Finite Group Databasebeta

← Group #72267839

Character table — Group #72267839

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size11112233333333333344666666666612121212121212121212121224242424242424242424242424242424323232324848484848484848646464646464
order1222442222222222224422224444444444444444448888888888888888366622444444121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ3111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ4111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ51-11-11-1111-1-1-1-1-1-1111i−i11-1-1111-1-1-11-1iiiii−i−i−i−i−iii−i−iiiiiii−i−i−i−i−i−i1-11-11-1111-1-1-11-1ii−i−i
χ61-11-11-1111-1-1-1-1-1-1111i−i11-1-1111-1-1-11-1iiiii−i−i−i−i−i−i−iii−i−i−i−i−i−iiiiiii1-11-1-11-1-1-11111-1ii−i−i
χ71-11-11-1111-1-1-1-1-1-1111−ii11-1-1111-1-1-11-1−i−i−i−i−iiiiiiii−i−iiiiiii−i−i−i−i−i−i1-11-1-11-1-1-11111-1−i−iii
χ81-11-11-1111-1-1-1-1-1-1111−ii11-1-1111-1-1-11-1−i−i−i−i−iiiiii−i−iii−i−i−i−i−i−iiiiiii1-11-11-1111-1-1-11-1−i−iii
χ92222222222222222222222222222222222222222220000000000000000-1-1-1-100000000-1-1-1-1-1-1
χ10222222222222222222-2-2222222222222-2-2-2-2-2-2-2-2-2-20000000000000000-1-1-1-100000000-1-11111
χ112222-2-2222222222222002222-2-2-2-2-2-2-2-200000000000000000000000000222200000000-2-20000
χ122222-2-2222222222222002222-2-2-2-2-2-2-2-200000000000000000000000000-1-1-1-10000000011−i3i3−i3i3
χ132222-2-2222222222222002222-2-2-2-2-2-2-2-200000000000000000000000000-1-1-1-10000000011i3−i3i3−i3
χ1422-2-200-2-2-2222-2-2-2222002-22-2000000000000000000−i2i2−i2i2−i2−i2−i2i2i2i2−i2−i2−i2i2i2i222-2-200000000000000
χ1522-2-200-2-2-2222-2-2-2222002-22-2000000000000000000i2−i2i2−i2i2i2i2−i2−i2−i2i2i2i2−i2−i2−i222-2-200000000000000
χ162-22-22-2222-2-2-2-2-2-22222i−2i22-2-2222-2-2-22-22i2i2i2i2i−2i−2i−2i−2i−2i0000000000000000-11-1100000000-11−i−iii
χ172-22-22-2222-2-2-2-2-2-2222−2i2i22-2-2222-2-2-22-2−2i−2i−2i−2i−2i2i2i2i2i2i0000000000000000-11-1100000000-11ii−i−i
χ182-22-2-22222-2-2-2-2-2-22220022-2-2-2-2-2222-22000000000000000000000000002-22-200000000-220000
χ192-22-2-22222-2-2-2-2-2-22220022-2-2-2-2-2222-2200000000000000000000000000-11-11000000001-13−3−33
χ202-22-2-22222-2-2-2-2-2-22220022-2-2-2-2-2222-2200000000000000000000000000-11-11000000001-1−333−3
χ212-2-2200-2-2-2-2-2-2222222002-2-220000000000000000002−2−22222−2−2−2−2−2−22222-2-2200000000000000
χ222-2-2200-2-2-2-2-2-2222222002-2-22000000000000000000−222−2−2−2−2222222−2−2−22-2-2200000000000000
χ233333333-1-13-1-13-1-13-1-133-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-111111-1-11-1-11-1-11-1-10000111-1-11-1-1000000
χ243333333-1-13-1-13-1-13-1-133-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-1-1-1-1-111-111-111-1110000-1-1-111-111000000
χ253333333-1-13-1-13-1-13-1-1-3-3-1-1-1-13-1-13-1-1-1-1-31111-3111111111-1-11-1-11-1-11-1-10000-1-1-111-111000000
χ263333333-1-13-1-13-1-13-1-1-3-3-1-1-1-13-1-13-1-1-1-1-31111-31111-1-1-1-1-111-111-111-1110000111-1-11-1-1000000
χ27333333-13-1-13-1-13-1-13-133-1-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-11111-11-1-11-1-11-1-11-1000011-11-1-11-1000000
χ28333333-13-1-13-1-13-1-13-133-1-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-1-1-11-111-111-111-110000-1-11-111-11000000
χ29333333-13-1-13-1-13-1-13-1-3-3-1-1-1-1-13-1-13-1-1-11-31111-31111111-11-1-11-1-11-1-11-10000-1-11-111-11000000
χ30333333-13-1-13-1-13-1-13-1-3-3-1-1-1-1-13-1-13-1-1-11-31111-3111-1-1-1-11-111-111-111-11000011-11-1-11-1000000
χ31333333-1-13-1-13-1-13-1-1333-1-1-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-11111-1-11-1-11-1-11-1-11000011-1-11-1-11000000
χ32333333-1-13-1-13-1-13-1-1333-1-1-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-1-111-111-111-111-10000-1-111-111-1000000
χ33333333-1-13-1-13-1-13-1-13-3-3-1-1-1-1-1-13-1-13-1-111-31111-3111111-1-11-1-11-1-11-1-110000-1-111-111-1000000
χ34333333-1-13-1-13-1-13-1-13-3-3-1-1-1-1-1-13-1-13-1-111-31111-311-1-1-1-111-111-111-111-1000011-1-11-1-11000000
χ353-33-33-33-1-1-311-3113-1-13i−3i-1-1113-1-1-311-113i−i−i−i−i−3iiiiiii−i−ii−i−ii−i−i−iii−iii00001-11-1-1-111000000
χ363-33-33-33-1-1-311-3113-1-13i−3i-1-1113-1-1-311-113i−i−i−i−i−3iiiii−i−iii−iii−iiii−i−ii−i−i0000-11-1111-1-1000000
χ373-33-33-33-1-1-311-3113-1-1−3i3i-1-1113-1-1-311-11−3iiiii3i−i−i−i−iii−i−ii−i−ii−i−i−iii−iii0000-11-1111-1-1000000
χ383-33-33-33-1-1-311-3113-1-1−3i3i-1-1113-1-1-311-11−3iiiii3i−i−i−i−i−i−iii−iii−iiii−i−ii−i−i00001-11-1-1-111000000
χ393-33-33-3-13-11-311-31-13-13i−3i-1-111-13-11-31-11−i3i−i−i−ii−3iiiiii−i−i−ii−i−ii−ii−iii−ii00001-1-11-11-11000000
χ403-33-33-3-13-11-311-31-13-13i−3i-1-111-13-11-31-11−i3i−i−i−ii−3iiii−i−iiii−iii−ii−ii−i−ii−i0000-111-11-11-1000000
χ413-33-33-3-13-11-311-31-13-1−3i3i-1-111-13-11-31-11i−3iiii−i3i−i−i−iii−i−i−ii−i−ii−ii−iii−ii0000-111-11-11-1000000
χ423-33-33-3-13-11-311-31-13-1−3i3i-1-111-13-11-31-11i−3iiii−i3i−i−i−i−i−iiii−iii−ii−ii−i−ii−i00001-1-11-11-11000000
χ433-33-33-3-1-1311-311-3-1-133i−3i-1-111-1-1311-3-11−i−i3i−i−iii−3iiiii−i−i−i−ii−i−iiii−iii−i00001-1-1-1111-1000000
χ443-33-33-3-1-1311-311-3-1-133i−3i-1-111-1-1311-3-11−i−i3i−i−iii−3iii−i−iiiii−iii−i−i−ii−i−ii0000-1111-1-1-11000000
χ453-33-33-3-1-1311-311-3-1-13−3i3i-1-111-1-1311-3-11ii−3iii−i−i3i−i−iii−i−i−i−ii−i−iiii−iii−i0000-1111-1-1-11000000
χ463-33-33-3-1-1311-311-3-1-13−3i3i-1-111-1-1311-3-11ii−3iii−i−i3i−i−i−i−iiiii−iii−i−i−ii−i−ii00001-1-1-1111-1000000
χ4744-4-400-4-4-4444-4-4-4444004-44-40000000000000000000000000000000000-2-22200000000000000
χ484-4-4400-4-4-4-4-4-4444444004-4-440000000000000000000000000000000000-222-200000000000000
χ49666666-2-2-2-2-2-2-2-2-2-2-2-2662222-2-2-2-2-2-222-2-2-222-2-2-2220000000000000000000000000000000000
χ50666666-2-2-2-2-2-2-2-2-2-2-2-2-6-62222-2-2-2-2-2-222222-2-2222-2-20000000000000000000000000000000000
χ516666-6-66-2-26-2-26-2-26-2-200-2-2-2-2-622-6222200000000000000000000000000000000000000000000
χ526666-6-6-26-2-26-2-26-2-26-200-2-2-2-22-622-622200000000000000000000000000000000000000000000
χ536666-6-6-2-26-2-26-2-26-2-2600-2-2-2-222-622-62200000000000000000000000000000000000000000000
χ546666-6-6-2-2-2-2-2-2-2-2-2-2-2-2002222222222-2-20004-40004-40000000000000000000000000000000000
χ556666-6-6-2-2-2-2-2-2-2-2-2-2-2-2002222222222-2-2000-44000-440000000000000000000000000000000000
χ5666-6-60022-6-2-2622-6-2-2600-22-22000000000000000000−i2i2−i2i2i2i2−i2−i2−i2i2i2i2−i2−i2−i2i2000000000000000000
χ5766-6-60022-6-2-2622-6-2-2600-22-22000000000000000000i2−i2i2−i2−i2−i2i2i2i2−i2−i2−i2i2i2i2−i2000000000000000000
χ5866-6-6002-62-26-22-62-26-200-22-22000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ5966-6-6002-62-26-22-62-26-200-22-22000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ6066-6-600-6226-2-2-6226-2-200-22-22000000000000000000−i2i2−i2i2−i2i2i2i2−i2−i2−i2i2i2i2−i2−i2000000000000000000
χ6166-6-600-6226-2-2-6226-2-200-22-22000000000000000000i2−i2i2−i2i2−i2−i2−i2i2i2i2−i2−i2−i2i2i2000000000000000000
χ626-66-66-6-2-2-2222222-2-2-26i−6i22-2-2-2-2-22222-2−2i−2i−2i2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ636-66-66-6-2-2-2222222-2-2-2−6i6i22-2-2-2-2-22222-22i2i2i−2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ646-66-6-666-2-2-622-6226-2-200-2-222-6226-2-22-200000000000000000000000000000000000000000000
χ656-66-6-66-26-22-622-62-26-200-2-2222-62-26-22-200000000000000000000000000000000000000000000
χ666-66-6-66-2-2622-622-6-2-2600-2-22222-6-2-262-200000000000000000000000000000000000000000000
χ676-66-6-66-2-2-2222222-2-2-20022-2-2222-2-2-2-220004i−4i000−4i4i0000000000000000000000000000000000
χ686-66-6-66-2-2-2222222-2-2-20022-2-2222-2-2-2-22000−4i4i0004i−4i0000000000000000000000000000000000
χ696-6-660022-622-6-2-26-2-2600-222-20000000000000000002−2−22−2−2222−222−2−2−22000000000000000000
χ706-6-660022-622-6-2-26-2-2600-222-2000000000000000000−222−222−2−2−22−2−2222−2000000000000000000
χ716-6-66002-622-62-26-2-26-200-222-20000000000000000002−2−22−22−22−222−22−22−2000000000000000000
χ726-6-66002-622-62-26-2-26-200-222-2000000000000000000−222−22−22−22−2−22−22−22000000000000000000
χ736-6-6600-622-6226-2-26-2-200-222-20000000000000000002−2−222−2−2−222−2222−2−2000000000000000000
χ746-6-6600-622-6226-2-26-2-200-222-2000000000000000000−222−2−2222−2−22−2−2−222000000000000000000
χ751212-12-1200444-4-4-4444-4-4-4004-44-40000000000000000000000000000000000000000000000000000
χ7612-12-121200444444-4-4-4-4-4-4004-4-440000000000000000000000000000000000000000000000000000

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