Finite Group Databasebeta

← Group #13141066

Character table — Group #13141066

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order12442346121224612336612121212612888836666612121212121244448888882424242466661212121224888812121212242424242424242424246122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ51111111111-1-11111111111-1-1111111-1-1111-1-111111111111111111-11-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ61111111111-1-11111111111-1-1111111-1-1111-1-1111-1-1-1-111-1-1-1-11111-11-1-1-11-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-1-1-1-1-111-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-11111-1-11111-1-11111-1-1-1-111-1-1
χ81111111111-1-11111111111-1-1-1-1-1-111-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-11-1-1-11-1-1-1-11111-1-1-1-1-1-111111111-1-111
χ911-1-1-1111-1-11-1-111111-1-1-1-11-1ii−i−i1-111-111-1-1-1-11ii−i−ii−i11-1-1ii−i−i1-111-11-1-11-1i−ii−iii−i−ii−iii−i−i11-1-11-1i−i
χ1011-1-1-1111-1-11-1-111111-1-1-1-11-1ii−i−i1-111-111-1-1-1-11−i−iiii−i-1-111ii−i−i1-111-11-1-1-11i−i−ii−i−iiii−iii−i−i-1-111-11−ii
χ1111-1-1-1111-1-11-1-111111-1-1-1-11-1−i−iii1-111-111-1-1-1-11ii−i−i−ii-1-111−i−iii1-111-11-1-1-11−iii−iii−i−i−ii−i−iii-1-111-11i−i
χ1211-1-1-1111-1-11-1-111111-1-1-1-11-1−i−iii1-111-111-1-1-1-11−i−iii−ii11-1-1−i−iii1-111-11-1-11-1−ii−ii−i−iii−ii−i−iii11-1-11-1−ii
χ1311-1-1-1111-1-1-11-111111-1-1-1-1-11ii−i−i1-1-1-1-11111-1-11ii−i−ii−i11-1-1ii−i−i-1-1-1-11111-11−ii−iiii−i−ii−i−i−iii11-1-1-11−ii
χ1411-1-1-1111-1-1-11-111111-1-1-1-1-11ii−i−i1-1-1-1-11111-1-11−i−iiii−i-1-111ii−i−i-1-1-1-111111-1−iii−i−i−iiii−i−i−iii-1-1111-1i−i
χ1511-1-1-1111-1-1-11-111111-1-1-1-1-11−i−iii1-1-1-1-11111-1-11ii−i−i−ii-1-111−i−iii-1-1-1-111111-1i−i−iiii−i−i−iiii−i−i-1-1111-1−ii
χ1611-1-1-1111-1-1-11-111111-1-1-1-1-11−i−iii1-1-1-1-11111-1-11−i−iii−ii11-1-1−i−iii-1-1-1-11111-11i−ii−i−i−iii−iiii−i−i11-1-1-11i−i
χ17222222222222222-12-1-1-122220000-1222-1-1222-1-1-100000022220000-1-1-1-1-1-1-1-12200000000000000-1-1-1-1-1-100
χ18222222222222222-12-1-1-122220000-1222-1-1222-1-1-1000000-2-2-2-20000-1-1-1-1-1-1-1-1-2-20000000000000011111100
χ1922222222222222-12-1222-1-1222222-1-1-1-12-1-1-1-1-1-120000220000-1-1-1-12-1-1-12-1-1-10022000000-1-1-1-1-1-100000000
χ2022222222222222-12-1222-1-122-2-2-2-2-1-1-1-12-1-1-1-1-1-120000-2-2000011112-1-1-12-1-1-100-2-200000011111100000000
χ212222222222-2-2222-12-1-1-122-2-20000-12-2-2-1-12-2-2-1-1-1000000222200001-1111-111-2-200000000000000-1-1-1-11100
χ222222222222-2-2222-12-1-1-122-2-20000-12-2-2-1-12-2-2-1-1-1000000-2-2-2-200001-1111-11122000000000000001111-1-100
χ232222222222-2-222-12-1222-1-1-2-22222-1-1112-1-111-1-120000220000-1-1-1-1-2-111-2-11100-2-2000000-1-1111100000000
χ242222222222-2-222-12-1222-1-1-2-2-2-2-2-2-1-1112-1-111-1-120000-2-200001111-2-111-2-111002200000011-1-1-1-100000000
χ252222-22-222200-2-2222222220022222-200-22-20022-20000-2-2000022220-2000-2000000000000-2-2000000000000
χ262222-22-222200-2-22222222200-2-2-2-22-200-22-20022-20000220000-2-2-2-20-2000-200000000000022000000000000
χ272222-22-222200-2-2-12-1222-1-1002222-11−i3i3-2-11−i3i3-1-1-20000-2-20000-1-1-1-101−i3i301−i3i3000000000011−i3i3−i3i300000000
χ282222-22-222200-2-2-12-1222-1-1002222-11i3−i3-2-11i3−i3-1-1-20000-2-20000-1-1-1-101i3−i301i3−i3000000000011i3−i3i3−i300000000
χ292222-22-222200-2-2-12-1222-1-100-2-2-2-2-11−i3i3-2-11−i3i3-1-1-20000220000111101−i3i301−i3i30000000000-1-1i3−i3i3−i300000000
χ302222-22-222200-2-2-12-1222-1-100-2-2-2-2-11i3−i3-2-11i3−i3-1-1-20000220000111101i3−i301i3−i30000000000-1-1−i3i3−i3i300000000
χ3122-2-222-22-2-2002-22222-2-2-2-2002i2i−2i−2i220022-200-2-2-20000−2i2i00002i2i−2i−2i02000-2000000000000−2i2i000000000000
χ3222-2-222-22-2-2002-22222-2-2-2-200−2i−2i2i2i220022-200-2-2-200002i−2i0000−2i−2i2i2i02000-20000000000002i−2i000000000000
χ3322-2-222-22-2-2002-2-12-12-2-211002i2i−2i−2i-1-1−i3i32-11i3−i311-20000−2i2i0000−i−iii0-1−i3i301i3−i30000000000i−i3−3−3300000000
χ3422-2-222-22-2-2002-2-12-12-2-211002i2i−2i−2i-1-1i3−i32-11−i3i311-20000−2i2i0000−i−iii0-1i3−i301−i3i30000000000i−i−333−300000000
χ3522-2-222-22-2-2002-2-12-12-2-21100−2i−2i2i2i-1-1−i3i32-11i3−i311-200002i−2i0000ii−i−i0-1−i3i301i3−i30000000000−ii−333−300000000
χ3622-2-222-22-2-2002-2-12-12-2-21100−2i−2i2i2i-1-1i3−i32-11−i3i311-200002i−2i0000ii−i−i0-1i3−i301−i3i30000000000−ii3−3−3300000000
χ3722-2-2-2222-2-22-2-222-12-111-2-22-20000-1-2221-12-2-211-100000022-2-20000-11-1-11-1112-200000000000000-1-111-1100
χ3822-2-2-2222-2-22-2-222-12-111-2-22-20000-1-2221-12-2-211-1000000-2-2220000-11-1-11-111-220000000000000011-1-11-100
χ3922-2-2-2222-2-22-2-22-12-12-2-2112-22i2i−2i−2i-11-1-1-2-1-11111200002i−2i0000−i−iii21-1-1-2-111002i−2i000000−ii−i−iii00000000
χ4022-2-2-2222-2-22-2-22-12-12-2-2112-2−2i−2i2i2i-11-1-1-2-1-1111120000−2i2i0000ii−i−i21-1-1-2-11100−2i2i000000i−iii−i−i00000000
χ4122-2-2-2222-2-2-22-222-12-111-2-2-220000-1-2-2-21-122211-100000022-2-200001111-1-1-1-1-2200000000000000-1-1111-100
χ4222-2-2-2222-2-2-22-222-12-111-2-2-220000-1-2-2-21-122211-1000000-2-22200001111-1-1-1-12-20000000000000011-1-1-1100
χ4322-2-2-2222-2-2-22-22-12-12-2-211-222i2i−2i−2i-1111-2-1-1-1-111200002i−2i0000−i−iii-21112-1-1-100−2i2i000000−iiii−i−i00000000
χ4422-2-2-2222-2-2-22-22-12-12-2-211-22−2i−2i2i2i-1111-2-1-1-1-11120000−2i2i0000ii−i−i-21112-1-1-1002i−2i000000i−i−i−iii00000000
χ452-22i−2i020-22i−2i000022-2-22i−2i2i−2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1320000-20002i−2i01+i−1−i1−i−1+i002−2−i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000001+i−1−i1−i−1+i0000002−2−i2i20000
χ462-22i−2i020-22i−2i000022-2-22i−2i2i−2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1320000-20002i−2i0−1−i1+i−1+i1−i00−22i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000−1−i1+i−1+i1−i000000−22i2−i20000
χ472-22i−2i020-22i−2i000022-2-22i−2i2i−2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1320000-20002i−2i01+i−1−i1−i−1+i00−22i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000001+i−1−i1−i−1+i000000−22i2−i20000
χ482-22i−2i020-22i−2i000022-2-22i−2i2i−2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1320000-20002i−2i0−1−i1+i−1+i1−i002−2−i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−1−i1+i−1+i1−i0000002−2−i2i20000
χ492-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2320000-2000−2i2i01−i−1+i1+i−1−i002−2i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000001−i−1+i1+i−1−i0000002−2i2−i20000
χ502-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2320000-2000−2i2i0−1+i1−i−1−i1+i00−22−i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000−1+i1−i−1−i1+i000000−22−i2i20000
χ512-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2320000-2000−2i2i01−i−1+i1+i−1−i00−22−i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000001−i−1+i1+i−1−i000000−22−i2i20000
χ522-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2320000-2000−2i2i0−1+i1−i−1−i1+i002−2i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−1+i1−i−1−i1+i0000002−2i2−i20000
χ5344444444444444-2-2-2-2-2-2-2-24400001-2-2-2-21-2-2-211-200000000000000-2111-2111000000000000000000000000
χ544444444444-4-444-2-2-2-2-2-2-2-2-4-400001-222-21-22211-20000000000000021-1-121-1-1000000000000000000000000
χ554444-44-444400-4-44-24-2-2-244000000-2-4002-2-400-2-220000000000000002000200000000000000000000000000
χ564444-44-444400-4-4-2-2-2-2-2-2-2-200000012−2i32i3212−2i32i3112000000000000000-1i3−i30-1i3−i3000000000000000000000000
χ574444-44-444400-4-4-2-2-2-2-2-2-2-2000000122i3−2i32122i3−2i3112000000000000000-1−i3i30-1−i3i3000000000000000000000000
χ5844-4-444-44-4-4004-44-24-222-4-4000000-2400-2-2-400222000000000000000-2000200000000000000000000000000
χ5944-4-444-44-4-4004-4-2-2-2-222220000001-2−2i32i3-2122i3−2i3-1-120000000000000001i3−i30-1−i3i3000000000000000000000000
χ6044-4-444-44-4-4004-4-2-2-2-222220000001-22i3−2i3-212−2i32i3-1-120000000000000001−i3i30-1i3−i3000000000000000000000000
χ6144-4-4-4444-4-44-4-44-2-2-2-222224-4000012-2-221-222-1-1-200000000000000-2-11121-1-1000000000000000000000000
χ6244-4-4-4444-4-4-44-44-2-2-2-22222-440000122221-2-2-2-1-1-2000000000000002-1-1-1-2111000000000000000000000000
χ634-44i−4i040-44i−4i00004-2-42−2i2i4i−4i000000-200002000−2i2i000000022−22−2i22i20000000000000000000000000000−22i2−i20000
χ644-44i−4i040-44i−4i00004-2-42−2i2i4i−4i000000-200002000−2i2i0000000−22222i2−2i200000000000000000000000000002−2−i2i20000
χ654-44i−4i040-44i−4i0000-242-44i−4i−2i2i004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13-200002000−2i2i00000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ664-44i−4i040-44i−4i0000-242-44i−4i−2i2i00−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13-200002000−2i2i000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ674-4−4i4i040-4−4i4i00004-2-422i−2i−4i4i000000-2000020002i−2i000000022−222i2−2i20000000000000000000000000000−22−i2i20000
χ684-4−4i4i040-4−4i4i00004-2-422i−2i−4i4i000000-2000020002i−2i0000000−2222−2i22i200000000000000000000000000002−2i2−i20000
χ694-4−4i4i040-4−4i4i0000-242-4−4i4i2i−2i00−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23-2000020002i−2i000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ704-4−4i4i040-4−4i4i0000-242-4−4i4i2i−2i004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23-2000020002i−2i00000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ7166666-36-3-3-366-3-300000000-3-300000000000000002222000000000000000000000022-1-1-1-1000000000000-1-1
χ7266666-36-3-3-366-3-300000000-3-30000000000000000-2-2-2-20000000000000000000000-2-2111100000000000011
χ7366666-36-3-3-3-6-6-3-30000000033000000000000000022220000000000000000000000-2-2-1-1-1-100000000000011
χ7466666-36-3-3-3-6-6-3-300000000330000000000000000-2-2-2-20000000000000000000000221111000000000000-1-1
χ7566-6-6-6-36-3336-63-300000000-3300000000000000002i2i−2i−2i00000000000000000000002i−2i−i−iii000000000000−ii
χ7666-6-6-6-36-3336-63-300000000-330000000000000000−2i−2i2i2i0000000000000000000000−2i2iii−i−i000000000000i−i
χ7766-6-6-6-36-333-663-3000000003-300000000000000002i2i−2i−2i0000000000000000000000−2i2i−i−iii000000000000i−i
χ7866-6-6-6-36-333-663-3000000003-30000000000000000−2i−2i2i2i00000000000000000000002i−2iii−i−i000000000000−ii
χ798-88i−8i080-88i−8i0000-4-444−4i4i−4i4i00000020000-20002i−2i00000000000000000000000000000000000000000000000
χ808-8−8i8i080-8−8i8i0000-4-4444i−4i4i−4i00000020000-2000−2i2i00000000000000000000000000000000000000000000000
χ8112121212-12-6-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-1212-6-12-66600-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212i−12i0-606−6i6i0000000000000000000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000−1−i1+i−1+i1−i00000000000000
χ8412-1212i−12i0-606−6i6i000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000000000001+i−1−i1−i−1+i00000000000000
χ8512-12−12i12i0-6066i−6i0000000000000000000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000−1+i1−i−1−i1+i00000000000000
χ8612-12−12i12i0-6066i−6i000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000000000001−i−1+i1+i−1−i00000000000000

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