Finite Group Databasebeta

← Group #13139946

Character table — Group #13139946

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order122222344666666641212121233666666121212123666666666661212121212121212121212121212444488881212121212121212242424242424242424661212
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
χ51111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ61111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111
χ71111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ81111-1-11111-1-1-1-111-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ92222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ12222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ132222222-2-22222222-2-2-2-2-222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ142222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-2111111111100000000000000000000000000−i3i3−i3i3
χ152222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-2111111111100000000000000000000000000i3−i3i3−i3
χ162222222-2-22222222-2-2-2-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−333−3−3000000
χ172222222-2-22222222-2-2-2-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−333−3−333000000
χ182222-2-22222-2-2-2-222-222-2-22-122-12-1-12222-1-2-211-1-11111-1-1-1-2-211-1-1-1-111110000000000000000000000002-2-1-111
χ192222-2-22222-2-2-2-222-222-2-22-122-12-1-12222-1-2-211-1-11111-1-1-1-2-211-1-1-1-11111000000000000000000000000-2211-1-1
χ202222-2-22222-2-2-2-222-222-2-2-12-1-12-122-1-1-1-1-111-2-2-1-11111-12211-2-2-1-1-1-11111000022-2-200000000-1-1-1-11111000000
χ212222-2-22222-2-2-2-222-222-2-2-12-1-12-122-1-1-1-1-111-2-2-1-11111-12211-2-2-1-1-1-111110000-2-222000000001111-1-1-1-1000000
χ222222-2-22-2-22-2-2-2-2222-2-22222222222-2-2-2-22-2-2-2-222-2-2-2-22-2-22222-2-2-2-22222000000000000000000000000000000
χ232222-2-22-2-22-2-2-2-2222-2-2222-122-12-1-1-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ242222-2-22-2-22-2-2-2-2222-2-2222-122-12-1-1-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ252222-2-22-2-22-2-2-2-2222-2-222-12-1-12-1221111-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-1000000000000000033−3−3−3−333000000
χ262222-2-22-2-22-2-2-2-2222-2-222-12-1-12-1221111-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-10000000000000000−3−33333−3−3000000
χ2722-2-20022-2-200002-202-20022-2-2-222-222-2-220000-2-2000022-2000022-2-20000002i−2i000000002i2i−2i−2i00000000000000
χ2822-2-20022-2-200002-202-20022-2-2-222-222-2-220000-2-2000022-2000022-2-2000000−2i2i00000000−2i−2i2i2i00000000000000
χ2922-2-2002-22-200002-20-220022-2-2-222-2-2-22220000-2-200002-220000-2-22200002i−2i0000002i2i−2i−2i000000000000000000
χ3022-2-2002-22-200002-20-220022-2-2-222-2-2-22220000-2-200002-220000-2-2220000−2i2i000000−2i−2i2i2i000000000000000000
χ312-22-22-2200222-2-2-2-200000222-2-2-2-22000022-22-22-222-2-2-2000000000000000000−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2000000
χ322-22-22-2200222-2-2-2-200000222-2-2-2-22000022-22-22-222-2-2-2000000000000000000i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2000000
χ332-22-22-2200222-2-2-2-200000-12-11-21-223−33−3-1-112-2-11-1-1111003−3003−33−333−3−30000−i2i2−i2i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ342-22-22-2200222-2-2-2-200000-12-11-21-223−33−3-1-112-2-11-1-1111003−3003−33−333−3−30000i2−i2i2−i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ352-22-22-2200222-2-2-2-200000-12-11-21-22−33−33-1-112-2-11-1-111100−3300−33−33−3−3330000−i2i2−i2i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ362-22-22-2200222-2-2-2-200000-12-11-21-22−33−33-1-112-2-11-1-111100−3300−33−33−3−3330000i2−i2i2−i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ372-22-2-222002-2-222-2-200000222-2-2-2-2200002-22-222-2-2-222-2000000000000000000−i2i2i2−i200000000−i2i2−i2i2i2−i2i2−i2000000
χ382-22-2-222002-2-222-2-200000222-2-2-2-2200002-22-222-2-2-222-2000000000000000000i2−i2−i2i200000000i2−i2i2−i2−i2i2−i2i2000000
χ392-22-2-222002-2-222-2-200000-12-11-21-223−33−3-11-1-22-1111-1-1100−33003−33−3−3−3330000−i2i2i2−i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ402-22-2-222002-2-222-2-200000-12-11-21-223−33−3-11-1-22-1111-1-1100−33003−33−3−3−3330000i2−i2−i2i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ412-22-2-222002-2-222-2-200000-12-11-21-22−33−33-11-1-22-1111-1-11003−300−33−3333−3−30000−i2i2i2−i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ422-22-2-222002-2-222-2-200000-12-11-21-22−33−33-11-1-22-1111-1-11003−300−33−3333−3−30000i2−i2−i2i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ444444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ454444-4-44444-4-4-4-444-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000
χ464444-4-44-4-44-4-4-4-4444-4-444-2-2-2-2-2-2-2-222221222211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000
χ4744-4-40044-4-400004-404-4004-2-4-424-2244-4-4-20000220000-2-220000-2-2220000000000000000000000000000000000
χ4844-4-40044-4-400004-404-400-2422-4-24-4-2-222-20000220000-24-40000-2-2220000000000000000000000000000000000
χ4944-4-40044-4-400004-404-400-2-2222-2-22-2-22210000-1-13-33-31-22000011-1-13-33-3000000000000000000000000000000
χ5044-4-40044-4-400004-404-400-2-2222-2-22-2-22210000-1-1-33-331-22000011-1-1-33-33000000000000000000000000000000
χ5144-4-4004-44-400004-40-44004-2-4-424-22-4-444-20000220000-22-2000022-2-20000000000000000000000000000000000
χ5244-4-4004-44-400004-40-4400-2422-4-24-422-2-2-20000220000-2-44000022-2-20000000000000000000000000000000000
χ5344-4-4004-44-400004-40-4400-2-2222-2-2222-2-210000-1-13-33-312-20000-1-111-33-33000000000000000000000000000000
χ5444-4-4004-44-400004-40-4400-2-2222-2-2222-2-210000-1-1-33-3312-20000-1-1113-33-3000000000000000000000000000000
χ554-44-44-4400444-4-4-4-4000004-24-42-42-20000-24-4-22-22-2-222200000000000000000000000000000000000000000000
χ564-44-44-4400444-4-4-4-400000-2-2-22222-223−2323−231-22-221-111-1-1-10023−2300−33−33−3−333000000000000000000000000000000
χ574-44-44-4400444-4-4-4-400000-2-2-22222-2−2323−23231-22-221-111-1-1-100−2323003−33−333−3−3000000000000000000000000000000
χ584-44-4-444004-4-444-4-4000004-24-42-42-20000-2-442-2-2222-2-2200000000000000000000000000000000000000000000
χ594-44-4-444004-4-444-4-400000-2-2-22222-223−2323−2312-22-21-1-1-111-100−232300−33−3333−3−3000000000000000000000000000000
χ604-44-4-444004-4-444-4-400000-2-2-22222-2−2323−232312-22-21-1-1-111-10023−23003−33−3−3−333000000000000000000000000000000
χ614-4-4400400-40000-440000044-444-4-4-4000040000-440000-400000000000000000000000000000000000000000000
χ624-4-4400400-40000-44000004-2-44-2-4220000-200002-200002000023−23000023−23−2323000000000000000000000000000000
χ634-4-4400400-40000-44000004-2-44-2-4220000-200002-2000020000−23230000−232323−23000000000000000000000000000000
χ644-4-4400400-40000-4400000-242-242-4-423−23−2323-200002-20000200000023−23−23230000000000000000000000000000000000
χ654-4-4400400-40000-4400000-242-242-4-4−232323−23-200002-200002000000−232323−230000000000000000000000000000000000
χ664-4-4400400-40000-4400000-2-22-2-222223−23−232310000-113-3-33-10000−2323−333−33−3−33000000000000000000000000000000
χ674-4-4400400-40000-4400000-2-22-2-222223−23−232310000-11-333-3-1000023−23−333−3−333−3000000000000000000000000000000
χ684-4-4400400-40000-4400000-2-22-2-2222−232323−2310000-113-3-33-1000023−233−3−33−333−3000000000000000000000000000000
χ694-4-4400400-40000-4400000-2-22-2-2222−232323−2310000-11-333-3-10000−23233−3−333−3−33000000000000000000000000000000
χ70666666-366-3-3-3-3-3-3-36-3-3-3-30000000000000000000000000000000000000022220000-1-1-1-1-1-1-1-100000000000000
χ71666666-366-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-200001111111100000000000000
χ72666666-3-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i300000000000000
χ73666666-3-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i300000000000000
χ746666-6-6-366-33333-3-3-6-3-3330000000000000000000000000000000000000022-2-20000-1-1-1-1111100000000000000
χ756666-6-6-366-33333-3-3-6-3-33300000000000000000000000000000000000000-2-22200001111-1-1-1-100000000000000
χ766666-6-6-3-6-6-33333-3-3633-3-30000000000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i300000000000000
χ776666-6-6-3-6-6-33333-3-3633-3-30000000000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i300000000000000
χ7866-6-600-36-63−3i33i3−3i33i3-330-33−3i33i300000000000000000000000000000000000000002i−2i00003−3−33−i−iii00000000000000
χ7966-6-600-36-63−3i33i3−3i33i3-330-33−3i33i30000000000000000000000000000000000000000−2i2i0000−333−3ii−i−i00000000000000
χ8066-6-600-36-633i3−3i33i3−3i3-330-333i3−3i300000000000000000000000000000000000000002i−2i0000−333−3−i−iii00000000000000
χ8166-6-600-36-633i3−3i33i3−3i3-330-333i3−3i30000000000000000000000000000000000000000−2i2i00003−3−33ii−i−i00000000000000
χ8266-6-600-3-663−3i33i3−3i33i3-3303-33i3−3i3000000000000000000000000000000000000002i−2i000000−i−iii3−3−3300000000000000
χ8366-6-600-3-663−3i33i3−3i33i3-3303-33i3−3i300000000000000000000000000000000000000−2i2i000000ii−i−i−333−300000000000000
χ8466-6-600-3-6633i3−3i33i3−3i3-3303-3−3i33i3000000000000000000000000000000000000002i−2i000000−i−iii−333−300000000000000
χ8566-6-600-3-6633i3−3i33i3−3i3-3303-3−3i33i300000000000000000000000000000000000000−2i2i000000ii−i−i3−3−3300000000000000
χ8612-1212-1212-12-600-6-6-666660000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-12-1212-600-666-6-6660000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-121200-6006−6i36i36i3−6i36-60000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-121200-60066i3−6i3−6i36i36-60000000000000000000000000000000000000000000000000000000000000000000000000

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