Finite Group Databasebeta

← Group #13140190

Character table — Group #13140190

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order122234444666121212122661212336666661212121236666666666612121212121212121212121212122244666688881212121224242424242424244412121212
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
χ511111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ611111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ711111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ811111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
χ92222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-1000000
χ12222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-2000011111111000000
χ132222222-2-22222222-2-2-2-2-222222222-2-2-2-22-2-2-2-222-2-2-2-2222-2-222-2-2-2-22222000000000000000000000000000000
χ142222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-1-2-211-1-11111-12211-1-11111-1-1-1-100000000000000000000000000−i3i3−i3i3
χ152222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-1-2-211-1-11111-12211-1-11111-1-1-1-100000000000000000000000000i3−i3i3−i3
χ162222222-2-22222222-2-2-2-2-2-12-1-12-1221111-111-2-2-1-11111-1-1-1-2-2221111-1-1-1-1000000000000000033−3−333−3−3000000
χ172222222-2-22222222-2-2-2-2-2-12-1-12-1221111-111-2-2-1-11111-1-1-1-2-2221111-1-1-1-10000000000000000−3−333−3−333000000
χ1822222-2-222222-2-2-2-2-2-2-2222-122-12-1-12222-1-2-211-1-11111-1-2-2-1-111-1-1-1-111110000000000000000000000002-2-1-111
χ1922222-2-222222-2-2-2-2-2-2-2222-122-12-1-12222-1-2-211-1-11111-1-2-2-1-111-1-1-1-11111000000000000000000000000-2211-1-1
χ2022222-2-222222-2-2-2-2-2-2-222-12-1-12-122-1-1-1-1-111-2-2-1-11111-11122-2-2-1-1-1-111110000000022-2-20000-1-1-1-11111000000
χ2122222-2-222222-2-2-2-2-2-2-222-12-1-12-122-1-1-1-1-111-2-2-1-11111-11122-2-2-1-1-1-1111100000000-2-22200001111-1-1-1-1000000
χ2222222-2-2-2-2222-2-2-2-2222-2-222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ2322222-2-2-2-2222-2-2-2-2222-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000000000000000−i3i3i3−i3
χ2422222-2-2-2-2222-2-2-2-2222-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000000000000000i3−i3−i3i3
χ2522222-2-2-2-2222-2-2-2-2222-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-111-2-2-2-211111111000000000000000033−3−3−3−333000000
χ2622222-2-2-2-2222-2-2-2-2222-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-111-2-2-2-2111111110000000000000000−3−33333−3−3000000
χ272-22-222i−2i002-2-22i2i−2i−2i00000222-2-2-22-20000200002-20000-22i−2i002i−2i00002i2i−2i−2i000000002−2−i2i200002−22−2−i2i2−i2i2000000
χ282-22-222i−2i002-2-22i2i−2i−2i00000222-2-2-22-20000200002-20000-22i−2i002i−2i00002i2i−2i−2i00000000−22i2−i20000−22−22i2−i2i2−i2000000
χ292-22-222i−2i002-2-22i2i−2i−2i00000-12-11-212-233−3−3-1−i3i300-11−i3−i3i3i31−ii002i−2i33−3−3−i−iii000000002−2−i2i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ302-22-222i−2i002-2-22i2i−2i−2i00000-12-11-212-233−3−3-1−i3i300-11−i3−i3i3i31−ii002i−2i33−3−3−i−iii00000000−22i2−i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ312-22-222i−2i002-2-22i2i−2i−2i00000-12-11-212-2−3−333-1i3−i300-11i3i3−i3−i31−ii002i−2i−3−333−i−iii000000002−2−i2i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ322-22-222i−2i002-2-22i2i−2i−2i00000-12-11-212-2−3−333-1i3−i300-11i3i3−i3−i31−ii002i−2i−3−333−i−iii00000000−22i2−i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ332-22-22−2i2i002-2-2−2i−2i2i2i00000222-2-2-22-20000200002-20000-2−2i2i00−2i2i0000−2i−2i2i2i000000002−2i2−i200002−22−2i2−i2i2−i2000000
χ342-22-22−2i2i002-2-2−2i−2i2i2i00000222-2-2-22-20000200002-20000-2−2i2i00−2i2i0000−2i−2i2i2i00000000−22−i2i20000−22−22−i2i2−i2i2000000
χ352-22-22−2i2i002-2-2−2i−2i2i2i00000-12-11-212-233−3−3-1i3−i300-11i3i3−i3−i31i−i00−2i2i33−3−3ii−i−i000000002−2i2−i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ362-22-22−2i2i002-2-2−2i−2i2i2i00000-12-11-212-233−3−3-1i3−i300-11i3i3−i3−i31i−i00−2i2i33−3−3ii−i−i00000000−22−i2i20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ372-22-22−2i2i002-2-2−2i−2i2i2i00000-12-11-212-2−3−333-1−i3i300-11−i3−i3i3i31i−i00−2i2i−3−333ii−i−i000000002−2i2−i20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ382-22-22−2i2i002-2-2−2i−2i2i2i00000-12-11-212-2−3−333-1−i3i300-11−i3−i3i3i31i−i00−2i2i−3−333ii−i−i00000000−22−i2i20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ392-2-222002-2-2-2200000002-222-2-2-22-222-22-220000-2-200002002-2002-22-20000002-20000000022-2-200000000000000
χ402-2-222002-2-2-2200000002-222-2-2-22-222-22-220000-2-200002002-2002-22-2000000-2200000000-2-22200000000000000
χ412-2-22200-22-2-220000000-2222-2-2-22-22-22-2220000-2-20000200-2200-22-2200002-20022-2-20000000000000000000000
χ422-2-22200-22-2-220000000-2222-2-2-22-22-22-2220000-2-20000200-2200-22-220000-2200-2-2220000000000000000000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ444444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-222-2-2-1-1-1-11111000000000000000000000000000000
χ4544444-4-444444-4-4-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-2221111-1-1-1-1000000000000000000000000000000
χ4644444-4-4-4-4444-4-4-4-4444-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4744-4-440000-44-400000000044-444-4-4-4000040000-440000-400000000000000000000000000000000000000000000
χ4844-4-440000-44-40000000004-2-44-2-4220000-200−2i32i32-2−2i32i3−2i32i3200000000000000000000000000000000000000000000
χ4944-4-440000-44-40000000004-2-44-2-4220000-2002i3−2i32-22i3−2i32i3−2i3200000000000000000000000000000000000000000000
χ5044-4-440000-44-4000000000-242-242-4-423−23−2323-200002-20000200000023−23−23230000000000000000000000000000000000
χ5144-4-440000-44-4000000000-242-242-4-4−232323−23-200002-200002000000−232323−230000000000000000000000000000000000
χ5244-4-440000-44-4000000000-2-22-2-222223−23−2323100−2i32i3-11i3−i3i3−i3-1000000−333−33i−3i3i−3i000000000000000000000000000000
χ5344-4-440000-44-4000000000-2-22-2-222223−23−23231002i3−2i3-11−i3i3−i3i3-1000000−333−3−3i3i−3i3i000000000000000000000000000000
χ5444-4-440000-44-4000000000-2-22-2-2222−232323−23100−2i32i3-11i3−i3i3−i3-10000003−3−33−3i3i−3i3i000000000000000000000000000000
χ5544-4-440000-44-4000000000-2-22-2-2222−232323−231002i3−2i3-11−i3i3−i3i3-10000003−3−333i−3i3i−3i000000000000000000000000000000
χ564-44-444i−4i004-4-44i4i−4i−4i000004-24-42-4-220000-20000-22000024i−4i00−2i2i0000−2i−2i2i2i000000000000000000000000000000
χ574-44-444i−4i004-4-44i4i−4i−4i00000-2-2-2222-222323−23−231−2i32i3001-1i3i3−i3−i3-1−2i2i00−2i2i−3−333ii−i−i000000000000000000000000000000
χ584-44-444i−4i004-4-44i4i−4i−4i00000-2-2-2222-22−23−23232312i3−2i3001-1−i3−i3i3i3-1−2i2i00−2i2i33−3−3ii−i−i000000000000000000000000000000
χ594-44-44−4i4i004-4-4−4i−4i4i4i000004-24-42-4-220000-20000-2200002−4i4i002i−2i00002i2i−2i−2i000000000000000000000000000000
χ604-44-44−4i4i004-4-4−4i−4i4i4i00000-2-2-2222-222323−23−2312i3−2i3001-1−i3−i3i3i3-12i−2i002i−2i−3−333−i−iii000000000000000000000000000000
χ614-44-44−4i4i004-4-4−4i−4i4i4i00000-2-2-2222-22−23−2323231−2i32i3001-1i3i3−i3−i3-12i−2i002i−2i33−3−3−i−iii000000000000000000000000000000
χ624-4-444004-4-4-4400000004-44-2-4-4242-24-44-4-20000220000-200-2200-22-220000000000000000000000000000000000
χ634-4-444004-4-4-4400000004-4-2422-4-2-44-22-22-20000220000-2004-400-22-220000000000000000000000000000000000
χ644-4-444004-4-4-4400000004-4-2-2222-22-2-22-2210000-1-13-3-33100-22001-11-1-333-3000000000000000000000000000000
χ654-4-444004-4-4-4400000004-4-2-2222-22-2-22-2210000-1-1-333-3100-22001-11-13-3-33000000000000000000000000000000
χ664-4-44400-44-4-440000000-444-2-4-4242-2-44-44-20000220000-2002-2002-22-20000000000000000000000000000000000
χ674-4-44400-44-4-440000000-44-2422-4-2-442-22-2-20000220000-200-44002-22-20000000000000000000000000000000000
χ684-4-44400-44-4-440000000-44-2-2222-22-22-22-210000-1-13-3-331002-200-11-113-3-33000000000000000000000000000000
χ694-4-44400-44-4-440000000-44-2-2222-22-22-22-210000-1-1-333-31002-200-11-11-333-3000000000000000000000000000000
χ706666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000002222-1-1-1-10000-1-1-1-100000000000000
χ716666-36666-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-211110000111100000000000000
χ726666-366-6-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000−i3i3−i3i30000−i3i3−i3i300000000000000
χ736666-366-6-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000i3−i3i3−i30000i3−i3i3−i300000000000000
χ746666-3-6-666-3-3-33333-633-3-30000000000000000000000000000000000000022-2-2-1-1-1-10000111100000000000000
χ756666-3-6-666-3-3-33333-633-3-300000000000000000000000000000000000000-2-22211110000-1-1-1-100000000000000
χ766666-3-6-6-6-6-3-3-333336-3-333000000000000000000000000000000000000000000−i3i3−i3i30000i3−i3i3−i300000000000000
χ776666-3-6-6-6-6-3-3-333336-3-333000000000000000000000000000000000000000000i3−i3i3−i30000−i3i3−i3i300000000000000
χ786-6-66-3006-633-3−3i33i3−3i33i30−3i33i3-3300000000000000000000000000000000000000002-2−i3i3i3−i30000-1-11100000000000000
χ796-6-66-3006-633-3−3i33i3−3i33i30−3i33i3-330000000000000000000000000000000000000000-22i3−i3−i3i3000011-1-100000000000000
χ806-6-66-3006-633-33i3−3i33i3−3i303i3−3i3-3300000000000000000000000000000000000000002-2i3−i3−i3i30000-1-11100000000000000
χ816-6-66-3006-633-33i3−3i33i3−3i303i3−3i3-330000000000000000000000000000000000000000-22−i3i3i3−i3000011-1-100000000000000
χ826-6-66-300-6633-3−3i33i3−3i33i303i3−3i33-3000000000000000000000000000000000000002-200-1-1110000−i3i3i3−i300000000000000
χ836-6-66-300-6633-3−3i33i3−3i33i303i3−3i33-300000000000000000000000000000000000000-220011-1-10000i3−i3−i3i300000000000000
χ846-6-66-300-6633-33i3−3i33i3−3i30−3i33i33-3000000000000000000000000000000000000002-200-1-1110000i3−i3−i3i300000000000000
χ856-6-66-300-6633-33i3−3i33i3−3i30−3i33i33-300000000000000000000000000000000000000-220011-1-10000−i3i3i3−i300000000000000
χ861212-12-12-600006-6663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-12-600006-66−636363−630000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-1212-12-612i−12i00-666−6i−6i6i6i0000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-1212-12-6−12i12i00-6666i6i−6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000

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