Finite Group Databasebeta

← Group #13140069

Character table — Group #13140069

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212444444444444444444121212121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911-11-1-11-1111-1-1-11-11-111-1-111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-111-1-11111-1-1-1-1ii−i−i11-1-1ii−i−ii−i1-1i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1011-11-1-11-1111-1-1-11-11-111-1-111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-111-1-11111-1-1-1-1ii−i−i-1-111−i−iiii−i-11−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ1111-11-1-11-1111-1-1-11-11-111-1-111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-111-1-11111-1-1-1-1−i−iii11-1-1−i−iii−ii1-1−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ1211-11-1-11-1111-1-1-11-11-111-1-111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-111-1-11111-1-1-1-1−i−iii-1-111ii−i−i−ii-11i−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ1311-11-1-11-1111-1-1-11-1-11-1-11111111-1-1-1-1-1-111-1-11111-1-1-1-11-1-111-1-111-1-1-1-11111ii−i−i11-1-1ii−i−i−ii-11−iiii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ1411-11-1-11-1111-1-1-11-1-11-1-11111111-1-1-1-1-1-111-1-11111-1-1-1-11-1-111-1-111-1-1-1-11111ii−i−i-1-111−i−iii−ii1-1i−i−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ1511-11-1-11-1111-1-1-11-1-11-1-11111111-1-1-1-1-1-111-1-11111-1-1-1-11-1-111-1-111-1-1-1-11111−i−iii11-1-1−i−iiii−i-11i−i−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ1611-11-1-11-1111-1-1-11-1-11-1-11111111-1-1-1-1-1-111-1-11111-1-1-1-11-1-111-1-111-1-1-1-11111−i−iii-1-111ii−i−ii−i1-1−iiii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ1722222222222222222222222-122-122-1-1-1-12-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000022000000000000000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222-122-122-1-1-1-12-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000-2-200000000000000000011111111
χ192222222222222222222222-12-1-12-1-12222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220000000022000000000000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222-12-1-12-1-12222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200000000-2-20000000000001111111100000000
χ212222222222222222-2-2-2-2-2-22-122-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100002222000000-2-20000000000000000001111-1-1-1-1
χ222222222222222222-2-2-2-2-2-22-122-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000-2-2-2-200000022000000000000000000-1-1-1-11111
χ232222222222222222-2-2-2-2-2-2-12-1-12-1-12222-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-211111111222200000000-2-2000000000000-1-1-1-1111100000000
χ242222222222222222-2-2-2-2-2-2-12-1-12-1-12222-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-211111111-2-2-2-200000000220000000000001111-1-1-1-100000000
χ25222-22-2-2-222-222-2-2-2000000222-222-222-2-2-2-22-2-222-222-2-2-200000000000000002-22-200000000000000000000002-22-2000000000000
χ26222-22-2-2-222-222-2-2-2000000222-222-222-2-2-2-22-2-222-222-2-2-20000000000000000-22-220000000000000000000000-22-22000000000000
χ27222-22-2-2-222-222-2-2-2000000-12-112-1122-2-21-2-11-2-1-11-1-11113−33−3000033−3−333−3−32-22-20000000000000000000000-11-113−33−300000000
χ28222-22-2-2-222-222-2-2-2000000-12-112-1122-2-21-2-11-2-1-11-1-11113−33−3000033−3−333−3−3-22-2200000000000000000000001-11-1−33−3300000000
χ29222-22-2-2-222-222-2-2-2000000-12-112-1122-2-21-2-11-2-1-11-1-1111−33−330000−3−333−3−3332-22-20000000000000000000000-11-11−33−3300000000
χ30222-22-2-2-222-222-2-2-2000000-12-112-1122-2-21-2-11-2-1-11-1-1111−33−330000−3−333−3−333-22-2200000000000000000000001-11-13−33−300000000
χ3122-22-2-22-2222-2-2-22-22-222-2-22-122-1-2-211112-1-2-2-1-1-1-11111-122-2-2-1-111-1-1-1-11111000022-2-20000002-2000000000000000000-1-111-1-111
χ3222-22-2-22-2222-2-2-22-22-222-2-22-122-1-2-211112-1-2-2-1-1-1-11111-122-2-2-1-111-1-1-1-111110000-2-222000000-2200000000000000000011-1-111-1-1
χ3322-22-2-22-2222-2-2-22-22-222-2-2-12-1-1211-2-2-2-2-12112-1-1-11111-1-1-11122-2-2-1-1-1-111112i2i−2i−2i000000002i−2i000000000000−i−iii−i−iii00000000
χ3422-22-2-22-2222-2-2-22-22-222-2-2-12-1-1211-2-2-2-2-12112-1-1-11111-1-1-11122-2-2-1-1-1-11111−2i−2i2i2i00000000−2i2i000000000000ii−i−iii−i−i00000000
χ3522-22-2-22-2222-2-2-22-2-22-2-2222-122-1-2-211112-1-2-2-1-1-1-11111-1-2-22211-1-11111-1-1-1-1000022-2-2000000-2200000000000000000011-1-1-1-111
χ3622-22-2-22-2222-2-2-22-2-22-2-2222-122-1-2-211112-1-2-2-1-1-1-11111-1-2-22211-1-11111-1-1-1-10000-2-2220000002-2000000000000000000-1-11111-1-1
χ3722-22-2-22-2222-2-2-22-2-22-2-222-12-1-1211-2-2-2-2-12112-1-1-11111-111-1-1-2-2221111-1-1-1-12i2i−2i−2i00000000−2i2i000000000000−i−iiiii−i−i00000000
χ3822-22-2-22-2222-2-2-22-2-22-2-222-12-1-1211-2-2-2-2-12112-1-1-11111-111-1-1-2-2221111-1-1-1-1−2i−2i2i2i000000002i−2i000000000000ii−i−i−i−iii00000000
χ3922-2-2-22-2222-2-2-22-22000000222-22-22-2-222-2-2-22-222-2-2-222-200000000000000002i−2i−2i2i00000000000000000000002i−2i−2i2i000000000000
χ4022-2-2-22-2222-2-2-22-22000000222-22-22-2-222-2-2-22-222-2-2-222-20000000000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i000000000000
χ4122-2-2-22-2222-2-2-22-22000000-12-1121-1-2-2221-21-1-2-1-1111-1-113−3−33000033−3−3−3−3332i−2i−2i2i0000000000000000000000−iii−ii3−i3−i3i300000000
χ4222-2-2-22-2222-2-2-22-22000000-12-1121-1-2-2221-21-1-2-1-1111-1-113−3−33000033−3−3−3−333−2i2i2i−2i0000000000000000000000i−i−ii−i3i3i3−i300000000
χ4322-2-2-22-2222-2-2-22-22000000-12-1121-1-2-2221-21-1-2-1-1111-1-11−333−30000−3−33333−3−32i−2i−2i2i0000000000000000000000−iii−i−i3i3i3−i300000000
χ4422-2-2-22-2222-2-2-22-22000000-12-1121-1-2-2221-21-1-2-1-1111-1-11−333−30000−3−33333−3−3−2i2i2i−2i0000000000000000000000i−i−iii3−i3−i3i300000000
χ452-222-2-2-222-222-2-2-2200000022-22-2222-22-2-22-2-2-22-222-22-2-2000000000000000000002i−2i2i−2i0000000000000000000000000000002i−2i2i−2i
χ462-222-2-2-222-222-2-2-2200000022-22-2222-22-2-22-2-2-22-222-22-2-200000000000000000000−2i2i−2i2i000000000000000000000000000000−2i2i−2i2i
χ472-222-2-2-222-222-2-2-220000002-1-22122-11-11-2-1-2-21-11-1-11-11100003−33−33−33−33−33−300002i−2i2i−2i00000000000000000000000000−i3i3−i3i3−ii−ii
χ482-222-2-2-222-222-2-2-220000002-1-22122-11-11-2-1-2-21-11-1-11-11100003−33−33−33−33−33−30000−2i2i−2i2i00000000000000000000000000i3−i3i3−i3i−ii−i
χ492-222-2-2-222-222-2-2-220000002-1-22122-11-11-2-1-2-21-11-1-11-1110000−33−33−33−33−33−3300002i−2i2i−2i00000000000000000000000000i3−i3i3−i3−ii−ii
χ502-222-2-2-222-222-2-2-220000002-1-22122-11-11-2-1-2-21-11-1-11-1110000−33−33−33−33−33−330000−2i2i−2i2i00000000000000000000000000−i3i3−i3i3i−ii−i
χ512-22-2-222-22-2-22-222-200000022-2-2-22-22-2-222-2-2222-2-22-2-2220000000000000000000000002i−2i2i−2i0000002i−2i2i−2i00000000000000000000
χ522-22-2-222-22-2-22-222-200000022-2-2-22-22-2-222-2-2222-2-22-2-222000000000000000000000000−2i2i−2i2i000000−2i2i−2i2i00000000000000000000
χ532-2-2222-2-22-22-222-2-200000022-22-2-2-2-22-22-2222-22-22-22-22-2000000000000000000002i−2i−2i2i0000000000000000000000000000002i−2i−2i2i
χ542-2-2222-2-22-22-222-2-200000022-22-2-2-2-22-22-2222-22-22-22-22-200000000000000000000−2i2i2i−2i000000000000000000000000000000−2i2i2i−2i
χ552-2-2222-2-22-22-222-2-20000002-1-221-2-21-11-1-2-1221-11-11-11-1100003−3−333−33−3−33−3300002i−2i−2i2i00000000000000000000000000−i3i3i3−i3−iii−i
χ562-2-2222-2-22-22-222-2-20000002-1-221-2-21-11-1-2-1221-11-11-11-1100003−3−333−33−3−33−330000−2i2i2i−2i00000000000000000000000000i3−i3−i3i3i−i−ii
χ572-2-2222-2-22-22-222-2-20000002-1-221-2-21-11-1-2-1221-11-11-11-110000−333−3−33−333−33−300002i−2i−2i2i00000000000000000000000000i3−i3−i3i3−iii−i
χ582-2-2222-2-22-22-222-2-20000002-1-221-2-21-11-1-2-1221-11-11-11-110000−333−3−33−333−33−30000−2i2i2i−2i00000000000000000000000000−i3i3i3−i3i−i−ii
χ592-2-2-22-2222-2-2-22-22200000022-2-2-2-22-222-22-22-222-2-2-222-220000000000000000000000002-2-220000002-2-2200000000000000000000
χ602-2-2-22-2222-2-2-22-22200000022-2-2-2-22-222-22-22-222-2-2-222-22000000000000000000000000-222-2000000-222-200000000000000000000
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ63444-44-4-4-444-444-4-4-40000004-24-4-24-4-2-222-424-42-2-22-2-22220000000000000000000000000000000000000000000000000000000000
χ64444-44-4-4-444-444-4-4-4000000-2-2-22-2-22-2-22222-22211-111-1-1-123−2323−230000−3−333−3−333000000000000000000000000000000000000000000
χ65444-44-4-4-444-444-4-4-4000000-2-2-22-2-22-2-22222-22211-111-1-1-1−2323−2323000033−3−333−3−3000000000000000000000000000000000000000000
χ6644-44-4-44-4444-4-4-44-44-444-4-4-2-2-2-2-2222222-2-222-2111-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000000000000000
χ6744-44-4-44-4444-4-4-44-4-44-4-444-2-2-2-2-2222222-2-222-2111-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000000000000000
χ6844-4-4-44-4444-4-4-44-440000004-24-4-2-4422-2-2-42-442-2-2222-2-220000000000000000000000000000000000000000000000000000000000
χ6944-4-4-44-4444-4-4-44-44000000-2-2-22-22-222-2-2222-2211-1-1-111-123−23−23230000−3−33333−3−3000000000000000000000000000000000000000000
χ7044-4-4-44-4444-4-4-44-44000000-2-2-22-22-222-2-2222-2211-1-1-111-1−232323−23000033−3−3−3−333000000000000000000000000000000000000000000
χ714-444-4-4-444-444-4-4-44000000-242-2-4-2-24-44-42422-4-22-2-22-2220000000000000000000000000000000000000000000000000000000000
χ724-444-4-4-444-444-4-4-44000000-2-22-22-2-2-22-222-22221-111-11-1-1000023−2323−23−33−33−33−33000000000000000000000000000000000000000000
χ734-444-4-4-444-444-4-4-44000000-2-22-22-2-2-22-222-22221-111-11-1-10000−2323−23233−33−33−33−3000000000000000000000000000000000000000000
χ744-44-4-444-44-4-44-444-40000004-2-4-424-4-222-242-44-2-222-222-2-20000000000000000000000000000000000000000000000000000000000
χ754-44-4-444-44-4-44-444-4000000-2422-4-224-4-44-2-42-24-222-222-2-20000000000000000000000000000000000000000000000000000000000
χ764-44-4-444-44-4-44-444-4000000-2-2222-22-222-2-222-2-21-1-11-1-111000000003-3-333-3-33000000000000000000000000000000000000000000
χ774-44-4-444-44-4-44-444-4000000-2-2222-22-222-2-222-2-21-1-11-1-11100000000-333-3-333-3000000000000000000000000000000000000000000
χ784-4-4444-4-44-44-444-4-4000000-242-2-422-44-4424-2-2-4-22-22-22-220000000000000000000000000000000000000000000000000000000000
χ794-4-4444-4-44-44-444-4-4000000-2-22-22222-22-22-2-2-221-11-11-11-1000023−23−2323−33−333−33−3000000000000000000000000000000000000000000
χ804-4-4444-4-44-44-444-4-4000000-2-22-22222-22-22-2-2-221-11-11-11-10000−232323−233−33−3−33−33000000000000000000000000000000000000000000
χ814-4-4-44-4444-4-4-44-4440000004-2-4-42-442-2-22424-4-2-2222-2-22-20000000000000000000000000000000000000000000000000000000000
χ824-4-4-44-4444-4-4-44-444000000-2422-42-2-444-4-2-4-224-2222-2-22-20000000000000000000000000000000000000000000000000000000000
χ834-4-4-44-4444-4-4-44-444000000-2-22222-22-2-22-22-22-21-1-1-111-11000000003-3-33-333-3000000000000000000000000000000000000000000
χ844-4-4-44-4444-4-4-44-444000000-2-22222-22-2-22-22-22-21-1-1-111-1100000000-333-33-3-33000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000000000002222000022-1-1-1-1-1-1-1-10000000000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000000000000000-2-2-2-20000-2-2111111110000000000000000
χ8766666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000000022220000-2-2-1-1-1-111110000000000000000
χ8866666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000000000-2-2-2-20000221111-1-1-1-10000000000000000
χ8966-66-6-66-6-3-3-3333-336-6-3-3330000000000000000000000000000000000000000000000002i2i−2i−2i00002i−2i−i−iii−i−iii0000000000000000
χ9066-66-6-66-6-3-3-3333-336-6-3-333000000000000000000000000000000000000000000000000−2i−2i2i2i0000−2i2iii−i−iii−i−i0000000000000000
χ9166-66-6-66-6-3-3-3333-33-6633-3-30000000000000000000000000000000000000000000000002i2i−2i−2i0000−2i2i−i−iiiii−i−i0000000000000000
χ9266-66-6-66-6-3-3-3333-33-6633-3-3000000000000000000000000000000000000000000000000−2i−2i2i2i00002i−2iii−i−i−i−iii0000000000000000
χ936-66-6-666-6-333-33-3-3300−3i33i3−3i33i30000000000000000000000000000000000000000000000002i−2i2i−2i000000−ii−ii3−33−30000000000000000
χ946-66-6-666-6-333-33-3-3300−3i33i3−3i33i3000000000000000000000000000000000000000000000000−2i2i−2i2i000000i−ii−i−33−330000000000000000
χ956-66-6-666-6-333-33-3-33003i3−3i33i3−3i30000000000000000000000000000000000000000000000002i−2i2i−2i000000−ii−ii−33−330000000000000000
χ966-66-6-666-6-333-33-3-33003i3−3i33i3−3i3000000000000000000000000000000000000000000000000−2i2i−2i2i000000i−ii−i3−33−30000000000000000
χ976-6-6-66-666-3333-33-3-300−3i33i33i3−3i30000000000000000000000000000000000000000000000002-2-22000000-111-1−i3i3i3−i30000000000000000
χ986-6-6-66-666-3333-33-3-300−3i33i33i3−3i3000000000000000000000000000000000000000000000000-222-20000001-1-11i3−i3−i3i30000000000000000
χ996-6-6-66-666-3333-33-3-3003i3−3i3−3i33i30000000000000000000000000000000000000000000000002-2-22000000-111-1i3−i3−i3i30000000000000000
χ1006-6-6-66-666-3333-33-3-3003i3−3i3−3i33i3000000000000000000000000000000000000000000000000-222-20000001-1-11−i3i3i3−i30000000000000000
χ101121212-1212-12-12-12-6-66-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-12-12-1212-1212-6-6666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-121212-12-12-1212-66-6-6666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12121212-12-12-66-66-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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