Finite Group Databasebeta

← Group #13146600

Character table — Group #13146600

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size112212121212181818181818181818363636363636112212121212181818181818181818363636363636112212121212181818181818181818363636363636112212121212181818181818181818363636363636
order123633664881212242424244412121212441212121212124881212242424244412121212226666664881212242424244412121212441212121212124881212242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1
χ3111111111-1-111-1-1-1-11-111-1-1111111111-1-111-1-1-1-11-111-1-1111111111-1-111-1-1-1-11-111-1-1111111111-1-111-1-1-1-11-111-1-1
χ4111111111-1-111-1-1-1-1-11-1-111111111111-1-111-1-1-1-1-11-1-111111111111-1-111-1-1-1-1-11-1-111111111111-1-111-1-1-1-1-11-1-111
χ522222222-200-2-2000000000022222222-200-2-2000000000022222222-200-2-2000000000022222222-200-2-20000000000
χ62-22-222-2-202−20022−2−20000002-22-222-2-202−20022−2−20000002-22-222-2-202−20022−2−20000002-22-222-2-202−20022−2−2000000
χ72-22-222-2-20−2200−2−2220000002-22-222-2-20−2200−2−2220000002-22-222-2-20−2200−2−2220000002-22-222-2-20−2200−2−222000000
χ844441-21-20000000000200-1-144441-21-20000000000200-1-144441-21-20000000000200-1-144441-21-20000000000200-1-1
χ944441-21-20000000000-2001144441-21-20000000000-2001144441-21-20000000000-2001144441-21-20000000000-20011
χ104444-21-2100000000020-1-1004444-21-2100000000020-1-1004444-21-2100000000020-1-1004444-21-2100000000020-1-100
χ114444-21-21000000000-2011004444-21-21000000000-2011004444-21-21000000000-2011004444-21-21000000000-201100
χ124-44-41-2-1200000000000003−34-44-41-2-1200000000000003−34-44-41-2-1200000000000003−34-44-41-2-1200000000000003−3
χ134-44-41-2-120000000000000−334-44-41-2-120000000000000−334-44-41-2-120000000000000−334-44-41-2-120000000000000−33
χ144-44-4-212-1000000000003−3004-44-4-212-1000000000003−3004-44-4-212-1000000000003−3004-44-4-212-1000000000003−300
χ154-44-4-212-100000000000−33004-44-4-212-100000000000−33004-44-4-212-100000000000−33004-44-4-212-100000000000−3300
χ1666-3-30000200-1-13−33−300000066-3-30000200-1-13−33−300000066-3-30000200-1-13−33−300000066-3-30000200-1-13−33−3000000
χ1766-3-30000200-1-1−33−3300000066-3-30000200-1-1−33−3300000066-3-30000200-1-1−33−3300000066-3-30000200-1-1−33−33000000
χ1866-3-30000-22211-1-1-1-100000066-3-30000-22211-1-1-1-100000066-3-30000-22211-1-1-1-100000066-3-30000-22211-1-1-1-1000000
χ1966-3-30000-2-2-211111100000066-3-30000-2-2-211111100000066-3-30000-2-2-211111100000066-3-30000-2-2-2111111000000
χ206-6-33000002−23−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000006-6-33000002−23−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000006-6-33000002−23−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000006-6-33000002−23−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000
χ216-6-33000002−2−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000006-6-33000002−2−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000006-6-33000002−2−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000006-6-33000002−2−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000
χ226-6-3300000−223−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000006-6-3300000−223−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000006-6-3300000−223−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000006-6-3300000−223−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000
χ236-6-3300000−22−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000006-6-3300000−22−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000006-6-3300000−22−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000006-6-3300000−22−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000
χ2411111111111111111111111iiiiiiiiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ2511111111111111111-1-1-1-1-1-1iiiiiiiiiiiiiiiii−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiii
χ26111111111-1-111-1-1-1-11-111-1-1iiiiiiiii−i−iii−i−i−i−ii−iii−i−i-1-1-1-1-1-1-1-1-111-1-11111-11-1-111−i−i−i−i−i−i−i−i−iii−i−iiiii−ii−i−iii
χ27111111111-1-111-1-1-1-1-11-1-111iiiiiiiii−i−iii−i−i−i−i−ii−i−iii-1-1-1-1-1-1-1-1-111-1-111111-111-1-1−i−i−i−i−i−i−i−i−iii−i−iiiiii−iii−i−i
χ2822222222-200-2-200000000002i2i2i2i2i2i2i2i−2i00−2i−2i0000000000-2-2-2-2-2-2-2-2200220000000000−2i−2i−2i−2i−2i−2i−2i−2i2i002i2i0000000000
χ292-22-222-2-202−20022−2−20000002i−2i2i−2i2i2i−2i−2i0i2−i200i2i2−i2−i2000000-22-22-2-2220−2200−2−222000000−2i2i−2i2i−2i−2i2i2i0−i2i200−i2−i2i2i2000000
χ302-22-222-2-20−2200−2−2220000002i−2i2i−2i2i2i−2i−2i0−i2i200−i2−i2i2i2000000-22-22-2-22202−20022−2−2000000−2i2i−2i2i−2i−2i2i2i0i2−i200i2i2−i2−i2000000
χ3144441-21-20000000000200-1-14i4i4i4ii−2ii−2i00000000002i00−i−i-4-4-4-4-12-120000000000-20011−4i−4i−4i−4i−i2i−i2i0000000000−2i00ii
χ3244441-21-20000000000-200114i4i4i4ii−2ii−2i0000000000−2i00ii-4-4-4-4-12-120000000000200-1-1−4i−4i−4i−4i−i2i−i2i00000000002i00−i−i
χ334444-21-2100000000020-1-1004i4i4i4i−2ii−2ii0000000002i0−i−i00-4-4-4-42-12-1000000000-201100−4i−4i−4i−4i2i−i2i−i000000000−2i0ii00
χ344444-21-21000000000-2011004i4i4i4i−2ii−2ii000000000−2i0ii00-4-4-4-42-12-100000000020-1-100−4i−4i−4i−4i2i−i2i−i0000000002i0−i−i00
χ354-44-41-2-1200000000000003−34i−4i4i−4ii−2i−i2i0000000000000i3−i3-44-44-121-20000000000000−33−4i4i−4i4i−i2ii−2i0000000000000−i3i3
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χ446-6-33000002−2−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000006i−6i−3i3i00000i2−i2−i3i3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000-663-300000−223−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000−6i6i3i−3i00000−i2i2i3−i3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000
χ456-6-3300000−223−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000006i−6i−3i3i00000−i2i2i3−i3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000-663-3000002−2−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000−6i6i3i−3i00000i2−i2−i3i3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ466-6-3300000−22−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000006i−6i−3i3i00000−i2i2−i3i3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000-663-3000002−23−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000−6i6i3i−3i00000i2−i2i3−i3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ4711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4811111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ49111111111-1-111-1-1-1-11-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-1-111111111111-1-111-1-1-1-11-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-1-111
χ50111111111-1-111-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-111-1-111111-111-1-1111111111-1-111-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-111-1-111111-111-1-1
χ5122222222-200-2-20000000000-2-2-2-2-2-2-2-220022000000000022222222-200-2-20000000000-2-2-2-2-2-2-2-2200220000000000
χ522-22-222-2-202−20022−2−2000000-22-22-2-2220−2200−2−2220000002-22-222-2-202−20022−2−2000000-22-22-2-2220−2200−2−222000000
χ532-22-222-2-20−2200−2−222000000-22-22-2-22202−20022−2−20000002-22-222-2-20−2200−2−222000000-22-22-2-22202−20022−2−2000000
χ5444441-21-20000000000200-1-1-4-4-4-4-12-120000000000-2001144441-21-20000000000200-1-1-4-4-4-4-12-120000000000-20011
χ5544441-21-20000000000-20011-4-4-4-4-12-120000000000200-1-144441-21-20000000000-20011-4-4-4-4-12-120000000000200-1-1
χ564444-21-2100000000020-1-100-4-4-4-42-12-1000000000-2011004444-21-2100000000020-1-100-4-4-4-42-12-1000000000-201100
χ574444-21-21000000000-201100-4-4-4-42-12-100000000020-1-1004444-21-21000000000-201100-4-4-4-42-12-100000000020-1-100
χ584-44-41-2-1200000000000003−3-44-44-121-20000000000000−334-44-41-2-1200000000000003−3-44-44-121-20000000000000−33
χ594-44-41-2-120000000000000−33-44-44-121-200000000000003−34-44-41-2-120000000000000−33-44-44-121-200000000000003−3
χ604-44-4-212-1000000000003−300-44-442-1-2100000000000−33004-44-4-212-1000000000003−300-44-442-1-2100000000000−3300
χ614-44-4-212-100000000000−3300-44-442-1-21000000000003−3004-44-4-212-100000000000−3300-44-442-1-21000000000003−300
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χ6366-3-30000200-1-1−33−33000000-6-6330000-200113−33−300000066-3-30000200-1-1−33−33000000-6-6330000-200113−33−3000000
χ6466-3-30000-22211-1-1-1-1000000-6-63300002-2-2-1-1111100000066-3-30000-22211-1-1-1-1000000-6-63300002-2-2-1-11111000000
χ6566-3-30000-2-2-2111111000000-6-6330000222-1-1-1-1-1-100000066-3-30000-2-2-2111111000000-6-6330000222-1-1-1-1-1-1000000
χ666-6-33000002−23−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000-663-300000−22−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000006-6-33000002−23−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000-663-300000−22−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000
χ676-6-33000002−2−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000-663-300000−223−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000006-6-33000002−2−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000-663-300000−223−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000
χ686-6-3300000−223−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000-663-3000002−2−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000006-6-3300000−223−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000-663-3000002−2−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000
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χ7011111111111111111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiii
χ7111111111111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiiiiiiiiiiiiiiii−i−i−i−i−i−i
χ72111111111-1-111-1-1-1-11-111-1-1−i−i−i−i−i−i−i−i−iii−i−iiiii−ii−i−iii-1-1-1-1-1-1-1-1-111-1-11111-11-1-111iiiiiiiii−i−iii−i−i−i−ii−iii−i−i
χ73111111111-1-111-1-1-1-1-11-1-111−i−i−i−i−i−i−i−i−iii−i−iiiiii−iii−i−i-1-1-1-1-1-1-1-1-111-1-111111-111-1-1iiiiiiiii−i−iii−i−i−i−i−ii−i−iii
χ7422222222-200-2-20000000000−2i−2i−2i−2i−2i−2i−2i−2i2i002i2i0000000000-2-2-2-2-2-2-2-22002200000000002i2i2i2i2i2i2i2i−2i00−2i−2i0000000000
χ752-22-222-2-202−20022−2−2000000−2i2i−2i2i−2i−2i2i2i0−i2i200−i2−i2i2i2000000-22-22-2-2220−2200−2−2220000002i−2i2i−2i2i2i−2i−2i0i2−i200i2i2−i2−i2000000
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χ794444-21-2100000000020-1-100−4i−4i−4i−4i2i−i2i−i000000000−2i0ii00-4-4-4-42-12-1000000000-2011004i4i4i4i−2ii−2ii0000000002i0−i−i00
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χ824-44-41-2-120000000000000−33−4i4i−4i4i−i2ii−2i0000000000000i3−i3-44-44-121-200000000000003−34i−4i4i−4ii−2i−i2i0000000000000−i3i3
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χ8766-3-30000-22211-1-1-1-1000000−6i−6i3i3i00002i−2i−2i−i−iiiii000000-6-63300002-2-2-1-111110000006i6i−3i−3i0000−2i2i2iii−i−i−i−i000000
χ8866-3-30000-2-2-2111111000000−6i−6i3i3i00002i2i2i−i−i−i−i−i−i000000-6-6330000222-1-1-1-1-1-10000006i6i−3i−3i0000−2i−2i−2iiiiiii000000
χ896-6-33000002−23−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000−6i6i3i−3i00000−i2i2−i3i3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000-663-300000−22−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000006i−6i−3i3i00000i2−i2i3−i3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000
χ906-6-33000002−2−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000−6i6i3i−3i00000−i2i2i3−i3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000-663-300000−223−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000006i−6i−3i3i00000i2−i2−i3i3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000
χ916-6-3300000−223−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000−6i6i3i−3i00000i2−i2−i3i3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000-663-3000002−2−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000006i−6i−3i3i00000−i2i2i3−i3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000
χ926-6-3300000−22−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000−6i6i3i−3i00000i2−i2i3−i3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000-663-3000002−23−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000006i−6i−3i3i00000−i2i2−i3i3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.