Finite Group Databasebeta

← Group #72341316

Character table — Group #72341316

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444466668812121212121212122424242424242424242424242424242424242424323232323232323232323232323232324848484848484848
order1222444444224422224444442244444444444444444436666666121212121212121244448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ3111111-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1
χ4111111-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-11111
χ51111-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1111-1-1-1-11-1-1-1-1111111-1-111-1-1
χ61111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-111111-1-1-1-11-1-1-1-11111-1-111-1-111
χ71111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ81111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ911-1-1i−iii−i−i1-1i−i1-11-1i−ii−i1-11-1i−i1-1i−ii−i1-11-1i−ii−i1-111-111-1-1-1ii−i−iii−i−i1-1i−ii−i1-1
χ1011-1-1i−iii−i−i1-1i−i1-11-1i−ii−i1-1-11−ii-11−iii−i1-1-11−ii−ii-1111-111-1-1-1ii−i−iii−i−i-11−ii−ii-11
χ1111-1-1i−i−i−iii1-1i−i-111-1i−ii−i1-11-1i−i-11−ii−ii-111-1i−i−ii-1111-1-1-111-1ii−i−i−i−iii1-1i−i−ii-11
χ1211-1-1i−i−i−iii1-1i−i-111-1i−ii−i1-1-11−ii1-1i−i−ii-11-11−iii−i1-111-1-1-111-1ii−i−i−i−iii-11−iii−i1-1
χ1311-1-1−iiii−i−i1-1−ii-111-1−ii−ii1-11-1−ii-11i−ii−i-111-1−iii−i-1111-1-1-111-1−i−iiiii−i−i1-1−iii−i-11
χ1411-1-1−iiii−i−i1-1−ii-111-1−ii−ii1-1-11i−i1-1−iii−i-11-11i−i−ii1-111-1-1-111-1−i−iiiii−i−i-11i−i−ii1-1
χ1511-1-1−ii−i−iii1-1−ii1-11-1−ii−ii1-11-1−ii1-1−ii−ii1-11-1−ii−ii1-111-111-1-1-1−i−iii−i−iii1-1−ii−ii1-1
χ1611-1-1−ii−i−iii1-1−ii1-11-1−ii−ii1-1-11i−i-11i−i−ii1-1-11i−ii−i-1111-111-1-1-1−i−iii−i−iii-11i−ii−i-11
χ1722222222222222222222222200000000222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ18222222-2-2-2-22222-2-22222222200000000-2-2-2-200000000-1-1-11111-1-1-1-1-1111100000000
χ192222-2-2222222-2-2-2-222-2-2-2-2220000000022-2-200000000-1-1-11111-11111-1-1-1-100000000
χ202222-2-2-2-2-2-222-2-22222-2-2-2-22200000000-2-22200000000-1-1-1-1-1-1-1-11111111100000000
χ2122-2-22i−2i2i2i−2i−2i2-22i−2i2-22-22i−2i2i−2i2-2000000002i−2i2-200000000-1-11-1-1111−i−iii−i−iii00000000
χ2222-2-22i−2i−2i−2i2i2i2-22i−2i-222-22i−2i2i−2i2-200000000−2i2i-2200000000-1-1111-1-11−i−iiiii−i−i00000000
χ2322-2-2−2i2i2i2i−2i−2i2-2−2i2i-222-2−2i2i−2i2i2-2000000002i−2i-2200000000-1-1111-1-11ii−i−i−i−iii00000000
χ2422-2-2−2i2i−2i−2i2i2i2-2−2i2i2-22-2−2i2i−2i2i2-200000000−2i2i2-200000000-1-11-1-1111ii−i−iii−i−i00000000
χ253333333333333333-1-1-1-1-1-1-1-111111111-1-1-1-1111111110000000000000000-1-1-1-1-1-1-1-1
χ263333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000011111111
χ27333333-3-3-3-33333-3-3-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-10000000000000000-1-1-1-11111
χ28333333-3-3-3-33333-3-3-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111100000000000000001111-1-1-1-1
χ293333-3-3333333-3-3-3-3-1-11111-1-111-1-1-1-111-1-11111-1-111-1-10000000000000000-1-111-1-111
χ303333-3-3333333-3-3-3-3-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111000000000000000011-1-111-1-1
χ313333-3-3-3-3-3-333-3-333-1-11111-1-111-1-111-1-111-1-111-1-1-1-1110000000000000000-1-11111-1-1
χ323333-3-3-3-3-3-333-3-333-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1000000000000000011-1-1-1-111
χ3333-3-33i−3i3i3i−3i−3i3-33i−3i3-3-11−ii−ii-111-1i−i1-1i−i−ii-111-1i−ii−i1-10000000000000000-11−ii−ii-11
χ3433-3-33i−3i3i3i−3i−3i3-33i−3i3-3-11−ii−ii-11-11−ii-11−ii−ii-11-11−ii−ii-1100000000000000001-1i−ii−i1-1
χ3533-3-33i−3i−3i−3i3i3i3-33i−3i-33-11−ii−ii-111-1i−i-11−iii−i1-11-1i−i−ii-110000000000000000-11−iii−i1-1
χ3633-3-33i−3i−3i−3i3i3i3-33i−3i-33-11−ii−ii-11-11−ii1-1i−ii−i1-1-11−iii−i1-100000000000000001-1i−i−ii-11
χ3733-3-3−3i3i3i3i−3i−3i3-3−3i3i-33-11i−ii−i-111-1−ii-11i−i−ii1-11-1−iii−i-110000000000000000-11i−i−ii1-1
χ3833-3-3−3i3i3i3i−3i−3i3-3−3i3i-33-11i−ii−i-11-11i−i1-1−ii−ii1-1-11i−i−ii1-100000000000000001-1−iii−i-11
χ3933-3-3−3i3i−3i−3i3i3i3-3−3i3i3-3-11i−ii−i-111-1−ii1-1−iii−i-111-1−ii−ii1-10000000000000000-11i−ii−i-11
χ4033-3-3−3i3i−3i−3i3i3i3-3−3i3i3-3-11i−ii−i-11-11i−i-11i−ii−i-11-11i−ii−i-1100000000000000001-1−ii−ii1-1
χ416666660000-2-2-2-20022-2-222-2-2222200000000-2-2-2-20000000000000000000000000000
χ426666660000-2-2-2-20022-2-222-2-2-2-2-2-20000000022220000000000000000000000000000
χ436666660000-2-2-2-200-2-222-2-2220000222200000000-2-2-2-2000000000000000000000000
χ446666660000-2-2-2-200-2-222-2-2220000-2-2-2-2000000002222000000000000000000000000
χ456666-6-60000-2-222002222-2-2-2-222-2-200000000-2-2220000000000000000000000000000
χ466666-6-60000-2-222002222-2-2-2-2-2-2220000000022-2-20000000000000000000000000000
χ476666-6-60000-2-22200-2-2-2-22222000022-2-20000000022-2-2000000000000000000000000
χ486666-6-60000-2-22200-2-2-2-222220000-2-22200000000-2-222000000000000000000000000
χ4966-6-66i−6i0000-22−2i2i002-2−2i2i2i−2i-222-22i−2i00000000-22−2i2i0000000000000000000000000000
χ5066-6-66i−6i0000-22−2i2i002-2−2i2i2i−2i-22-22−2i2i000000002-22i−2i0000000000000000000000000000
χ5166-6-66i−6i0000-22−2i2i00-222i−2i−2i2i2-200002-22i−2i00000000−2i2i-22000000000000000000000000
χ5266-6-66i−6i0000-22−2i2i00-222i−2i−2i2i2-20000-22−2i2i000000002i−2i2-2000000000000000000000000
χ5366-6-6−6i6i0000-222i−2i002-22i−2i−2i2i-222-2−2i2i00000000-222i−2i0000000000000000000000000000
χ5466-6-6−6i6i0000-222i−2i002-22i−2i−2i2i-22-222i−2i000000002-2−2i2i0000000000000000000000000000
χ5566-6-6−6i6i0000-222i−2i00-22−2i2i2i−2i2-200002-2−2i2i000000002i−2i-22000000000000000000000000
χ5666-6-6−6i6i0000-222i−2i00-22−2i2i2i−2i2-20000-222i−2i00000000−2i2i2-2000000000000000000000000
χ578-88-8004i−4i4i−4i00000000000000000000000000000000002-220000-200002i−2i2i−2i00000000
χ588-88-8004i−4i4i−4i0000000000000000000000000000000000-11-1−i3i3−i3i313−33−3−ii−ii00000000
χ598-88-8004i−4i4i−4i0000000000000000000000000000000000-11-1i3−i3i3−i31−33−33−ii−ii00000000
χ608-88-800−4i4i−4i4i00000000000000000000000000000000002-220000-20000−2i2i−2i2i00000000
χ618-88-800−4i4i−4i4i0000000000000000000000000000000000-11-1−i3i3−i3i31−33−33i−ii−i00000000
χ628-88-800−4i4i−4i4i0000000000000000000000000000000000-11-1i3−i3i3−i313−33−3i−ii−i00000000
χ638-8-88004-4-4400000000000000000000000000000000002-2-20000200002-2-2200000000
χ648-8-88004-4-440000000000000000000000000000000000-111−i3i3i3−i3-1−i3i3i3−i3-111-100000000
χ658-8-88004-4-440000000000000000000000000000000000-111i3−i3−i3i3-1i3−i3−i3i3-111-100000000
χ668-8-8800-444-400000000000000000000000000000000002-2-2000020000-222-200000000
χ678-8-8800-444-40000000000000000000000000000000000-111−i3i3i3−i3-1i3−i3−i3i31-1-1100000000
χ688-8-8800-444-40000000000000000000000000000000000-111i3−i3−i3i3-1−i3i3i3−i31-1-1100000000

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