Finite Group Databasebeta

← Group #13140192

Character table — Group #13140192

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order122234444666266121212123366666612121212121212123666666666661212121212121212121212122244666688881212121224242424242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111-1-111111-1-1-111-1-111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-111111-1-1-111-1-111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-111111-1-1-111-1-111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ811111-1-111111-1-1-111-1-111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
χ922222222222222222222-122-1-12-1-1-1-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-1-1-1-100000000000000
χ1022222222222222222222-122-1-12-1-1-1-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000111100000000000000
χ112222222222222222222-12-1-122-122222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-1000000
χ122222222222222222222-12-1-122-122222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-2-2-2000011111111000000
χ132222222-2-2222-2-2-2-2-222222222222222-2-2-2-22-2-2-2-222-2-2-2-2222-2-2-2-2-2-22222000000000000000000000000000000
χ142222222-2-2222-2-2-2-2-2222-122-1-12-1-1-1-1-1-2-2-2-2-1-2-211-1-11111-122111111-1-1-1-10000−i3−i3i3i30000−i3−i3i3i300000000000000
χ152222222-2-2222-2-2-2-2-2222-122-1-12-1-1-1-1-1-2-2-2-2-1-2-211-1-11111-122111111-1-1-1-10000i3i3−i3−i30000i3i3−i3−i300000000000000
χ162222222-2-2222-2-2-2-2-222-12-1-122-1222221111-111-2-2-1-11111-1-1-1-2-21111-1-1-1-1000000000000000033−3−333−3−3000000
χ172222222-2-2222-2-2-2-2-222-12-1-122-1222221111-111-2-2-1-11111-1-1-1-2-21111-1-1-1-10000000000000000−3−333−3−333000000
χ1822222-2-222222-2-2-222-2-22-122-1-12-111112222-1-2-211-1-11111-1-2-2-1-1-1-1-1-1111122-2-2-1-1-1-10000111100000000000000
χ1922222-2-222222-2-2-222-2-22-122-1-12-111112222-1-2-211-1-11111-1-2-2-1-1-1-1-1-11111-2-22211110000-1-1-1-100000000000000
χ2022222-2-222222-2-2-222-2-2-12-1-122-12-2-2-2-2-1-1-1-1-111-2-2-1-11111-11122-1-1-1-111110000000022-2-20000-1-1-1-11111000000
χ2122222-2-222222-2-2-222-2-2-12-1-122-12-2-2-2-2-1-1-1-1-111-2-2-1-11111-11122-1-1-1-1111100000000-2-22200001111-1-1-1-1000000
χ2222222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ2322222-2-2-2-2222222-2-2-2-22-122-1-12-11111-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111110000−i3−i3i3i30000i3i3−i3−i300000000000000
χ2422222-2-2-2-2222222-2-2-2-22-122-1-12-11111-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111110000i3i3−i3−i30000−i3−i3i3i300000000000000
χ2522222-2-2-2-2222222-2-2-2-2-12-1-122-12-2-2-2-21111-1-1-122-1-1-1-1-1-1-111-2-211111111000000000000000033−3−3−3−333000000
χ2622222-2-2-2-2222222-2-2-2-2-12-1-122-12-2-2-2-21111-1-1-122-1-1-1-1-1-1-111-2-2111111110000000000000000−3−33333−3−3000000
χ272-22-222i−2i00-22-2000002i−2i222-22-2-2-22i2i−2i−2i0000200002-20000-22i−2i0000002i2i−2i−2i000000002−2−i2i200002−22−2−i2i2−i2i2000000
χ282-22-222i−2i00-22-2000002i−2i222-22-2-2-22i2i−2i−2i0000200002-20000-22i−2i0000002i2i−2i−2i00000000−22i2−i20000−22−22i2−i2i2−i2000000
χ292-22-222i−2i00-22-2000002i−2i-12-112-21-22i2i−2i−2i33−3−3-1−i3i300-11−i3−i3i3i31−ii0033−3−3−i−iii000000002−2−i2i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ302-22-222i−2i00-22-2000002i−2i-12-112-21-22i2i−2i−2i33−3−3-1−i3i300-11−i3−i3i3i31−ii0033−3−3−i−iii00000000−22i2−i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ312-22-222i−2i00-22-2000002i−2i-12-112-21-22i2i−2i−2i−3−333-1i3−i300-11i3i3−i3−i31−ii00−3−333−i−iii000000002−2−i2i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ322-22-222i−2i00-22-2000002i−2i-12-112-21-22i2i−2i−2i−3−333-1i3−i300-11i3i3−i3−i31−ii00−3−333−i−iii00000000−22i2−i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ332-22-22−2i2i00-22-200000−2i2i222-22-2-2-2−2i−2i2i2i0000200002-20000-2−2i2i000000−2i−2i2i2i000000002−2i2−i200002−22−2i2−i2i2−i2000000
χ342-22-22−2i2i00-22-200000−2i2i222-22-2-2-2−2i−2i2i2i0000200002-20000-2−2i2i000000−2i−2i2i2i00000000−22−i2i20000−22−22−i2i2−i2i2000000
χ352-22-22−2i2i00-22-200000−2i2i-12-112-21-2−2i−2i2i2i33−3−3-1i3−i300-11i3i3−i3−i31i−i0033−3−3ii−i−i000000002−2i2−i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ362-22-22−2i2i00-22-200000−2i2i-12-112-21-2−2i−2i2i2i33−3−3-1i3−i300-11i3i3−i3−i31i−i0033−3−3ii−i−i00000000−22−i2i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ372-22-22−2i2i00-22-200000−2i2i-12-112-21-2−2i−2i2i2i−3−333-1−i3i300-11−i3−i3i3i31i−i00−3−333ii−i−i000000002−2i2−i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ382-22-22−2i2i00-22-200000−2i2i-12-112-21-2−2i−2i2i2i−3−333-1−i3i300-11−i3−i3i3i31i−i00−3−333ii−i−i00000000−22−i2i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ392-2-222002-2-2-220002-20022-2-2-2-22200002-22-220000-2-200002002-22-22-20000002-2000000002-22-200000000000000
χ402-2-222002-2-2-220002-20022-2-2-2-22200002-22-220000-2-200002002-22-22-2000000-2200000000-22-2200000000000000
χ412-2-222002-2-2-220002-2002-1-2-2112-1−i3i3−i3i32-22-2-100−i3i311−i3i3−i3i3-100-11-11-11−i3i3−i3i3002-2−i3i3−i3i30000-11-1100000000000000
χ422-2-222002-2-2-220002-2002-1-2-2112-1−i3i3−i3i32-22-2-100−i3i311−i3i3−i3i3-100-11-11-11−i3i3−i3i300-22i3−i3i3−i300001-11-100000000000000
χ432-2-222002-2-2-220002-2002-1-2-2112-1i3−i3i3−i32-22-2-100i3−i311i3−i3i3−i3-100-11-11-11i3−i3i3−i3002-2i3−i3i3−i30000-11-1100000000000000
χ442-2-222002-2-2-220002-2002-1-2-2112-1i3−i3i3−i32-22-2-100i3−i311i3−i3i3−i3-100-11-11-11i3−i3i3−i300-22−i3i3−i3i300001-11-100000000000000
χ452-2-22200-22-2-22000-220022-2-2-2-2220000-22-2220000-2-20000200-22-22-2200002-2002-2-220000000000000000000000
χ462-2-22200-22-2-22000-220022-2-2-2-2220000-22-2220000-2-20000200-22-22-220000-2200-222-20000000000000000000000
χ472-2-22200-22-2-22000-22002-1-2-2112-1−i3i3−i3i3-22-22-100i3−i311i3−i3i3−i3-1001-11-11-1−i3i3−i3i32-200-111-10000−i3i3i3−i300000000000000
χ482-2-22200-22-2-22000-22002-1-2-2112-1−i3i3−i3i3-22-22-100i3−i311i3−i3i3−i3-1001-11-11-1−i3i3−i3i3-22001-1-110000i3−i3−i3i300000000000000
χ492-2-22200-22-2-22000-22002-1-2-2112-1i3−i3i3−i3-22-22-100−i3i311−i3i3−i3i3-1001-11-11-1i3−i3i3−i32-200-111-10000i3−i3−i3i300000000000000
χ502-2-22200-22-2-22000-22002-1-2-2112-1i3−i3i3−i3-22-22-100−i3i311−i3i3−i3i3-1001-11-11-1i3−i3i3−i3-22001-1-110000−i3i3i3−i300000000000000
χ514444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000
χ524444444-4-4444-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-222-1-1-1-11111000000000000000000000000000000
χ5344444-4-444444-4-4-444-4-4-2-2-2-2-2-2-2-22222-2-2-2-21222211-1-1-1-1122-2-21111-1-1-1-1000000000000000000000000000000
χ5444444-4-4-4-4444444-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ5544-4-4400004-4-4000000044-44-44-4-40000000040000-440000-4000000000000000000000000000000000000000000
χ5644-4-4400004-4-400000004-2-442-2-4223−23−23230000-200002-2000020000000023−23−2323000000000000000000000000000000
χ5744-4-4400004-4-400000004-2-442-2-42−232323−230000-200002-20000200000000−232323−23000000000000000000000000000000
χ5844-4-4400004-4-40000000-242-2-442-4000023−23−2323-200002-200002000023−23−23230000000000000000000000000000000000
χ5944-4-4400004-4-40000000-242-2-442-40000−232323−23-200002-2000020000−232323−230000000000000000000000000000000000
χ6044-4-4400004-4-40000000-2-22-22-22223−23−232323−23−232310000-11-333-3-10000−333−3−333−3000000000000000000000000000000
χ6144-4-4400004-4-40000000-2-22-22-22223−23−2323−232323−2310000-113-3-33-100003−3−33−333−3000000000000000000000000000000
χ6244-4-4400004-4-40000000-2-22-22-222−232323−2323−23−232310000-113-3-33-10000−333−33−3−33000000000000000000000000000000
χ6344-4-4400004-4-40000000-2-22-22-222−232323−23−232323−2310000-11-333-3-100003−3−333−3−33000000000000000000000000000000
χ644-44-444i−4i00-44-4000004i−4i4-24-4-22-42−2i−2i2i2i0000-20000-22000024i−4i000000−2i−2i2i2i000000000000000000000000000000
χ654-44-444i−4i00-44-4000004i−4i-2-2-22-2222−2i−2i2i2i2323−23−231−2i32i3001-1i3i3−i3−i3-1−2i2i00−3−333ii−i−i000000000000000000000000000000
χ664-44-444i−4i00-44-4000004i−4i-2-2-22-2222−2i−2i2i2i−23−23232312i3−2i3001-1−i3−i3i3i3-1−2i2i0033−3−3ii−i−i000000000000000000000000000000
χ674-44-44−4i4i00-44-400000−4i4i4-24-4-22-422i2i−2i−2i0000-20000-2200002−4i4i0000002i2i−2i−2i000000000000000000000000000000
χ684-44-44−4i4i00-44-400000−4i4i-2-2-22-22222i2i−2i−2i2323−23−2312i3−2i3001-1−i3−i3i3i3-12i−2i00−3−333−i−iii000000000000000000000000000000
χ694-44-44−4i4i00-44-400000−4i4i-2-2-22-22222i2i−2i−2i−23−2323231−2i32i3001-1i3i3−i3−i3-12i−2i0033−3−3−i−iii000000000000000000000000000000
χ704-4-444004-4-4-440004-400-2422-4-4-240000-22-22-20000220000-2004-4-22-220000000000000000000000000000000000
χ714-4-444004-4-4-440004-400-2-22222-2-2−2i32i3−2i32i3-22-22100−2i32i3-1-1i3−i3i3−i3100-221-11-1i3−i3i3−i3000000000000000000000000000000
χ724-4-444004-4-4-440004-400-2-22222-2-22i3−2i32i3−2i3-22-221002i3−2i3-1-1−i3i3−i3i3100-221-11-1−i3i3−i3i3000000000000000000000000000000
χ734-4-44400-44-4-44000-4400-2422-4-4-2400002-22-2-20000220000-200-442-22-20000000000000000000000000000000000
χ744-4-44400-44-4-44000-4400-2-22222-2-2−2i32i3−2i32i32-22-21002i3−2i3-1-1−i3i3−i3i31002-2-11-11i3−i3i3−i3000000000000000000000000000000
χ754-4-44400-44-4-44000-4400-2-22222-2-22i3−2i32i3−2i32-22-2100−2i32i3-1-1i3−i3i3−i31002-2-11-11−i3i3−i3i3000000000000000000000000000000
χ766666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000000000000000000022-1-1-1-1
χ776666-36666-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000000000000000000-2-21111
χ786666-366-6-6-3-3-3-63333-3-3000000000000000000000000000000000000000000000000000000000000000000−i3i3−i3i3
χ796666-366-6-6-3-3-3-63333-3-3000000000000000000000000000000000000000000000000000000000000000000i3−i3i3−i3
χ806666-3-6-666-3-3-3-633-3-33300000000000000000000000000000000000000000000000000000000000000002-2-1-111
χ816666-3-6-666-3-3-3-633-3-3330000000000000000000000000000000000000000000000000000000000000000-2211-1-1
χ826666-3-6-6-6-6-3-3-36-3-33333000000000000000000000000000000000000000000000000000000000000000000−i3i3i3−i3
χ836666-3-6-6-6-6-3-3-36-3-33333000000000000000000000000000000000000000000000000000000000000000000i3−i3−i3i3
χ841212-12-12-60000-6660−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000
χ851212-12-12-60000-66606i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-12-612i−12i006-6600000−6i6i0000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-6−12i12i006-66000006i−6i0000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-1212-60012-1266-6000-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-600-121266-60006-6000000000000000000000000000000000000000000000000000000000000000000000000

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