Finite Group Databasebeta

← Group #13146674

Character table — Group #13146674

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122221212121212121212181818181818181818181818181818181818363636363636363636363636111122221212121212121212181818181818181818181818181818181818363636363636363636363636
order1222366633666666448888121212122424242424242424224466661212121222226666666666664488881212121224242424242424242244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ4111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51-11-11-1-11111-11-1-1-11-1ii−i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-11-11-1-11111-11-1-1-11-1ii−i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i
χ61-11-11-1-11111-11-1-1-11-1ii−i−i11-1-1iiii−i−i−i−i-11−ii-1-111−i−iii1-11-11-1-11111-11-1-1-11-1ii−i−i11-1-1iiii−i−i−i−i-11−ii-1-111−i−iii
χ71-11-11-1-11111-11-1-1-11-1−i−iii11-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-11-11-1-11111-11-1-1-11-1−i−iii11-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii
χ81-11-11-1-11111-11-1-1-11-1−i−iii11-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i1-11-11-1-11111-11-1-1-11-1−i−iii11-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i
χ92222222222222222-2-20000-2-2-2-2000000000000000000002222222222222222-2-20000-2-2-2-200000000000000000000
χ1022-2-222-2-222-22-22-2-200−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i200000000000022-2-222-2-222-22-22-2-200−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i2000000000000
χ1122-2-222-2-222-22-22-2-200i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i200000000000022-2-222-2-222-22-22-2-200i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i2000000000000
χ122-22-22-2-22222-22-2-2-2-220000-2-222000000000000000000002-22-22-2-22222-22-2-2-2-220000-2-22200000000000000000000
χ132-2-222-22-222-2-2-2-222002−2−22000022−2−2−2−2220000000000002-2-222-22-222-2-2-2-222002−2−22000022−2−2−2−222000000000000
χ142-2-222-22-222-2-2-2-22200−222−20000−2−22222−2−20000000000002-2-222-22-222-2-2-2-22200−222−20000−2−22222−2−2000000000000
χ15444444441-211-2-2-2100000000000000000000220000-1-1-1-1444444441-211-2-2-2100000000000000000000220000-1-1-1-1
χ16444444441-211-2-2-2100000000000000000000-2-200001111444444441-211-2-2-2100000000000000000000-2-200001111
χ1744444444-21-2-2111-20000000000000000002200-1-1-1-1000044444444-21-2-2111-20000000000000000002200-1-1-1-10000
χ1844444444-21-2-2111-2000000000000000000-2-2001111000044444444-21-2-2111-2000000000000000000-2-20011110000
χ1944-4-444-4-41-2-112-22-1000000000000000000000000003−33−344-4-444-4-41-2-112-22-1000000000000000000000000003−33−3
χ2044-4-444-4-41-2-112-22-100000000000000000000000000−33−3344-4-444-4-41-2-112-22-100000000000000000000000000−33−33
χ2144-4-444-4-4-212-2-11-120000000000000000000000−i3i3−i3i3000044-4-444-4-4-212-2-11-120000000000000000000000−i3i3−i3i30000
χ2244-4-444-4-4-212-2-11-120000000000000000000000i3−i3i3−i3000044-4-444-4-4-212-2-11-120000000000000000000000i3−i3i3−i30000
χ234-44-44-4-441-21-1-222-1000000000000000000002i−2i0000−i−iii4-44-44-4-441-21-1-222-1000000000000000000002i−2i0000−i−iii
χ244-44-44-4-441-21-1-222-100000000000000000000−2i2i0000ii−i−i4-44-44-4-441-21-1-222-100000000000000000000−2i2i0000ii−i−i
χ254-44-44-4-44-21-221-1-120000000000000000002-200-1-11100004-44-44-4-44-21-221-1-120000000000000000002-200-1-1110000
χ264-44-44-4-44-21-221-1-12000000000000000000-220011-1-100004-44-44-4-44-21-221-1-12000000000000000000-220011-1-10000
χ274-4-444-44-41-2-1-122-2100000000000000000000000000−i3i3i3−i34-4-444-44-41-2-1-122-2100000000000000000000000000−i3i3i3−i3
χ284-4-444-44-41-2-1-122-2100000000000000000000000000i3−i3−i3i34-4-444-44-41-2-1-122-2100000000000000000000000000i3−i3−i3i3
χ294-4-444-44-4-2122-1-11-20000000000000000000000−i3i3i3−i300004-4-444-44-4-2122-1-11-20000000000000000000000−i3i3i3−i30000
χ304-4-444-44-4-2122-1-11-20000000000000000000000i3−i3−i3i300004-4-444-44-4-2122-1-11-20000000000000000000000i3−i3−i3i30000
χ316666-3-3-3-300000000220000-1-1-1-13−33−33−33−30000000000006666-3-3-3-300000000220000-1-1-1-13−33−33−33−3000000000000
χ326666-3-3-3-300000000220000-1-1-1-1−33−33−33−330000000000006666-3-3-3-300000000220000-1-1-1-1−33−33−33−33000000000000
χ336666-3-3-3-300000000-2-222221111-1-1-1-1-1-1-1-10000000000006666-3-3-3-300000000-2-222221111-1-1-1-1-1-1-1-1000000000000
χ346666-3-3-3-300000000-2-2-2-2-2-21111111111110000000000006666-3-3-3-300000000-2-2-2-2-2-2111111111111000000000000
χ3566-6-6-3-3330000000000−i2i2−i2i23−33−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2300000000000066-6-6-3-3330000000000−i2i2−i2i23−33−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ3666-6-6-3-3330000000000−i2i2−i2i2−33−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ700000000000066-6-6-3-3330000000000−i2i2−i2i2−33−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ3766-6-6-3-3330000000000i2−i2i2−i23−33−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300000000000066-6-6-3-3330000000000i2−i2i2−i23−33−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ3866-6-6-3-3330000000000i2−i2i2−i2−33−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ700000000000066-6-6-3-3330000000000i2−i2i2−i2−33−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ396-66-6-333-3000000002-20000-1-111−i3i3−i3i3i3−i3i3−i30000000000006-66-6-333-3000000002-20000-1-111−i3i3−i3i3i3−i3i3−i3000000000000
χ406-66-6-333-3000000002-20000-1-111i3−i3i3−i3−i3i3−i3i30000000000006-66-6-333-3000000002-20000-1-111i3−i3i3−i3−i3i3−i3i3000000000000
χ416-66-6-333-300000000-222i2i−2i−2i11-1-1−i−i−i−iiiii0000000000006-66-6-333-300000000-222i2i−2i−2i11-1-1−i−i−i−iiiii000000000000
χ426-66-6-333-300000000-22−2i−2i2i2i11-1-1iiii−i−i−i−i0000000000006-66-6-333-300000000-22−2i−2i2i2i11-1-1iiii−i−i−i−i000000000000
χ436-6-66-33-3300000000002−2−223−3−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000006-6-66-33-3300000000002−2−223−3−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ446-6-66-33-3300000000002−2−22−333−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000006-6-66-33-3300000000002−2−22−333−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000
χ456-6-66-33-330000000000−222−23−3−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000006-6-66-33-330000000000−222−23−3−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ466-6-66-33-330000000000−222−2−333−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000006-6-66-33-330000000000−222−2−333−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ481111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ49111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-11111
χ50111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-1
χ511-11-11-1-11111-11-1-1-11-1ii−i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i-11-11-111-1-1-1-11-1111-11−i−iii-1-111−i−i−i−iiiii-11−ii-1-111−i−iii
χ521-11-11-1-11111-11-1-1-11-1ii−i−i11-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11-11-111-1-1-1-11-1111-11−i−iii-1-111−i−i−i−iiiii1-1i−i11-1-1ii−i−i
χ531-11-11-1-11111-11-1-1-11-1−i−iii11-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii-11-11-111-1-1-1-11-1111-11ii−i−i-1-111iiii−i−i−i−i-11i−i-1-111ii−i−i
χ541-11-11-1-11111-11-1-1-11-1−i−iii11-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11-11-111-1-1-1-11-1111-11ii−i−i-1-111iiii−i−i−i−i1-1−ii11-1-1−i−iii
χ552222222222222222-2-20000-2-2-2-200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000222200000000000000000000
χ5622-2-222-2-222-22-22-2-200−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i2000000000000-2-222-2-222-2-22-22-22200i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i2000000000000
χ5722-2-222-2-222-22-22-2-200i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i2000000000000-2-222-2-222-2-22-22-22200−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i2000000000000
χ582-22-22-2-22222-22-2-2-2-220000-2-22200000000000000000000-22-22-222-2-2-2-22-22222-2000022-2-200000000000000000000
χ592-2-222-22-222-2-2-2-222002−2−22000022−2−2−2−222000000000000-222-2-22-22-2-22222-2-200−222−20000−2−22222−2−2000000000000
χ602-2-222-22-222-2-2-2-22200−222−20000−2−22222−2−2000000000000-222-2-22-22-2-22222-2-2002−2−22000022−2−2−2−222000000000000
χ61444444441-211-2-2-2100000000000000000000220000-1-1-1-1-4-4-4-4-4-4-4-4-12-1-1222-100000000000000000000-2-200001111
χ62444444441-211-2-2-2100000000000000000000-2-200001111-4-4-4-4-4-4-4-4-12-1-1222-100000000000000000000220000-1-1-1-1
χ6344444444-21-2-2111-20000000000000000002200-1-1-1-10000-4-4-4-4-4-4-4-42-122-1-1-12000000000000000000-2-20011110000
χ6444444444-21-2-2111-2000000000000000000-2-20011110000-4-4-4-4-4-4-4-42-122-1-1-120000000000000000002200-1-1-1-10000
χ6544-4-444-4-41-2-112-22-1000000000000000000000000003−33−3-4-444-4-444-121-1-22-2100000000000000000000000000−33−33
χ6644-4-444-4-41-2-112-22-100000000000000000000000000−33−33-4-444-4-444-121-1-22-21000000000000000000000000003−33−3
χ6744-4-444-4-4-212-2-11-120000000000000000000000−i3i3−i3i30000-4-444-4-4442-1-221-11-20000000000000000000000i3−i3i3−i30000
χ6844-4-444-4-4-212-2-11-120000000000000000000000i3−i3i3−i30000-4-444-4-4442-1-221-11-20000000000000000000000−i3i3−i3i30000
χ694-44-44-4-441-21-1-222-1000000000000000000002i−2i0000−i−iii-44-44-444-4-12-112-2-2100000000000000000000−2i2i0000ii−i−i
χ704-44-44-4-441-21-1-222-100000000000000000000−2i2i0000ii−i−i-44-44-444-4-12-112-2-21000000000000000000002i−2i0000−i−iii
χ714-44-44-4-44-21-221-1-120000000000000000002-200-1-1110000-44-44-444-42-12-2-111-2000000000000000000-220011-1-10000
χ724-44-44-4-44-21-221-1-12000000000000000000-220011-1-10000-44-44-444-42-12-2-111-20000000000000000002-200-1-1110000
χ734-4-444-44-41-2-1-122-2100000000000000000000000000−i3i3i3−i3-444-4-44-44-1211-2-22-100000000000000000000000000i3−i3−i3i3
χ744-4-444-44-41-2-1-122-2100000000000000000000000000i3−i3−i3i3-444-4-44-44-1211-2-22-100000000000000000000000000−i3i3i3−i3
χ754-4-444-44-4-2122-1-11-20000000000000000000000−i3i3i3−i30000-444-4-44-442-1-2-211-120000000000000000000000i3−i3−i3i30000
χ764-4-444-44-4-2122-1-11-20000000000000000000000i3−i3−i3i30000-444-4-44-442-1-2-211-120000000000000000000000−i3i3i3−i30000
χ776666-3-3-3-300000000220000-1-1-1-13−33−33−33−3000000000000-6-6-6-6333300000000-2-200001111−33−33−33−33000000000000
χ786666-3-3-3-300000000220000-1-1-1-1−33−33−33−33000000000000-6-6-6-6333300000000-2-2000011113−33−33−33−3000000000000
χ796666-3-3-3-300000000-2-222221111-1-1-1-1-1-1-1-1000000000000-6-6-6-633330000000022-2-2-2-2-1-1-1-111111111000000000000
χ806666-3-3-3-300000000-2-2-2-2-2-2111111111111000000000000-6-6-6-6333300000000222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ8166-6-6-3-3330000000000−i2i2−i2i23−33−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000-6-66633-3-30000000000i2−i2i2−i2−33−33−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ8266-6-6-3-3330000000000−i2i2−i2i2−33−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000-6-66633-3-30000000000i2−i2i2−i23−33−3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ8366-6-6-3-3330000000000i2−i2i2−i23−33−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000-6-66633-3-30000000000−i2i2−i2i2−33−33ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ8466-6-6-3-3330000000000i2−i2i2−i2−33−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000-6-66633-3-30000000000−i2i2−i2i23−33−3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ856-66-6-333-3000000002-20000-1-111−i3i3−i3i3i3−i3i3−i3000000000000-66-663-3-3300000000-22000011-1-1i3−i3i3−i3−i3i3−i3i3000000000000
χ866-66-6-333-3000000002-20000-1-111i3−i3i3−i3−i3i3−i3i3000000000000-66-663-3-3300000000-22000011-1-1−i3i3−i3i3i3−i3i3−i3000000000000
χ876-66-6-333-300000000-222i2i−2i−2i11-1-1−i−i−i−iiiii000000000000-66-663-3-33000000002-2−2i−2i2i2i-1-111iiii−i−i−i−i000000000000
χ886-66-6-333-300000000-22−2i−2i2i2i11-1-1iiii−i−i−i−i000000000000-66-663-3-33000000002-22i2i−2i−2i-1-111−i−i−i−iiiii000000000000
χ896-6-66-33-3300000000002−2−223−3−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000-666-63-33-30000000000−222−2−333−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ906-6-66-33-3300000000002−2−22−333−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000-666-63-33-30000000000−222−23−3−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ916-6-66-33-330000000000−222−23−3−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000-666-63-33-300000000002−2−22−333−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ926-6-66-33-330000000000−222−2−333−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000-666-63-33-300000000002−2−223−3−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000

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