Finite Group Databasebeta

← Group #13152061

Character table — Group #13152061

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12222222366626666663366666666666666366666666666666666666666224444442244444466661212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-11-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-11-1-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-11111-111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-111-1-111-1-11111-1-1-1-1-111-1
χ6111111-1-11111-111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-111-1-11111-11-1-1-1-11111-1-111-1-1-1-1-1-111111-1-11
χ7111111-1-11111-111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11-11-11-1-111-1-1111111-1-1-1-11-1-11
χ8111111-1-11111-111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1111-1-1-111-1-111-1-1-1-11111-111-1
χ91111-1-1111111-1-1-111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1111-1-1-11-1-111111-1-1-1-111-1-111-1-1-11-11
χ101111-1-1111111-1-1-111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-11-11111-1-1-1-1-1-111-1-1111-11-1
χ111111-1-1111111-1-1-111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1111111-111-1-11-1-1-1-1-1-1111111-1-111-1-11-11-1
χ121111-1-1111111-1-1-111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-11111-1-111-1-111-11-11
χ131111-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1111-111-1-1-1-11111-1-1-1-11111-1-1
χ141111-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-11-1111-1-1-1-111-1-11111-1-1-1-111
χ151111-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-111-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-11-11-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ161111-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-1-1-1-1-11111-1-1-1-11111-1-111-1-1
χ1722222222222222222222-122222-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12200220020000200-1-1-1-1-1-1-1-1000000000000
χ1822222222222222222222-122222-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-200-20000-20011111111000000000000
χ192222222222222222222-12-1-1-1-1-1222222-1-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002200220002002000000000-1-1-1-1-1-1-1-10000
χ202222222222222222222-12-1-1-1-1-1222222-1-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-2000-200-2000000000111111110000
χ21222222-2-22222-222-2-2-2-22-122222-1-1111122-1-1-2-2-2-2-1-111-1-1-1-1-1-1-11111111122002200-20000-200-1-111-1-111000000000000
χ22222222-2-22222-222-2-2-2-22-122222-1-1111122-1-1-2-2-2-2-1-111-1-1-1-1-1-1-111111111-2-200-2-2002000020011-1-111-1-1000000000000
χ23222222-2-22222-222-2-2-2-2-12-1-1-1-1-122-2-2-2-2-1-12-1111122-2-2-1-1-1-1-1-1-111111111002200-2-2000200-2000000000-1-1-1-111110000
χ24222222-2-22222-222-2-2-2-2-12-1-1-1-1-122-2-2-2-2-1-12-1111122-2-2-1-1-1-1-1-1-11111111100-2-20022000-20020000000001111-1-1-1-10000
χ252222-2-2222222-2-2-222-2-22-12-2-2-2-2-1-1-1-1-1-122-1-122-2-21111-1-1-11111-1-1-1-111112200-2-20020000-200-1-1-1-11111000000000000
χ262222-2-2222222-2-2-222-2-22-12-2-2-2-2-1-1-1-1-1-122-1-122-2-21111-1-1-11111-1-1-1-11111-2-2002200-200002001111-1-1-1-1000000000000
χ272222-2-2222222-2-2-222-2-2-12-11111222222-1-12-1-1-111-2-2-2-2-1-1-11111-1-1-1-1111100220022000-200-2000000000-1-111-1-1110000
χ282222-2-2222222-2-2-222-2-2-12-11111222222-1-12-1-1-111-2-2-2-2-1-1-11111-1-1-1-1111100-2-200-2-2000200200000000011-1-111-1-10000
χ292222-2-2-2-222222-2-2-2-2222-12-2-2-2-2-1-1111122-1-1-2-22211-1-1-1-1-111111111-1-1-1-12200-2-200-20000200-1-11111-1-1000000000000
χ302222-2-2-2-222222-2-2-2-2222-12-2-2-2-2-1-1111122-1-1-2-22211-1-1-1-1-111111111-1-1-1-1-2-200220020000-20011-1-1-1-111000000000000
χ312222-2-2-2-222222-2-2-2-222-12-1111122-2-2-2-2-1-12-111-1-1-2-222-1-1-111111111-1-1-1-1002200-2-2000-2002000000000-1-11111-1-10000
χ322222-2-2-2-222222-2-2-2-222-12-1111122-2-2-2-2-1-12-111-1-1-2-222-1-1-111111111-1-1-1-100-2-20022000200-200000000011-1-1-1-1110000
χ3322-2-2002-222-2-20002-20022200002-222-2-2-2-2-222-20000002-2-2000022-2-20000002i−2i002i−2i00000000000000002i−2i002i−2i000000
χ3422-2-2002-222-2-20002-20022200002-222-2-2-2-2-222-20000002-2-2000022-2-2000000−2i2i00−2i2i0000000000000000−2i2i00−2i2i000000
χ3522-2-2002-222-2-20002-200-12-1−i3−i3i3i32-222-2-211-2-1-11−i3i30000-111−i3−i3i3i3-1-111−i3−i3i3i3002i−2i002i−2i0000000000000000−ii3−3−ii3−30000
χ3622-2-2002-222-2-20002-200-12-1−i3−i3i3i32-222-2-211-2-1-11−i3i30000-111−i3−i3i3i3-1-111−i3−i3i3i300−2i2i00−2i2i0000000000000000i−i−33i−i−330000
χ3722-2-2002-222-2-20002-200-12-1i3i3−i3−i32-222-2-211-2-1-11i3−i30000-111i3i3−i3−i3-1-111i3i3−i3−i3002i−2i002i−2i0000000000000000−ii−33−ii−330000
χ3822-2-2002-222-2-20002-200-12-1i3i3−i3−i32-222-2-211-2-1-11i3−i30000-111i3i3−i3−i3-1-111i3i3−i3−i300−2i2i00−2i2i0000000000000000i−i3−3i−i3−30000
χ3922-2-200-2222-2-2000-220022200002-2-2-222-2-2-22-220000002-2-20000-2-2220000002i−2i00−2i2i00000000000000002i−2i00−2i2i000000
χ4022-2-200-2222-2-2000-220022200002-2-2-222-2-2-22-220000002-2-20000-2-222000000−2i2i002i−2i0000000000000000−2i2i002i−2i000000
χ4122-2-200-2222-2-2000-2200-12-1−i3−i3i3i32-2-2-22211-2-11-1i3−i30000-111−i3−i3i3i311-1-1i3i3−i3−i3002i−2i00−2i2i0000000000000000−ii3−3i−i−330000
χ4222-2-200-2222-2-2000-2200-12-1−i3−i3i3i32-2-2-22211-2-11-1i3−i30000-111−i3−i3i3i311-1-1i3i3−i3−i300−2i2i002i−2i0000000000000000i−i−33−ii3−30000
χ4322-2-200-2222-2-2000-2200-12-1i3i3−i3−i32-2-2-22211-2-11-1−i3i30000-111i3i3−i3−i311-1-1−i3−i3i3i3002i−2i00−2i2i0000000000000000−ii−33i−i3−30000
χ4422-2-200-2222-2-2000-2200-12-1i3i3−i3−i32-2-2-22211-2-11-1−i3i30000-111i3i3−i3−i311-1-1−i3−i3i3i300−2i2i002i−2i0000000000000000i−i3−3−ii−330000
χ452-2-222-2002-22-202-2000022-22-22-2-2-200002-22200002-200-22-22-22-2000000002-2002-200000000002-2002-200000000000000
χ462-2-222-2002-22-202-2000022-22-22-2-2-200002-22200002-200-22-22-22-200000000-2200-220000000000-2200-2200000000000000
χ472-2-222-2002-22-202-200002-1-22-22-211−i3i3−i3i32-2-1-10000-11−i3i31-11-11-11−i3i3−i3i3−i3i3−i3i32-2002-20000000000-11−i3i3-11−i3i3000000000000
χ482-2-222-2002-22-202-200002-1-22-22-211−i3i3−i3i32-2-1-10000-11−i3i31-11-11-11−i3i3−i3i3−i3i3−i3i3-2200-2200000000001-1i3−i31-1i3−i3000000000000
χ492-2-222-2002-22-202-200002-1-22-22-211i3−i3i3−i32-2-1-10000-11i3−i31-11-11-11i3−i3i3−i3i3−i3i3−i32-2002-20000000000-11i3−i3-11i3−i3000000000000
χ502-2-222-2002-22-202-200002-1-22-22-211i3−i3i3−i32-2-1-10000-11i3−i31-11-11-11i3−i3i3−i3i3−i3i3−i3-2200-2200000000001-1−i3i31-1−i3i3000000000000
χ512-2-22-22002-22-20-22000022-2-22-22-2-200002-2220000-2200-22-2-22-22000000002-200-2200000000002-200-2200000000000000
χ522-2-22-22002-22-20-22000022-2-22-22-2-200002-2220000-2200-22-2-22-2200000000-22002-20000000000-22002-200000000000000
χ532-2-22-22002-22-20-2200002-1-2-22-2211−i3i3−i3i32-2-1-100001-1i3−i31-111-11-1−i3i3−i3i3i3−i3i3−i32-200-220000000000-11−i3i31-1i3−i3000000000000
χ542-2-22-22002-22-20-2200002-1-2-22-2211−i3i3−i3i32-2-1-100001-1i3−i31-111-11-1−i3i3−i3i3i3−i3i3−i3-22002-200000000001-1i3−i3-11−i3i3000000000000
χ552-2-22-22002-22-20-2200002-1-2-22-2211i3−i3i3−i32-2-1-100001-1−i3i31-111-11-1i3−i3i3−i3−i3i3−i3i32-200-220000000000-11i3−i31-1−i3i3000000000000
χ562-2-22-22002-22-20-2200002-1-2-22-2211i3−i3i3−i32-2-1-100001-1−i3i31-111-11-1i3−i3i3−i3−i3i3−i3i3-22002-200000000001-1−i3i3-11i3−i3000000000000
χ574444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2111111111111111000000000000000000000000000000000000
χ58444444-4-44444-444-4-4-4-4-2-2-2-2-2-2-2-2-22222-2-2-212222-2-2221111111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ594444-4-4444444-4-4-444-4-4-2-2-22222-2-2-2-2-2-2-2-2-21-2-2222222111-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ604444-4-4-4-444444-4-4-4-444-2-2-22222-2-22222-2-2-2122-2-222-2-2111-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ6144-4-4004-444-4-40004-4004-240000-22-2-222-4-42-24-4000000-2220000-2-2220000000000000000000000000000000000000000
χ6244-4-4004-444-4-40004-400-2-2-2−2i3−2i32i32i3-22-2-2222221-22−2i32i300001-1-1i3i3−i3−i311-1-1i3i3−i3−i3000000000000000000000000000000000000
χ6344-4-4004-444-4-40004-400-2-2-22i32i3−2i3−2i3-22-2-2222221-222i3−2i300001-1-1−i3−i3i3i311-1-1−i3−i3i3i3000000000000000000000000000000000000
χ6444-4-400-4444-4-4000-44004-240000-2222-2-2-4-42-2-44000000-222000022-2-20000000000000000000000000000000000000000
χ6544-4-400-4444-4-4000-4400-2-2-2−2i3−2i32i32i3-2222-2-222212-22i3−2i300001-1-1i3i3−i3−i3-1-111−i3−i3i3i3000000000000000000000000000000000000
χ6644-4-400-4444-4-4000-4400-2-2-22i32i3−2i3−2i3-2222-2-222212-2−2i32i300001-1-1−i3−i3i3i3-1-111i3i3−i3−i3000000000000000000000000000000000000
χ674-44-400004-4-44000000044-40000-440000-44-4400000000-4-44000000000000000000000000000000000000000000000000
χ684-44-400004-4-4400000004-2-400002-2−2i32i32i3−2i3-442-20000000022-20000−2i32i32i3−2i30000000000000000000000000000000000000000
χ694-44-400004-4-4400000004-2-400002-22i3−2i3−2i32i3-442-20000000022-200002i3−2i3−2i32i30000000000000000000000000000000000000000
χ704-44-400004-4-440000000-242−2i32i32i3−2i3-4400002-2-4-20000000022-2−2i32i32i3−2i300000000000000000000000000000000000000000000
χ714-44-400004-4-440000000-2422i3−2i3−2i32i3-4400002-2-4-20000000022-22i3−2i3−2i32i300000000000000000000000000000000000000000000
χ724-44-400004-4-440000000-2-22−2i32i32i3−2i32-2−2i32i32i3−2i32-22100000000-1-11i3−i3−i3i3i3−i3−i3i3-333-3000000000000000000000000000000000000
χ734-44-400004-4-440000000-2-22−2i32i32i3−2i32-22i3−2i3−2i32i32-22100000000-1-11i3−i3−i3i3−i3i3i3−i33-3-33000000000000000000000000000000000000
χ744-44-400004-4-440000000-2-222i3−2i3−2i32i32-2−2i32i32i3−2i32-22100000000-1-11−i3i3i3−i3i3−i3−i3i33-3-33000000000000000000000000000000000000
χ754-44-400004-4-440000000-2-222i3−2i3−2i32i32-22i3−2i3−2i32i32-22100000000-1-11−i3i3i3−i3−i3i3i3−i3-333-3000000000000000000000000000000000000
χ764-4-444-4004-44-404-40000-242-22-22-4-40000-224-200004-4002-22-22-2200000000000000000000000000000000000000000000
χ774-4-444-4004-44-404-40000-2-22-22-2222−2i32i3−2i32i3-22-210000-22−2i32i3-11-11-11-1i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ784-4-444-4004-44-404-40000-2-22-22-22222i3−2i32i3−2i3-22-210000-222i3−2i3-11-11-11-1−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ794-4-44-44004-44-40-440000-2422-22-2-4-40000-224-20000-44002-222-22-200000000000000000000000000000000000000000000
χ804-4-44-44004-44-40-440000-2-222-22-222−2i32i3−2i32i3-22-2100002-22i3−2i3-11-1-11-11i3−i3i3−i3−i3i3−i3i3000000000000000000000000000000000000
χ814-4-44-44004-44-40-440000-2-222-22-2222i3−2i32i3−2i3-22-2100002-2−2i32i3-11-1-11-11−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000
χ8266666666-3-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000022020020000000000000000-1-1-1-1
χ8366666666-3-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000-2-20-200-200000000000000001111
χ84666666-6-6-3-3-3-3-6-3-3333300000000000000000000000000000000000000000000000002-20-20020000000000000000-111-1
χ85666666-6-6-3-3-3-3-6-3-333330000000000000000000000000000000000000000000000000-220200-200000000000000001-1-11
χ866666-6-666-3-3-3-3-633-3-3330000000000000000000000000000000000000000000000000220-200-20000000000000000-11-11
χ876666-6-666-3-3-3-3-633-3-3330000000000000000000000000000000000000000000000000-2-20200200000000000000001-11-1
χ886666-6-6-6-6-3-3-3-363333-3-300000000000000000000000000000000000000000000000002-20200-20000000000000000-1-111
χ896666-6-6-6-6-3-3-3-363333-3-30000000000000000000000000000000000000000000000000-220-2002000000000000000011-1-1
χ901212-12-120012-12-6-666000-66000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-1200-1212-6-6660006-6000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-120000-666-600000−6i36i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-120000-666-6000006i3−6i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-121212-1200-66-660-6600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-121200-66-6606-600000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).