Finite Group Databasebeta

← Group #72252552

Character table — Group #72252552

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size112444666666881212121212121212121212121224242424242424242424242432324848646464969696969696969696969696969696128128128128128128
order1222242222228822222222444444488888888883622612124444444444444446624242424
χ11111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3111111111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111-1-1-1-1
χ4111111111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111-111-1-1-1-1-1-111111111-1-1-1-1
χ51111-1-1111111i−i111-1-1-1-1-111-1-1-11-1iiiii−i−i−i−i−i11111-1-1-1i−i111-1-1-1iii−i−i−i1-1ii−i−i
χ61111-1-1111111i−i111-1-1-1-1-111-1-1-11-1iiiii−i−i−i−i−i11-1-11-1-11−ii-1-1-1111−i−i−iiii1-1ii−i−i
χ71111-1-1111111−ii111-1-1-1-1-111-1-1-11-1−i−i−i−i−iiiiii11111-1-1-1−ii111-1-1-1−i−i−iiii1-1−i−iii
χ81111-1-1111111−ii111-1-1-1-1-111-1-1-11-1−i−i−i−i−iiiiii11-1-11-1-11i−i-1-1-1111iii−i−i−i1-1−i−iii
χ9222222222222222222222222222222222222222-1-100-1-1-1000000000000000-1-1-1-1-1-1
χ10222222222222-2-2222222222222222-2-2-2-2-2-2-2-2-2-2-1-100-1-1-1000000000000000-1-11111
χ112222-2-22222222i−2i222-2-2-2-2-222-2-2-22-22i2i2i2i2i−2i−2i−2i−2i−2i-1-100-111000000000000000-11−i−iii
χ122222-2-2222222−2i2i222-2-2-2-2-222-2-2-22-2−2i−2i−2i−2i−2i2i2i2i2i2i-1-100-111000000000000000-11ii−i−i
χ13222-22-222222200-2-2-2-2-222222-2-2-2-22000000000022002-2-2000000000000000-220000
χ14222-22-222222200-2-2-2-2-222222-2-2-2-220000000000-1-100-1110000000000000001-13−33−3
χ15222-22-222222200-2-2-2-2-222222-2-2-2-220000000000-1-100-1110000000000000001-1−33−33
χ16222-2-2222222200-2-2-222-2-2-222222-2-200000000002200222000000000000000-2-20000
χ17222-2-2222222200-2-2-222-2-2-222222-2-20000000000-1-100-1-1-100000000000000011−i3i3i3−i3
χ18222-2-2222222200-2-2-222-2-2-222222-2-20000000000-1-100-1-1-100000000000000011i3−i3−i3i3
χ1933333333-1-1-1-1333-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-100110001111-1-11-1-11-1-11-1-1000000
χ2033333333-1-1-1-1333-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-100-1-1000-1-1-1-111-111-111-111000000
χ2133333333-1-1-1-1-3-33-1-1-1-13-1-1-1-13-1-1-1-1-31111-3111100110001-1-11-1-11-1-1-111-111000000
χ2233333333-1-1-1-1-3-33-1-1-1-13-1-1-1-13-1-1-1-1-31111-3111100-1-1000-111-111-1111-1-11-1-1000000
χ23333333-1-133-1-133-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-10011000111-11-1-11-1-11-1-11-1000000
χ24333333-1-133-1-133-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-100-1-1000-1-1-11-111-111-111-11000000
χ25333333-1-133-1-1-3-3-13-1-1-1-13-1-1-1-13-1-1-11-31111-311100110001-1-1-11-1-11-11-111-11000000
χ26333333-1-133-1-1-3-3-13-1-1-1-13-1-1-1-13-1-1-11-31111-311100-1-1000-1111-111-11-11-1-11-1000000
χ27333333-1-1-1-13333-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-10011000111-1-11-1-11-1-11-1-11000000
χ28333333-1-1-1-13333-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-100-1-1000-1-1-111-111-111-111-1000000
χ29333333-1-1-1-133-3-3-1-13-1-1-1-13-1-1-1-13-1-111-31111-31100110001-1-1-1-11-1-1111-111-1000000
χ30333333-1-1-1-133-3-3-1-13-1-1-1-13-1-1-1-13-1-111-31111-31100-1-1000-11111-111-1-1-11-1-11000000
χ313333-3-333-1-1-1-13i−3i3-1-111-311-1-1-311-113i−i−i−i−i−3iiiii0011000-1i−i1-1-1-111i−i−i−iii000000
χ323333-3-333-1-1-1-13i−3i3-1-111-311-1-1-311-113i−i−i−i−i−3iiiii00-1-10001−ii-1111-1-1−iiii−i−i000000
χ333333-3-333-1-1-1-1−3i3i3-1-111-311-1-1-311-11−3iiiii3i−i−i−i−i0011000-1−ii1-1-1-111−iiii−i−i000000
χ343333-3-333-1-1-1-1−3i3i3-1-111-311-1-1-311-11−3iiiii3i−i−i−i−i00-1-10001i−i-1111-1-1i−i−i−iii000000
χ353333-3-3-1-133-1-13i−3i-13-1111-31-1-11-31-11−i3i−i−i−ii−3iiii0011000-1i−i-11-11-11−ii−ii−ii000000
χ363333-3-3-1-133-1-13i−3i-13-1111-31-1-11-31-11−i3i−i−i−ii−3iiii00-1-10001−ii1-11-11-1i−ii−ii−i000000
χ373333-3-3-1-133-1-1−3i3i-13-1111-31-1-11-31-11i−3iiii−i3i−i−i−i0011000-1−ii-11-11-11i−ii−ii−i000000
χ383333-3-3-1-133-1-1−3i3i-13-1111-31-1-11-31-11i−3iiii−i3i−i−i−i00-1-10001i−i1-11-11-1−ii−ii−ii000000
χ393333-3-3-1-1-1-1333i−3i-1-131111-3-1-111-3-11−i−i3i−i−iii−3iii0011000-1i−i-1-1111-1−i−iiii−i000000
χ403333-3-3-1-1-1-1333i−3i-1-131111-3-1-111-3-11−i−i3i−i−iii−3iii00-1-10001−ii11-1-1-11ii−i−i−ii000000
χ413333-3-3-1-1-1-133−3i3i-1-131111-3-1-111-3-11ii−3iii−i−i3i−i−i0011000-1−ii-1-1111-1ii−i−i−ii000000
χ423333-3-3-1-1-1-133−3i3i-1-131111-3-1-111-3-11ii−3iii−i−i3i−i−i00-1-10001i−i11-1-1-11−i−iiii−i000000
χ4344-40004-44-44-400000000004-40000000000000004400-400000000000000000000000
χ4444-40004-44-44-400000000004-4000000000000000-2-2002−2i32i3000000000000000000000
χ4544-40004-44-44-400000000004-4000000000000000-2-20022i3−2i3000000000000000000000
χ46666666-2-2-2-2-2-266-2-2-222-2-2-222-2-2-222-2-2-222-2-2-2220000000000000000000000000000
χ47666666-2-2-2-2-2-2-6-6-2-2-222-2-2-222-2-2-222222-2-2222-2-20000000000000000000000000000
χ486666-6-6-2-2-2-2-2-26i−6i-2-2-2-2-2222222222-2−2i−2i−2i2i2i2i2i2i−2i−2i0000000000000000000000000000
χ496666-6-6-2-2-2-2-2-2−6i6i-2-2-2-2-2222222222-22i2i2i−2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ50666-66-666-2-2-2-200-622226-2-2-2-2-6222-200000000000000000000000000000000000000
χ51666-66-6-2-266-2-2002-6222-26-2-2-22-622-200000000000000000000000000000000000000
χ52666-66-6-2-2-2-2660022-622-2-26-2-222-62-200000000000000000000000000000000000000
χ53666-66-6-2-2-2-2-2-200222-2-2-2-2-222222-220004i−4i0004i−4i0000000000000000000000000000
χ54666-66-6-2-2-2-2-2-200222-2-2-2-2-222222-22000−4i4i000−4i4i0000000000000000000000000000
χ55666-6-6666-2-2-2-200-622-2-2-622-2-26-2-22200000000000000000000000000000000000000
χ56666-6-66-2-266-2-2002-62-2-22-62-2-2-26-22200000000000000000000000000000000000000
χ57666-6-66-2-2-2-2660022-6-2-222-6-2-2-2-262200000000000000000000000000000000000000
χ58666-6-66-2-2-2-2-2-2002222222222-2-2-2-2-20004-4000-440000000000000000000000000000
χ59666-6-66-2-2-2-2-2-2002222222222-2-2-2-2-2000-440004-40000000000000000000000000000
χ601212-1200012-12-44-440000000000-440000000000000000000000000000000000000000000
χ611212-12000-4412-12-440000000000-440000000000000000000000000000000000000000000
χ621212-12000-44-4412-120000000000-440000000000000000000000000000000000000000000
χ631212-12000-44-44-44000008-80004-40000000000000000000000000000000000000000000
χ641212-12000-44-44-4400000-880004-40000000000000000000000000000000000000000000
χ6516-1600000000000000000000000000000000000004-44-4000000000000000000000000
χ6616-1600000000000000000000000000000000000004-4-44000000000000000000000000
χ6732-320000000000000000000000000000000000000-4400000000000000000000000000

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