Finite Group Databasebeta

← Group #72341389

Character table — Group #72341389

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444466668812121212121212122424242424242424242424242424242424242424323232323232323232323232323232324848484848484848
order1222442222224444224444444444444444444444444436666666121212121212121244448888
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
χ3111111-1-1-1-11111-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1
χ4111111-1-1-1-11111-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-11111
χ51111-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111111-1-1-1-11-1-1-1-1111111-1-1-1-111
χ81111-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1111-1-1-1-11-1-1-1-11111-1-11111-1-1
χ91-11-1i−i11-1-11-1i−ii−i1-1i−ii−i1-11-11-1i−ii−i1-1i−i1-1i−i1-1i−i11-111-1-1-1ii−i−iii−i−i1-1i−i1-1i−i
χ101-11-1i−i11-1-11-1i−ii−i1-1i−ii−i1-1-11-11−ii−ii1-1i−i-11−ii-11−ii11-111-1-1-1ii−i−iii−i−i-11−ii-11−ii
χ111-11-1i−i-1-1111-1i−i−ii1-1i−ii−i1-11-1-11i−i−ii-11−ii1-1i−i-11−ii11-1-1-111-1ii−i−i−i−iii1-1i−i-11−ii
χ121-11-1i−i-1-1111-1i−i−ii1-1i−ii−i1-1-111-1−iii−i-11−ii-11−ii1-1i−i11-1-1-111-1ii−i−i−i−iii-11−ii1-1i−i
χ131-11-1−ii11-1-11-1−ii−ii1-1−ii−ii1-11-11-1−ii−ii1-1−ii1-1−ii1-1−ii11-111-1-1-1−i−iii−i−iii1-1−ii1-1−ii
χ141-11-1−ii11-1-11-1−ii−ii1-1−ii−ii1-1-11-11i−ii−i1-1−ii-11i−i-11i−i11-111-1-1-1−i−iii−i−iii-11i−i-11i−i
χ151-11-1−ii-1-1111-1−iii−i1-1−ii−ii1-11-1-11−iii−i-11i−i1-1−ii-11i−i11-1-1-111-1−i−iiiii−i−i1-1−ii-11i−i
χ161-11-1−ii-1-1111-1−iii−i1-1−ii−ii1-1-111-1i−i−ii-11i−i-11i−i1-1−ii11-1-1-111-1−i−iiiii−i−i-11i−i1-1−ii
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
χ192222-2-2222222-2-2-2-222-2-2-2-2220000000022-2-200000000-1-1-1-1-1-1-1-11111111100000000
χ202222-2-2-2-2-2-222-2-22222-2-2-2-22200000000-2-22200000000-1-1-11111-11111-1-1-1-100000000
χ212-22-22i−2i22-2-22-22i−2i2i−2i2-22i−2i2i−2i2-2000000002-22i−2i00000000-1-11-1-1111−i−iii−i−iii00000000
χ222-22-22i−2i-2-2222-22i−2i−2i2i2-22i−2i2i−2i2-200000000-22−2i2i00000000-1-1111-1-11−i−iiiii−i−i00000000
χ232-22-2−2i2i22-2-22-2−2i2i−2i2i2-2−2i2i−2i2i2-2000000002-2−2i2i00000000-1-11-1-1111ii−i−iii−i−i00000000
χ242-22-2−2i2i-2-2222-2−2i2i2i−2i2-2−2i2i−2i2i2-200000000-222i−2i00000000-1-1111-1-11ii−i−i−i−iii00000000
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
χ27333333-3-3-3-33333-3-3-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-10000000000000000-1-1-1-11111
χ28333333-3-3-3-33333-3-3-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111100000000000000001111-1-1-1-1
χ293333-3-3333333-3-3-3-3-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-10000000000000000-1-111-1-111
χ303333-3-3333333-3-3-3-3-1-11111-1-1-1-1-1-11111-1-111-1-111-1-111000000000000000011-1-111-1-1
χ313333-3-3-3-3-3-333-3-333-1-11111-1-111-1-1-1-11111-1-111-1-1-1-1110000000000000000-1-11111-1-1
χ323333-3-3-3-3-3-333-3-333-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1000000000000000011-1-1-1-111
χ333-33-33i−3i33-3-33-33i−3i3i−3i-11−ii−ii-111-11-1i−ii−i-11−ii1-1i−i1-1i−i0000000000000000-11−ii-11−ii
χ343-33-33i−3i33-3-33-33i−3i3i−3i-11−ii−ii-11-11-11−ii−ii-11−ii-11−ii-11−ii00000000000000001-1i−i1-1i−i
χ353-33-33i−3i-3-3333-33i−3i−3i3i-11−ii−ii-111-1-11i−i−ii1-1i−i1-1i−i-11−ii0000000000000000-11−ii1-1i−i
χ363-33-33i−3i-3-3333-33i−3i−3i3i-11−ii−ii-11-111-1−iii−i1-1i−i-11−ii1-1i−i00000000000000001-1i−i-11−ii
χ373-33-3−3i3i33-3-33-3−3i3i−3i3i-11i−ii−i-111-11-1−ii−ii-11i−i1-1−ii1-1−ii0000000000000000-11i−i-11i−i
χ383-33-3−3i3i33-3-33-3−3i3i−3i3i-11i−ii−i-11-11-11i−ii−i-11i−i-11i−i-11i−i00000000000000001-1−ii1-1−ii
χ393-33-3−3i3i-3-3333-3−3i3i3i−3i-11i−ii−i-111-1-11−iii−i1-1−ii1-1−ii-11i−i0000000000000000-11i−i1-1−ii
χ403-33-3−3i3i-3-3333-3−3i3i3i−3i-11i−ii−i-11-111-1i−i−ii1-1−ii-11i−i1-1−ii00000000000000001-1−ii-11i−i
χ416666660000-2-2-2-20022-2-222-2-2220022000000-2-2-2-20000000000000000000000000000
χ426666660000-2-2-2-20022-2-222-2-2-2-200-2-200000022220000000000000000000000000000
χ436666660000-2-2-2-200-2-222-2-2220022002200000000-2-2-2-2000000000000000000000000
χ446666660000-2-2-2-200-2-222-2-22200-2-200-2-2000000002222000000000000000000000000
χ456666-6-60000-2-222002222-2-2-2-22200-2-2000000-2-2220000000000000000000000000000
χ466666-6-60000-2-222002222-2-2-2-2-2-2002200000022-2-20000000000000000000000000000
χ476666-6-60000-2-22200-2-2-2-22222002200-2-200000000-2-222000000000000000000000000
χ486666-6-60000-2-22200-2-2-2-2222200-2-200220000000022-2-2000000000000000000000000
χ496-66-66i−6i0000-22−2i2i002-2−2i2i2i−2i-222-2002i−2i000000-22−2i2i0000000000000000000000000000
χ506-66-66i−6i0000-22−2i2i002-2−2i2i2i−2i-22-2200−2i2i0000002-22i−2i0000000000000000000000000000
χ516-66-66i−6i0000-22−2i2i00-222i−2i−2i2i2-2002-2002i−2i00000000-22−2i2i000000000000000000000000
χ526-66-66i−6i0000-22−2i2i00-222i−2i−2i2i2-200-2200−2i2i000000002-22i−2i000000000000000000000000
χ536-66-6−6i6i0000-222i−2i002-22i−2i−2i2i-222-200−2i2i000000-222i−2i0000000000000000000000000000
χ546-66-6−6i6i0000-222i−2i002-22i−2i−2i2i-22-22002i−2i0000002-2−2i2i0000000000000000000000000000
χ556-66-6−6i6i0000-222i−2i00-22−2i2i2i−2i2-2002-200−2i2i00000000-222i−2i000000000000000000000000
χ566-66-6−6i6i0000-222i−2i00-22−2i2i2i−2i2-200-22002i−2i000000002-2−2i2i000000000000000000000000
χ5788-8-8004-44-400000000000000000000000000000000002-222-22-2-20000000000000000
χ5888-8-8004-44-40000000000000000000000000000000000-11-1-11-1113−33−33−33−300000000
χ5988-8-8004-44-40000000000000000000000000000000000-11-1-11-111−33−33−33−3300000000
χ6088-8-800-44-4400000000000000000000000000000000002-22-22-22-20000000000000000
χ6188-8-800-44-440000000000000000000000000000000000-11-11-11-113−33−3−33−3300000000
χ6288-8-800-44-440000000000000000000000000000000000-11-11-11-11−33−333−33−300000000
χ638-8-88004-4-4400000000000000000000000000000000002-2-22-2-2220000000000000000
χ648-8-88004-4-440000000000000000000000000000000000-111-111-1-1−i3i3i3−i3−i3i3i3−i300000000
χ658-8-88004-4-440000000000000000000000000000000000-111-111-1-1i3−i3−i3i3i3−i3−i3i300000000
χ668-8-8800-444-400000000000000000000000000000000002-2-2-222-220000000000000000
χ678-8-8800-444-40000000000000000000000000000000000-1111-1-11-1−i3i3i3−i3i3−i3−i3i300000000
χ688-8-8800-444-40000000000000000000000000000000000-1111-1-11-1i3−i3−i3i3−i3i3i3−i300000000

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