Finite Group Databasebeta

← Group #13139940

Character table — Group #13139940

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order12223444466626612121212336666661212121212121212366666666666121212121212121212121212444488881212121212121212242424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
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
χ511111-1-111111-1-1-111-1-111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-111111-1-1-111-1-111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-111111-1-1-111-1-111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ811111-1-111111-1-1-111-1-111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ922222222222222222222-1222-1-1-1-1-1-1-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
χ1022222222222222222222-1222-1-1-1-1-1-1-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200001111111100000000000000
χ112222222222222222222-12-1-1-12222222-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ122222222222222222222-12-1-1-12222222-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ132222222-2-2222-2-2-2-2-222222222222222-2-2-2-22-2-2-2-222-2-2-2-22-2-222-2-2-2-22222000000000000000000000000000000
χ142222222-2-2222-2-2-2-2-2222-1222-1-1-1-1-1-1-1-2-2-2-2-1-2-211-1-11111-111221111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i300000000000000
χ152222222-2-2222-2-2-2-2-2222-1222-1-1-1-1-1-1-1-2-2-2-2-1-2-211-1-11111-111221111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i300000000000000
χ162222222-2-2222-2-2-2-2-222-12-1-1-122222221111-111-2-2-1-11111-1-2-2-1-11111-1-1-1-1000000000000000033−3−333−3−3000000
χ172222222-2-2222-2-2-2-2-222-12-1-1-122222221111-111-2-2-1-11111-1-2-2-1-11111-1-1-1-10000000000000000−3−333−3−333000000
χ1822222-2-222222-2-2-222-2-22-1222-1-1-111112222-1-2-211-1-11111-1-1-1-2-2-1-1-1-1111122-2-20000-1-1-1-1111100000000000000
χ1922222-2-222222-2-2-222-2-22-1222-1-1-111112222-1-2-211-1-11111-1-1-1-2-2-1-1-1-11111-2-22200001111-1-1-1-100000000000000
χ2022222-2-222222-2-2-222-2-2-12-1-1-1222-2-2-2-2-1-1-1-1-111-2-2-1-11111-12211-1-1-1-11111000022-2-200000000-1-1-1-11111000000
χ2122222-2-222222-2-2-222-2-2-12-1-1-1222-2-2-2-2-1-1-1-1-111-2-2-1-11111-12211-1-1-1-111110000-2-222000000001111-1-1-1-1000000
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
χ2322222-2-2-2-2222222-2-2-2-22-1222-1-1-11111-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-21111111100000000−i3−i3i3i3i3i3−i3−i300000000000000
χ2422222-2-2-2-2222222-2-2-2-22-1222-1-1-11111-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-21111111100000000i3i3−i3−i3−i3−i3i3i300000000000000
χ2522222-2-2-2-2222222-2-2-2-2-12-1-1-1222-2-2-2-21111-1-1-122-1-1-1-1-1-1-1-2-21111111111000000000000000033−3−3−3−333000000
χ2622222-2-2-2-2222222-2-2-2-2-12-1-1-1222-2-2-2-21111-1-1-122-1-1-1-1-1-1-1-2-211111111110000000000000000−3−33333−3−3000000
χ2722-2-22002-2-22-20002-20022-2-222-2-2000022-2-220000-2-2000022-20022-2-20000002i−2i000000002i−2i2i−2i00000000000000
χ2822-2-22002-2-22-20002-20022-2-222-2-2000022-2-220000-2-2000022-20022-2-2000000−2i2i00000000−2i2i−2i2i00000000000000
χ2922-2-22002-2-22-20002-2002-1-2-22-111−i3−i3i3i322-2-2-100−i3i311−i3−i3i3i3-1-1100-1-111−i3−i3i3i3002i−2i00003−33−3−ii−ii00000000000000
χ3022-2-22002-2-22-20002-2002-1-2-22-111−i3−i3i3i322-2-2-100−i3i311−i3−i3i3i3-1-1100-1-111−i3−i3i3i300−2i2i0000−33−33i−ii−i00000000000000
χ3122-2-22002-2-22-20002-2002-1-2-22-111i3i3−i3−i322-2-2-100i3−i311i3i3−i3−i3-1-1100-1-111i3i3−i3−i3002i−2i0000−33−33−ii−ii00000000000000
χ3222-2-22002-2-22-20002-2002-1-2-22-111i3i3−i3−i322-2-2-100i3−i311i3i3−i3−i3-1-1100-1-111i3i3−i3−i300−2i2i00003−33−3i−ii−i00000000000000
χ3322-2-2200-22-22-2000-220022-2-222-2-20000-2-22220000-2-200002-2200-2-22200002i−2i0000002i−2i−2i2i000000000000000000
χ3422-2-2200-22-22-2000-220022-2-222-2-20000-2-22220000-2-200002-2200-2-2220000−2i2i000000−2i2i2i−2i000000000000000000
χ3522-2-2200-22-22-2000-22002-1-2-22-111−i3−i3i3i3-2-222-100i3−i311i3i3−i3−i3-11-10011-1-1−i3−i3i3i32i−2i000000−iii−i3−3−3300000000000000
χ3622-2-2200-22-22-2000-22002-1-2-22-111−i3−i3i3i3-2-222-100i3−i311i3i3−i3−i3-11-10011-1-1−i3−i3i3i3−2i2i000000i−i−ii−333−300000000000000
χ3722-2-2200-22-22-2000-22002-1-2-22-111i3i3−i3−i3-2-222-100−i3i311−i3−i3i3i3-11-10011-1-1i3i3−i3−i32i−2i000000−iii−i−333−300000000000000
χ3822-2-2200-22-22-2000-22002-1-2-22-111i3i3−i3−i3-2-222-100−i3i311−i3−i3i3i3-11-10011-1-1i3i3−i3−i3−2i2i000000i−i−ii3−3−3300000000000000
χ392-22-222i−2i002-2-2000002i−2i222-2-2-22-22i−2i2i−2i0000200002-20000-2002i−2i00002i−2i2i−2i00002−2−i2i2000000002−22−2−i2i2−i2i2000000
χ402-22-222i−2i002-2-2000002i−2i222-2-2-22-22i−2i2i−2i0000200002-20000-2002i−2i00002i−2i2i−2i0000−22i2−i200000000−22−22i2−i2i2−i2000000
χ412-22-222i−2i002-2-2000002i−2i-12-111-22-22i−2i2i−2i3−33−3-1−i3i300-11−i3i3−i3i3100−ii3−33−3−ii−ii00002−2−i2i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ422-22-222i−2i002-2-2000002i−2i-12-111-22-22i−2i2i−2i3−33−3-1−i3i300-11−i3i3−i3i3100−ii3−33−3−ii−ii0000−22i2−i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ432-22-222i−2i002-2-2000002i−2i-12-111-22-22i−2i2i−2i−33−33-1i3−i300-11i3−i3i3−i3100−ii−33−33−ii−ii00002−2−i2i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ442-22-222i−2i002-2-2000002i−2i-12-111-22-22i−2i2i−2i−33−33-1i3−i300-11i3−i3i3−i3100−ii−33−33−ii−ii0000−22i2−i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ452-22-22−2i2i002-2-200000−2i2i222-2-2-22-2−2i2i−2i2i0000200002-20000-200−2i2i0000−2i2i−2i2i00002−2i2−i2000000002−22−2i2−i2i2−i2000000
χ462-22-22−2i2i002-2-200000−2i2i222-2-2-22-2−2i2i−2i2i0000200002-20000-200−2i2i0000−2i2i−2i2i0000−22−i2i200000000−22−22−i2i2−i2i2000000
χ472-22-22−2i2i002-2-200000−2i2i-12-111-22-2−2i2i−2i2i3−33−3-1i3−i300-11i3−i3i3−i3100i−i3−33−3i−ii−i00002−2i2−i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ482-22-22−2i2i002-2-200000−2i2i-12-111-22-2−2i2i−2i2i3−33−3-1i3−i300-11i3−i3i3−i3100i−i3−33−3i−ii−i0000−22−i2i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ492-22-22−2i2i002-2-200000−2i2i-12-111-22-2−2i2i−2i2i−33−33-1−i3i300-11−i3i3−i3i3100i−i−33−33i−ii−i00002−2i2−i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ502-22-22−2i2i002-2-200000−2i2i-12-111-22-2−2i2i−2i2i−33−33-1−i3i300-11−i3i3−i3i3100i−i−33−33i−ii−i0000−22−i2i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
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
χ524444444-4-4444-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-222221222211-1-1-1-1122-2-2-1-1-1-11111000000000000000000000000000000
χ5344444-4-444444-4-4-444-4-4-2-2-2-2-2-2-2-22222-2-2-2-21222211-1-1-1-11-2-2221111-1-1-1-1000000000000000000000000000000
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
χ5544-4-44004-4-44-40004-400-2422-24-4-40000-2-222-20000220000-24-400-2-2220000000000000000000000000000000000
χ5644-4-44004-4-44-40004-400-2-222-2-222−2i3−2i32i32i3-2-222100−2i32i3-1-1i3i3−i3−i31-220011-1-1i3i3−i3−i3000000000000000000000000000000
χ5744-4-44004-4-44-40004-400-2-222-2-2222i32i3−2i3−2i3-2-2221002i3−2i3-1-1−i3−i3i3i31-220011-1-1−i3−i3i3i3000000000000000000000000000000
χ5844-4-4400-44-44-4000-4400-2422-24-4-4000022-2-2-20000220000-2-440022-2-20000000000000000000000000000000000
χ5944-4-4400-44-44-4000-4400-2-222-2-222−2i3−2i32i32i322-2-21002i3−2i3-1-1−i3−i3i3i312-200-1-111i3i3−i3−i3000000000000000000000000000000
χ6044-4-4400-44-44-4000-4400-2-222-2-2222i32i3−2i3−2i322-2-2100−2i32i3-1-1i3i3−i3−i312-200-1-111−i3−i3i3i3000000000000000000000000000000
χ614-44-444i−4i004-4-4000004i−4i4-24-4-42-22−2i2i−2i2i0000-20000-2200002004i−4i0000−2i2i−2i2i000000000000000000000000000000
χ624-44-444i−4i004-4-4000004i−4i-2-2-2222-22−2i2i−2i2i23−2323−231−2i32i3001-1i3−i3i3−i3-100−2i2i−33−33i−ii−i000000000000000000000000000000
χ634-44-444i−4i004-4-4000004i−4i-2-2-2222-22−2i2i−2i2i−2323−232312i3−2i3001-1−i3i3−i3i3-100−2i2i3−33−3i−ii−i000000000000000000000000000000
χ644-44-44−4i4i004-4-400000−4i4i4-24-4-42-222i−2i2i−2i0000-20000-220000200−4i4i00002i−2i2i−2i000000000000000000000000000000
χ654-44-44−4i4i004-4-400000−4i4i-2-2-2222-222i−2i2i−2i23−2323−2312i3−2i3001-1−i3i3−i3i3-1002i−2i−33−33−ii−ii000000000000000000000000000000
χ664-44-44−4i4i004-4-400000−4i4i-2-2-2222-222i−2i2i−2i−2323−23231−2i32i3001-1i3−i3i3−i3-1002i−2i3−33−3−ii−ii000000000000000000000000000000
χ674-4-4440000-4-44000000044-44-4-4-440000000040000-440000-4000000000000000000000000000000000000000000
χ684-4-4440000-4-4400000004-2-44-422-223−23−23230000-200002-2000020000000023−23−2323000000000000000000000000000000
χ694-4-4440000-4-4400000004-2-44-422-2−232323−230000-200002-20000200000000−232323−23000000000000000000000000000000
χ704-4-4440000-4-440000000-242-22-4-44000023−23−2323-200002-200002000023−23−23230000000000000000000000000000000000
χ714-4-4440000-4-440000000-242-22-4-440000−232323−23-200002-2000020000−232323−230000000000000000000000000000000000
χ724-4-4440000-4-440000000-2-22-2222-223−23−232323−23−232310000-11-333-3-10000−333−3−333−3000000000000000000000000000000
χ734-4-4440000-4-440000000-2-22-2222-223−23−2323−232323−2310000-113-3-33-100003−3−33−333−3000000000000000000000000000000
χ744-4-4440000-4-440000000-2-22-2222-2−232323−2323−23−232310000-113-3-33-10000−333−33−3−33000000000000000000000000000000
χ754-4-4440000-4-440000000-2-22-2222-2−232323−23−232323−2310000-11-333-3-100003−3−333−3−33000000000000000000000000000000
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
χ841212-12-12-60012-126-66000-66000000000000000000000000000000000000000000000000000000000000000000000000
χ851212-12-12-600-12126-660006-6000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-12-612i−12i00-66600000−6i6i0000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-6−12i12i00-666000006i−6i0000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-1212-6000066-60−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-6000066-606i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000

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