Finite Group Databasebeta

← Group #13137469

Character table — Group #13137469

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11222222244444444666699121212121212121212121818181818181824242424242424242424363636363636363636363636363636367272727272727272
order122223666446612121212336644366666666644412121212661212121212121212224444444412121212121266121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-11111111111-1-1-1-1-1-1-111111111111-11-1-1-111-1-1-1-1-1-1-1-11-11-111-1-1
χ4111111111111111111111-1-11111111111-1-1-1-1-1-1-11111111111-11-11-1-1-1-111-1-1-1-1-1-1-11-11-1-111
χ5111111111-1-111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111-1-111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ7111111111-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-1111111-1-11-11-1-1-111
χ8111111111-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-111111-1-11111-1-1-11-1111-1-1
χ9111-1-11-1-11i−i1-1ii−i−i1111111111-1-1-1-1-1-11-1-111-1-11-1iiii−i−i−i−i1-1-11i−ii−ii−iii−i−i1-11-1-11i−ii−i
χ10111-1-11-1-11i−i1-1ii−i−i1111111111-1-1-1-1-1-11-1-111-1-11-1iiii−i−i−i−i-111-1i−i−ii−iiii−i−i1-1-111-1−ii−ii
χ11111-1-11-1-11i−i1-1ii−i−i1111-1-11111-1-1-1-1-1-1-111-1-1111-1iiii−i−i−i−i11-1-1−iii−i−ii−i−iii-1111-1-1i−i−ii
χ12111-1-11-1-11i−i1-1ii−i−i1111-1-11111-1-1-1-1-1-1-111-1-1111-1iiii−i−i−i−i-1-111−ii−iii−i−i−iii-11-1-111−iii−i
χ13111-1-11-1-11−ii1-1−i−iii1111111111-1-1-1-1-1-11-1-111-1-11-1−i−i−i−iiiii1-1-11−ii−ii−ii−i−iii1-11-1-11−ii−ii
χ14111-1-11-1-11−ii1-1−i−iii1111111111-1-1-1-1-1-11-1-111-1-11-1−i−i−i−iiiii-111-1−iii−ii−i−i−iii1-1-111-1i−ii−i
χ15111-1-11-1-11−ii1-1−i−iii1111-1-11111-1-1-1-1-1-1-111-1-1111-1−i−i−i−iiiii11-1-1i−i−iii−iii−i−i-1111-1-1−iii−i
χ16111-1-11-1-11−ii1-1−i−iii1111-1-11111-1-1-1-1-1-1-111-1-1111-1−i−i−i−iiiii-1-111i−ii−i−iiii−i−i-11-1-111i−i−ii
χ17222222222222222222-12-100-12-1-12-1-1-12-10000000-1-12-1-1-12-1-1-102020000220000000-10-100-1-1
χ18222222222222222222-12-100-12-1-12-1-1-12-10000000-1-12-1-1-12-1-1-10-20-20000-2-200000001010011
χ1922222222222222222-12-1200-1-12-1-12-1-1-120000000-1-1-12-1-1-12-1-12020002200000000-10-10-1-100
χ2022222222222222222-12-1200-1-12-1-12-1-1-120000000-1-1-12-1-1-12-1-1-20-2000-2-20000000010101100
χ21222222222-2-222-2-2-2-22-12-100-12-1-12-1-1-12-10000000-1-1-2111-211102020000-2-20000000-10-10011
χ22222222222-2-222-2-2-2-22-12-100-12-1-12-1-1-12-10000000-1-1-2111-21110-20-2000022000000010100-1-1
χ23222222222-2-222-2-2-2-2-12-1200-1-12-1-12-1-1-120000000-1-11-2111-211202000-2-200000000-10-101100
χ24222222222-2-222-2-2-2-2-12-1200-1-12-1-12-1-1-120000000-1-11-2111-211-20-200022000000001010-1-100
χ25222-2-22-2-222i−2i2-22i2i−2i−2i2-12-100-12-1-1-2111-210000000-112i−i−i−i−2iiii020-20000−2i2i0000000-10100i−i
χ26222-2-22-2-222i−2i2-22i2i−2i−2i2-12-100-12-1-1-2111-210000000-112i−i−i−i−2iiii0-20200002i−2i000000010-100−ii
χ27222-2-22-2-222i−2i2-22i2i−2i−2i-12-1200-1-12-11-2111-20000000-11−i2i−i−ii−2iii20-20002i−2i00000000-1010−ii00
χ28222-2-22-2-222i−2i2-22i2i−2i−2i-12-1200-1-12-11-2111-20000000-11−i2i−i−ii−2iii-202000−2i2i0000000010-10i−i00
χ29222-2-22-2-22−2i2i2-2−2i−2i2i2i2-12-100-12-1-1-2111-210000000-11−2iiii2i−i−i−i020-200002i−2i0000000-10100−ii
χ30222-2-22-2-22−2i2i2-2−2i−2i2i2i2-12-100-12-1-1-2111-210000000-11−2iiii2i−i−i−i0-2020000−2i2i000000010-100i−i
χ31222-2-22-2-22−2i2i2-2−2i−2i2i2i-12-1200-1-12-11-2111-20000000-11i−2iii−i2i−i−i20-2000−2i2i00000000-1010i−i00
χ32222-2-22-2-22−2i2i2-2−2i−2i2i2i-12-1200-1-12-11-2111-20000000-11i−2iii−i2i−i−i-2020002i−2i0000000010-10−ii00
χ3322-22-2222200-2-200002222222-2-222222-2-2-22-22222-2-20000000000000000000000-2-200000000
χ3422-22-2222200-2-200002222-2-22-2-222222-2-22-22-2-2-2-2-2-200000000000000000000002200000000
χ3522-2-222-2-2200-2200002222222-2-22-2-2-2-222-2-2222-2-2-220000000000000000000000-2200000000
χ3622-2-222-2-2200-2200002222-2-22-2-22-2-2-2-22222-2-2-222-2200000000000000000000002-200000000
χ3744444444444444444-2-2-2-2001-2-21-2-211-2-2000000011-2-211-2-211000000000000000000000000
χ38444444444-4-444-4-4-4-4-2-2-2-2001-2-21-2-211-2-200000001122-1-122-1-1000000000000000000000000
χ39444-4-44-4-444i−4i4-44i4i−4i−4i-2-2-2-2001-2-2122-1-12200000001-1−2i−2iii2i2i−i−i000000000000000000000000
χ40444-4-44-4-44−4i4i4-4−4i−4i4i4i-2-2-2-2001-2-2122-1-12200000001-12i2i−i−i−2i−2iii000000000000000000000000
χ4144-44-4444400-4-400004-24-200-2-42-24-2-2-2-4200000002200000000000000000000000000000000
χ4244-44-4444400-4-40000-24-2400-22-4-2-24-2-22-400000002200000000000000000000000000000000
χ4344-44-4444400-4-40000-2-2-2-2001221-2-211220000000-1-1003-3003-3000000000000000000000000
χ4444-44-4444400-4-40000-2-2-2-2001221-2-211220000000-1-100-3300-33000000000000000000000000
χ4544-4-444-4-4400-4400004-24-200-2-42-2-42224-200000002-200000000000000000000000000000000
χ4644-4-444-4-4400-440000-24-2400-22-4-22-422-2400000002-200000000000000000000000000000000
χ4744-4-444-4-4400-440000-2-2-2-200122122-1-1-2-20000000-11003i−3i00−3i3i000000000000000000000000
χ4844-4-444-4-4400-440000-2-2-2-200122122-1-1-2-20000000-1100−3i3i003i−3i000000000000000000000000
χ494-4000400-40000000044-4-44i−4i400-40000000004i−4i000000000000000000000000000000000000
χ504-4000400-40000000044-4-4−4i4i400-4000000000−4i4i000000000000000000000000000000000000
χ5166666-3-3-3-366-3-3-3-3-3-30000220000000000222-1-1-1-100000000000000220000-1-1-1-1-1-100000000
χ5266666-3-3-3-366-3-3-3-3-3-30000-2-20000000000-2-2-2111100000000000000-2-2000011111100000000
χ5366666-3-3-3-3-6-6-3-333330000220000000000222-1-1-1-100000000000000-2-200001111-1-100000000
χ5466666-3-3-3-3-6-6-3-333330000-2-20000000000-2-2-2111100000000000000220000-1-1-1-11100000000
χ55666-6-6-333-36i−6i-33−3i−3i3i3i00002200000000002-2-2-1-111000000000000002i−2i0000−i−iii-1100000000
χ56666-6-6-333-36i−6i-33−3i−3i3i3i0000-2-20000000000-22211-1-100000000000000−2i2i0000ii−i−i1-100000000
χ57666-6-6-333-3−6i6i-333i3i−3i−3i00002200000000002-2-2-1-11100000000000000−2i2i0000ii−i−i-1100000000
χ58666-6-6-333-3−6i6i-333i3i−3i−3i0000-2-20000000000-22211-1-1000000000000002i−2i0000−i−iii1-100000000
χ5966-66-6-3-3-3-30033−3i33i3−3i33i30000220000000000-22-2-1-1-1-100000000000000000000−i3i3−i3i31100000000
χ6066-66-6-3-3-3-30033−3i33i3−3i33i30000-2-200000000002-22111100000000000000000000i3−i3i3−i3-1-100000000
χ6166-66-6-3-3-3-300333i3−3i33i3−3i30000220000000000-22-2-1-1-1-100000000000000000000i3−i3i3−i31100000000
χ6266-66-6-3-3-3-300333i3−3i33i3−3i30000-2-200000000002-22111100000000000000000000−i3i3−i3i3-1-100000000
χ6366-6-66-333-3003-333−33−33330000220000000000-2-22-1-111000000000000000000003−3−331-100000000
χ6466-6-66-333-3003-333−33−33330000-2-2000000000022-211-1-100000000000000000000−333−3-1100000000
χ6566-6-66-333-3003-3−333333−330000220000000000-2-22-1-11100000000000000000000−333−31-100000000
χ6666-6-66-333-3003-3−333333−330000-2-2000000000022-211-1-1000000000000000000003−3−33-1100000000
χ678-8000800-8000000008-4-8400-400400000000000000000000000000000000000000000000000
χ688-8000800-800000000-484-800-400400000000000000000000000000000000000000000000000
χ698-8000800-800000000-4-44400200-2006-60000000000000000000000000000000000000000000
χ708-8000800-800000000-4-44400200-200-660000000000000000000000000000000000000000000
χ7112-12000-6−6i36i360000000000004i−4i0000000000000−2i2i23−230000000000000000000000000000000000
χ7212-12000-6−6i36i36000000000000−4i4i00000000000002i−2i−23230000000000000000000000000000000000
χ7312-12000-66i3−6i360000000000004i−4i0000000000000−2i2i−23230000000000000000000000000000000000
χ7412-12000-66i3−6i36000000000000−4i4i00000000000002i−2i23−230000000000000000000000000000000000

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