Finite Group Databasebeta

← Group #72268243

Character table — Group #72268243

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111111122226666666666661212121212122424242424242424242424242424242424242424323232323232323232323232323232324848484848484848
order12224444444422224444444424444424444444444488888888366612121212121212121212121288888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ311111111-1-1-1-11-1-111111-1-111-11-1-1-11-111-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111-1-1-1-11-1-111111-1-111-11-1-1-11-111-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ51111-1-1-1-111-1-1-111-11111-1-1-1-1-1111-1-1-11-11ii−i−iii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1i−ii−ii−ii−i
χ61111-1-1-1-111-1-1-111-11111-1-1-1-1-1111-1-1-11-11−i−iii−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii
χ71111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-11-111-1-1ii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-1-1-1-1-11111i−i−iii−i−ii
χ81111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-11-111-1-1−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−iii−i−iii−i
χ922222222222222222222222222222222220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1022222222-2-2-2-22-2-222222-2-222-22-2-2-22-222-20000000000000000-1-1-1-1-1-1-1-11111111100000000
χ112222-2-2-2-222-2-2-222-22222-2-2-2-2-2222-2-2-22-220000000000000000-1-1-1-11111-1-1-1-1111100000000
χ122222-2-2-2-2-2-222-2-2-2-2222222-2-222-2-22-222-2-20000000000000000-1-1-1-111111111-1-1-1-100000000
χ1322-2-22i−2i2i−2i2-22i−2i02-20002-22i−2i2i−2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i-111-1ii−i−i11-1-1ii−i−i00000000
χ1422-2-22i−2i2i−2i2-22i−2i02-20002-22i−2i2i−2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i-111-1ii−i−i11-1-1ii−i−i00000000
χ1522-2-22i−2i2i−2i-22−2i2i0-220002-2−2i2i2i−2i00000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1−i1+i−1+i1−i-111-1ii−i−i-1-111−i−iii00000000
χ1622-2-22i−2i2i−2i-22−2i2i0-220002-2−2i2i2i−2i0000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1−i1+i−1+i1−i1+i−1−i1−i−1+i-111-1ii−i−i-1-111−i−iii00000000
χ1722-2-2−2i2i−2i2i2-2−2i2i02-20002-2−2i2i−2i2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i-111-1−i−iii11-1-1−i−iii00000000
χ1822-2-2−2i2i−2i2i2-2−2i2i02-20002-2−2i2i−2i2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i-111-1−i−iii11-1-1−i−iii00000000
χ1922-2-2−2i2i−2i2i-222i−2i0-220002-22i−2i−2i2i00000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1+i1−i−1−i1+i-111-1−i−iii-1-111ii−i−i00000000
χ2022-2-2−2i2i−2i2i-222i−2i0-220002-22i−2i−2i2i0000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1+i1−i−1−i1+i1−i−1+i1+i−1−i-111-1−i−iii-1-111ii−i−i00000000
χ213333333333333-1-1333-1-1-1-1-1-1-1-13-13-1-1-1-1-111111111-1-1-1-1-1-1-1-100000000000000001111-1-1-1-1
χ223333333333333-1-1333-1-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-1-1-1-11111
χ23333333333333-133-1-1-1333333-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-1-1-1-1-1-1-1-1
χ24333333333333-133-1-1-1333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000011111111
χ25333333333333-1-1-1-1-1-1-1-1-1-1-1-133-13-13-1-1-1-111111111-1-1-1-1-1-1-1-10000000000000000-1-1-1-11111
χ26333333333333-1-1-1-1-1-1-1-1-1-1-1-133-13-13-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000001111-1-1-1-1
χ2733333333-3-3-3-3311333-1-111-1-11-1-31-3-11-1-111111-1-1-1-1-1-1-1-11111000000000000000011-1-1-1-111
χ2833333333-3-3-3-3311333-1-111-1-11-1-31-3-11-1-11-1-1-1-111111111-1-1-1-10000000000000000-1-11111-1-1
χ2933333333-3-3-3-3-111-1-1-1-1-111-1-1-331-3131-1-111111-1-1-1-1-1-1-1-111110000000000000000-1-11111-1-1
χ3033333333-3-3-3-3-111-1-1-1-1-111-1-1-331-3131-1-11-1-1-1-111111111-1-1-1-1000000000000000011-1-1-1-111
χ3133333333-3-3-3-3-1-3-3-1-1-133-3-3331-1111-11-1-111111-1-1-1-11111-1-1-1-10000000000000000-1-111-1-111
χ3233333333-3-3-3-3-1-3-3-1-1-133-3-3331-1111-11-1-11-1-1-1-11111-1-1-1-11111000000000000000011-1-111-1-1
χ333333-3-3-3-333-3-31331-1-133-3-3-3-31-1-1-1111-11-1ii−i−iii−i−iii−i−iii−i−i0000000000000000−ii−ii−ii−ii
χ343333-3-3-3-333-3-31331-1-133-3-3-3-31-1-1-1111-11-1−i−iii−i−iii−i−iii−i−iii0000000000000000i−ii−ii−ii−i
χ353333-3-3-3-333-3-31-1-11-1-1-1-11111-33-131-31-11-1ii−i−iii−i−i−i−iii−i−iii0000000000000000−ii−iii−ii−i
χ363333-3-3-3-333-3-31-1-11-1-1-1-11111-33-131-31-11-1−i−iii−i−iiiii−i−iii−i−i0000000000000000i−ii−i−ii−ii
χ373333-3-3-3-333-3-3-3-1-1-333-1-111111-13-1-311-11-1ii−i−iii−i−i−i−iii−i−iii0000000000000000i−ii−i−ii−ii
χ383333-3-3-3-333-3-3-3-1-1-333-1-111111-13-1-311-11-1−i−iii−i−iiiii−i−iii−i−i0000000000000000−ii−iii−ii−i
χ393333-3-3-3-3-3-3331111-1-1-1-1-1-111331-3-1-3-1-111ii−i−i−i−iii−i−iiiii−i−i0000000000000000−iii−ii−i−ii
χ403333-3-3-3-3-3-3331111-1-1-1-1-1-111331-3-1-3-1-111−i−iiiii−i−iii−i−i−i−iii0000000000000000i−i−ii−iii−i
χ413333-3-3-3-3-3-3331-3-31-1-13333-3-3-1-111-11-1-111ii−i−i−i−iiiii−i−i−i−iii0000000000000000−iii−i−iii−i
χ423333-3-3-3-3-3-3331-3-31-1-13333-3-3-1-111-11-1-111−i−iiiii−i−i−i−iiiii−i−i0000000000000000i−i−iii−i−ii
χ433333-3-3-3-3-3-333-311-333-1-1-1-111-1-1-3131-1-111ii−i−i−i−iii−i−iiiii−i−i0000000000000000i−i−ii−iii−i
χ443333-3-3-3-3-3-333-311-333-1-1-1-111-1-1-3131-1-111−i−iiiii−i−iii−i−i−i−iii0000000000000000−iii−ii−i−ii
χ4544-4-44i−4i4i−4i4-44i−4i04-40004-44i−4i4i−4i000000000000000000000000001-1-11−i−iii-1-111−i−iii00000000
χ4644-4-44i−4i4i−4i-44−4i4i0-440004-4−4i4i4i−4i000000000000000000000000001-1-11−i−iii11-1-1ii−i−i00000000
χ4744-4-4−4i4i−4i4i4-4−4i4i04-40004-4−4i4i−4i4i000000000000000000000000001-1-11ii−i−i-1-111ii−i−i00000000
χ4844-4-4−4i4i−4i4i-444i−4i0-440004-44i−4i−4i4i000000000000000000000000001-1-11ii−i−i11-1-1−i−iii00000000
χ494-44-444-4-40000400-44-40000000000000000000000000000000011-1-11-11-13−33−33−33−300000000
χ504-44-444-4-40000400-44-40000000000000000000000000000000011-1-11-11-1−33−33−33−3300000000
χ514-44-444-4-40000400-44-400000000000000000000000000000000-2-222-22-220000000000000000
χ524-44-4-4-4440000-40044-40000000000000000000000000000000011-1-1-11-113−33−3−33−3300000000
χ534-44-4-4-4440000-40044-40000000000000000000000000000000011-1-1-11-11−33−333−33−300000000
χ544-44-4-4-4440000-40044-400000000000000000000000000000000-2-2222-22-20000000000000000
χ55666666666666-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ5666666666-6-6-6-6-222-2-2-2-2-222-2-22-2222-2-222-20000000000000000000000000000000000000000
χ576666-6-6-6-666-6-62-2-22-2-2-2-222222-2-2-222-22-220000000000000000000000000000000000000000
χ586666-6-6-6-6-6-6662222-2-2-2-2-2-222-2-222-2222-2-20000000000000000000000000000000000000000
χ5966-6-66i−6i6i−6i6-66i−6i0-22000-22−2i2i−2i2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000000000000000
χ6066-6-66i−6i6i−6i6-66i−6i0-22000-22−2i2i−2i2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i1+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000000000000000
χ6166-6-66i−6i6i−6i-66−6i6i02-2000-222i−2i−2i2i00000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000000000000000
χ6266-6-66i−6i6i−6i-66−6i6i02-2000-222i−2i−2i2i0000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i1+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000000000000000
χ6366-6-6−6i6i−6i6i6-6−6i6i0-22000-222i−2i2i−2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000000000000000
χ6466-6-6−6i6i−6i6i6-6−6i6i0-22000-222i−2i2i−2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i1−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000000000000000
χ6566-6-6−6i6i−6i6i-666i−6i02-2000-22−2i2i2i−2i00000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000000000000000
χ6666-6-6−6i6i−6i6i-666i−6i02-2000-22−2i2i2i−2i0000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i1−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000000000000000
χ678-8-888i−8i−8i8i0000000000000000000000000000000000000000002-22-2−2i2i2i−2i0000000000000000
χ688-8-888i−8i−8i8i000000000000000000000000000000000000000000-11-11i−i−ii3−3−33i3−i3−i3i300000000
χ698-8-888i−8i−8i8i000000000000000000000000000000000000000000-11-11i−i−ii−333−3−i3i3i3−i300000000
χ708-8-88−8i8i8i−8i0000000000000000000000000000000000000000002-22-22i−2i−2i2i0000000000000000
χ718-8-88−8i8i8i−8i000000000000000000000000000000000000000000-11-11−iii−i3−3−33−i3i3i3−i300000000
χ728-8-88−8i8i8i−8i000000000000000000000000000000000000000000-11-11−iii−i−333−3i3−i3−i3i300000000
χ7312-1212-121212-12-120000-4004-4400000000000000000000000000000000000000000000000000000000
χ7412-1212-12-12-1212120000400-4-4400000000000000000000000000000000000000000000000000000000

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