000000000000000000000000000000
χ9316-16-16160000000000000000000000000000000000-22-2223−23−2323000000000000000000000000000000000000000000000000
χ9416-16-16160000000000000000000000000000000000-22-22−232323−23000000000000000000000000000000000000000000000000

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