Finite Group Databasebeta

← Group #72341854

Character table — Group #72341854

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112244666666666666121212121212121212121212121224242424323232324848484848484848484848484848646464646464
order12224444222222444444224444444444448888366622444444888888121212121212
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3111111-1-111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1
χ51-11-11-1i−i-1-1-1111111-1-1-11-1ii−i−i1-1iii−i−i−iii−i−i1-11-11-1111-1-1-1iii−i−i−i1-1ii−i−i
χ61-11-11-1i−i-1-1-1111111-1-1-11-1ii−i−i1-1iii−i−i−i−i−iii1-11-1-11-1-1-1111−i−i−iiii1-1ii−i−i
χ71-11-11-1−ii-1-1-1111111-1-1-11-1−i−iii1-1−i−i−iiiiii−i−i1-11-1-11-1-1-1111iii−i−i−i1-1−i−iii
χ81-11-11-1−ii-1-1-1111111-1-1-11-1−i−iii1-1−i−i−iiii−i−iii1-11-11-1111-1-1-1−i−i−iiii1-1−i−iii
χ922222222222222222222222222222222220000-1-1-1-100000000000000-1-1-1-1-1-1
χ10222222-2-222222222222222-2-2-2-222-2-2-2-2-2-20000-1-1-1-100000000000000-1-11111
χ112222-2-200222222-2-2-2-2-2-2-2-20000220000000000222200000000000000-2-20000
χ122222-2-200222222-2-2-2-2-2-2-2-20000220000000000-1-1-1-10000000000000011−i3i3−i3i3
χ132222-2-200222222-2-2-2-2-2-2-2-20000220000000000-1-1-1-10000000000000011i3−i3i3−i3
χ142-22-22-22i−2i-2-2-2222222-2-2-22-22i2i−2i−2i2-22i2i2i−2i−2i−2i0000-11-1100000000000000-11−i−iii
χ152-22-22-2−2i2i-2-2-2222222-2-2-22-2−2i−2i2i2i2-2−2i−2i−2i2i2i2i0000-11-1100000000000000-11ii−i−i
χ162-22-2-2200-2-2-2222-2-2-2222-2200002-200000000002-22-200000000000000-220000
χ172-22-2-2200-2-2-2222-2-2-2222-2200002-20000000000-11-11000000000000001-13−3−33
χ182-22-2-2200-2-2-2222-2-2-2222-2200002-20000000000-11-11000000000000001-1−333−3
χ19333333333-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-13-1-111110000111-1-11-1-11-1-11-1-1000000
χ20333333333-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-13-1-1-1-1-1-10000-1-1-111-111-111-111000000
χ2133333333-13-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-13-11111000011-11-1-11-1-11-1-11-1000000
χ2233333333-13-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-13-1-1-1-1-10000-1-11-111-111-111-11000000
χ2333333333-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-131111000011-1-11-1-11-1-11-1-11000000
χ2433333333-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-13-1-1-1-10000-1-111-111-111-111-1000000
χ25333333-3-33-1-13-1-13-1-13-1-1-1-11111-1-1-311-31111110000-1-1-111-1111-1-11-1-1000000
χ26333333-3-33-1-13-1-13-1-13-1-1-1-11111-1-1-311-311-1-1-1-10000111-1-11-1-1-111-111000000
χ27333333-3-3-13-1-13-1-13-1-13-1-1-11111-1-11-311-3111110000-1-11-111-11-11-1-11-1000000
χ28333333-3-3-13-1-13-1-13-1-13-1-1-11111-1-11-311-31-1-1-1-1000011-11-1-11-11-111-11000000
χ29333333-3-3-1-13-1-13-1-13-1-13-1-11111-1-111-311-311110000-1-111-111-1-1-11-1-11000000
χ30333333-3-3-1-13-1-13-1-13-1-13-1-11111-1-111-311-3-1-1-1-1000011-1-11-1-1111-111-1000000
χ313-33-33-33i−3i11-3-1-13-1-1311-3-11−i−iii-11−i−i3iii−3iii−i−i00001-1-1-1111-1−i−iiii−i000000
χ323-33-33-33i−3i11-3-1-13-1-1311-3-11−i−iii-11−i−i3iii−3i−i−iii0000-1111-1-1-11ii−i−i−ii000000
χ333-33-33-33i−3i1-31-13-1-13-11-31-11−i−iii-11−i3i−ii−3iiii−i−i00001-1-11-11-11−ii−ii−ii000000
χ343-33-33-33i−3i1-31-13-1-13-11-31-11−i−iii-11−i3i−ii−3ii−i−iii0000-111-11-11-1i−ii−ii−i000000
χ353-33-33-33i−3i-3113-1-13-1-1-311-11−i−iii-113i−i−i−3iiiii−i−i00001-11-1-1-111i−i−i−iii000000
χ363-33-33-33i−3i-3113-1-13-1-1-311-11−i−iii-113i−i−i−3iii−i−iii0000-11-1111-1-1−iiii−i−i000000
χ373-33-33-3−3i3i11-3-1-13-1-1311-3-11ii−i−i-11ii−3i−i−i3iii−i−i0000-1111-1-1-11−i−iiii−i000000
χ383-33-33-3−3i3i11-3-1-13-1-1311-3-11ii−i−i-11ii−3i−i−i3i−i−iii00001-1-1-1111-1ii−i−i−ii000000
χ393-33-33-3−3i3i1-31-13-1-13-11-31-11ii−i−i-11i−3ii−i3i−iii−i−i0000-111-11-11-1−ii−ii−ii000000
χ403-33-33-3−3i3i1-31-13-1-13-11-31-11ii−i−i-11i−3ii−i3i−i−i−iii00001-1-11-11-11i−ii−ii−i000000
χ413-33-33-3−3i3i-3113-1-13-1-1-311-11ii−i−i-11−3iii3i−i−iii−i−i0000-11-1111-1-1i−i−i−iii000000
χ423-33-33-3−3i3i-3113-1-13-1-1-311-11ii−i−i-11−3iii3i−i−i−i−iii00001-11-1-1-111−iiii−i−i000000
χ4366666666-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-20000000000000000000000000000
χ44666666-6-6-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222220000000000000000000000000000
χ456666-6-6006-2-26-2-2-622-622220000-2-20000000000000000000000000000000000
χ466666-6-600-26-2-26-22-622-62220000-2-20000000000000000000000000000000000
χ476666-6-600-2-26-2-2622-622-6220000-2-20000000000000000000000000000000000
χ486666-6-600-2-2-2-2-2-2222222-2-24-44-4220000000000000000000000000000000000
χ496666-6-600-2-2-2-2-2-2222222-2-2-44-44220000000000000000000000000000000000
χ506-66-66-66i−6i222-2-2-2-2-2-22222-22i2i−2i−2i2-2−2i−2i−2i2i2i2i0000000000000000000000000000
χ516-66-66-6−6i6i222-2-2-2-2-2-22222-2−2i−2i2i2i2-22i2i2i−2i−2i−2i0000000000000000000000000000
χ526-66-6-6600222-2-2-2222-2-2-2-224i−4i−4i4i2-20000000000000000000000000000000000
χ536-66-6-6600222-2-2-2222-2-2-2-22−4i4i4i−4i2-20000000000000000000000000000000000
χ546-66-6-660022-6-2-2622-6-2-262-20000-220000000000000000000000000000000000
χ556-66-6-66002-62-26-22-62-26-22-20000-220000000000000000000000000000000000
χ566-66-6-6600-6226-2-2-6226-2-22-20000-220000000000000000000000000000000000
χ5788-8-8000000000000000000000000000000−2i22i2−2i22i222-2-200000000000000000000
χ5888-8-80000000000000000000000000000002i2−2i22i2−2i222-2-200000000000000000000
χ598-8-8800000000000000000000000000000022−22−22222-2-2200000000000000000000
χ608-8-88000000000000000000000000000000−222222−222-2-2200000000000000000000
χ611616-16-160000000000000000000000000000000000-2-22200000000000000000000
χ6216-16-16160000000000000000000000000000000000-222-200000000000000000000

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