Finite Group Databasebeta

← Group #13139168

Character table — Group #13139168

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order124423461212688123366121212122424888836661212121224242424444488888824242424612242424242424224466881212121212122424242424246122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111-11-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ511111111111-1-1111111111-1-1111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ611111111111-1-1111111111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-1111111
χ711111111111-1-1111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-111
χ811111111111-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-111-1-1
χ911-1-1-1111-1-1-1i−i11111-1-1-1-1i−iii−i−i1-11-111-1-1ii−i−iii−i−ii−i11-1-1ii−i−i-11i−iii−i−i11-1-111i−i-1-1ii−i−i11-1-1i−i1-1i−i
χ1011-1-1-1111-1-1-1i−i11111-1-1-1-1i−iii−i−i1-11-111-1-1ii−i−i−i−iiii−i-1-111ii−i−i-11i−iii−i−i1-1-1111−ii-1-1−i−iii-1-111i−i-11−ii
χ1111-1-1-1111-1-1-1i−i11111-1-1-1-1i−i−i−iii1-11-111-1-1ii−i−iii−i−i−ii-1-111−i−iii-11i−iii−i−i-111-1-1-1−ii11ii−i−i-1-111−ii1-1−ii
χ1211-1-1-1111-1-1-1i−i11111-1-1-1-1i−i−i−iii1-11-111-1-1ii−i−i−i−iii−ii11-1-1−i−iii-11i−iii−i−i-1-111-1-1i−i11−i−iii11-1-1−ii-11i−i
χ1311-1-1-1111-1-1-1−ii11111-1-1-1-1−iiii−i−i1-11-111-1-1−i−iiiii−i−ii−i11-1-1ii−i−i-11−ii−i−iii-1-111-1-1−ii11ii−i−i11-1-1i−i-11−ii
χ1411-1-1-1111-1-1-1−ii11111-1-1-1-1−iiii−i−i1-11-111-1-1−i−iii−i−iiii−i-1-111ii−i−i-11−ii−i−iii-111-1-1-1i−i11−i−iii-1-111i−i1-1i−i
χ1511-1-1-1111-1-1-1−ii11111-1-1-1-1−ii−i−iii1-11-111-1-1−i−iiiii−i−i−ii-1-111−i−iii-11−ii−i−iii1-1-1111i−i-1-1ii−i−i-1-111−ii-11i−i
χ1611-1-1-1111-1-1-1−ii11111-1-1-1-1−ii−i−iii1-11-111-1-1−i−iii−i−iii−ii11-1-1−i−iii-11−ii−i−iii11-1-111−ii-1-1−i−iii11-1-1−ii1-1−ii
χ17222222222222222-12-122-1-1222222-1-1-122-1-1-1-1-1-1-10000220000-1-1-1-1-1-122-1-1-1-12020-1-100-1-100000000-1-10000
χ18222222222222222-12-122-1-122-2-2-2-2-1-1-122-1-1-1-1-1-1-10000-2-200001111-1-122-1-1-1-1-20-2011001100000000110000
χ1922222222222222-12-12-1-122220000-12-1-1-12-1-1222222220000000000-1-1-1-1-1-1-1-10202000000-1-1-1-1000000-1-100
χ2022222222222222-12-12-1-122220000-12-1-1-12-1-12222-2-2-2-20000000000-1-1-1-1-1-1-1-10-20-200000011110000001100
χ2122222222222-2-222-12-122-1-1-2-22222-1-1-122-1-1-111110000220000-1-1-1-1-1-1-2-21111-20-2011001100000000-1-10000
χ2222222222222-2-222-12-122-1-1-2-2-2-2-2-2-1-1-122-1-1-111110000-2-200001111-1-1-2-211112020-1-100-1-100000000110000
χ2322222222222-2-22-12-12-1-122-2-20000-12-1-1-12-1-1-2-2-2-222220000000000-1-11111110-20-2000000-1-1-1-10000001100
χ2422222222222-2-22-12-12-1-122-2-20000-12-1-1-12-1-1-2-2-2-2-2-2-2-20000000000-1-111111102020000001111000000-1-100
χ252222-22-2222-200-2222222220022222-22-2-2-22200000000-2-200002222-2-2000000000000000000000000-2-20000
χ262222-22-2222-200-22222222200-2-2-2-22-22-2-2-22200000000220000-2-2-2-2-2-2000000000000000000000000220000
χ272222-22-2222-200-22-12-122-1-1002222-11-1-2-21-1-1−i3i3−i3i30000-2-20000-1-1-1-11100−i3i3−i3i30000−i3i300−i3i300000000110000
χ282222-22-2222-200-22-12-122-1-1002222-11-1-2-21-1-1i3−i3i3−i30000-2-20000-1-1-1-11100i3−i3i3−i30000i3−i300i3−i300000000110000
χ292222-22-2222-200-22-12-122-1-100-2-2-2-2-11-1-2-21-1-1−i3i3−i3i3000022000011111100−i3i3−i3i30000i3−i300i3−i300000000-1-10000
χ302222-22-2222-200-22-12-122-1-100-2-2-2-2-11-1-2-21-1-1i3−i3i3−i3000022000011111100i3−i3i3−i30000−i3i300−i3i300000000-1-10000
χ3122-2-222-22-2-2200-22222-2-2-2-2002i2i−2i−2i2222-2-2-2-200000000−2i2i00002i2i−2i−2i2-2000000000000000000000000−2i2i0000
χ3222-2-222-22-2-2200-22222-2-2-2-200−2i−2i2i2i2222-2-2-2-2000000002i−2i0000−2i−2i2i2i2-20000000000000000000000002i−2i0000
χ3322-2-222-22-2-2200-22-12-1-2-211002i2i−2i−2i-1-1-12-21113−3−330000−2i2i0000−i−iii-11003−3−330000−i3i300i3−i300000000i−i0000
χ3422-2-222-22-2-2200-22-12-1-2-211002i2i−2i−2i-1-1-12-2111−333−30000−2i2i0000−i−iii-1100−333−30000i3−i300−i3i300000000i−i0000
χ3522-2-222-22-2-2200-22-12-1-2-21100−2i−2i2i2i-1-1-12-21113−3−3300002i−2i0000ii−i−i-11003−3−330000i3−i300−i3i300000000−ii0000
χ3622-2-222-22-2-2200-22-12-1-2-21100−2i−2i2i2i-1-1-12-2111−333−300002i−2i0000ii−i−i-1100−333−30000−i3i300i3−i300000000−ii0000
χ3722-2-2-2222-2-2-22i−2i22-12-1-2-2112i−2i2i2i−2i−2i-11-1-22-111−i−iii00002i−2i0000−i−iii1-12i−2i−i−iii20-20-1-1001100000000−ii0000
χ3822-2-2-2222-2-2-22i−2i22-12-1-2-2112i−2i−2i−2i2i2i-11-1-22-111−i−iii0000−2i2i0000ii−i−i1-12i−2i−i−iii-20201100-1-100000000i−i0000
χ3922-2-2-2222-2-2-22i−2i2-12-1211-2-22i−2i0000-1-2-11-12112i2i−2i−2i2i2i−2i−2i00000000001-1−ii−i−iii020-2000000−i−iii000000-1100
χ4022-2-2-2222-2-2-22i−2i2-12-1211-2-22i−2i0000-1-2-11-12112i2i−2i−2i−2i−2i2i2i00000000001-1−ii−i−iii0-202000000ii−i−i0000001-100
χ4122-2-2-2222-2-2-2−2i2i22-12-1-2-211−2i2i2i2i−2i−2i-11-1-22-111ii−i−i00002i−2i0000−i−iii1-1−2i2iii−i−i-20201100-1-100000000−ii0000
χ4222-2-2-2222-2-2-2−2i2i22-12-1-2-211−2i2i−2i−2i2i2i-11-1-22-111ii−i−i0000−2i2i0000ii−i−i1-1−2i2iii−i−i20-20-1-1001100000000i−i0000
χ4322-2-2-2222-2-2-2−2i2i2-12-1211-2-2−2i2i0000-1-2-11-1211−2i−2i2i2i2i2i−2i−2i00000000001-1i−iii−i−i0-202000000−i−iii0000001-100
χ4422-2-2-2222-2-2-2−2i2i2-12-1211-2-2−2i2i0000-1-2-11-1211−2i−2i2i2i−2i−2i2i2i00000000001-1i−iii−i−i020-2000000ii−i−i000000-1100
χ452-22i−2i020-22i−2i000022-2-22i−2i2i−2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1320-20002i−2i00001+i−1−i1−i−1+i002−2−i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000001+i−1−i1−i−1+i2−2−i2i2000000
χ462-22i−2i020-22i−2i000022-2-22i−2i2i−2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1320-20002i−2i0000−1−i1+i−1+i1−i00−22i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000−1−i1+i−1+i1−i−22i2−i2000000
χ472-22i−2i020-22i−2i000022-2-22i−2i2i−2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1320-20002i−2i00001+i−1−i1−i−1+i00−22i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000001+i−1−i1−i−1+i−22i2−i2000000
χ482-22i−2i020-22i−2i000022-2-22i−2i2i−2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1320-20002i−2i0000−1−i1+i−1+i1−i002−2−i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000−1−i1+i−1+i1−i2−2−i2i2000000
χ492-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2320-2000−2i2i00001−i−1+i1+i−1−i002−2i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000001−i−1+i1+i−1−i2−2i2−i2000000
χ502-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2320-2000−2i2i0000−1+i1−i−1−i1+i00−22−i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000−1+i1−i−1−i1+i−22−i2i2000000
χ512-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2320-2000−2i2i00001−i−1+i1+i−1−i00−22−i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000001−i−1+i1+i−1−i−22−i2i2000000
χ522-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2320-2000−2i2i0000−1+i1−i−1−i1+i002−2i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000−1+i1−i−1−i1+i2−2i2−i2000000
χ5344444444444444-2-2-2-2-2-2-2-24400001-21-2-2-211-2-2-2-20000000000000011-2-21111000000000000000000000000
χ5444444444444-4-44-2-2-2-2-2-2-2-2-4-400001-21-2-2-2112222000000000000001122-1-1-1-1000000000000000000000000
χ554444-44-4444-400-4-24-24-2-244000000-2-4-222-4-2-200000000000000000022000000000000000000000000000000
χ564444-44-4444-400-4-2-2-2-2-2-2-2-200000012122211−2i32i3−2i32i300000000000000-1-100i3−i3i3−i3000000000000000000000000
χ574444-44-4444-400-4-2-2-2-2-2-2-2-2000000121222112i3−2i32i3−2i300000000000000-1-100−i3i3−i3i3000000000000000000000000
χ5844-4-444-44-4-4400-4-24-2422-4-4000000-24-2-22-422000000000000000000-22000000000000000000000000000000
χ5944-4-444-44-4-4400-4-2-2-2-222220000001-21-222-1-123−23−2323000000000000001-100−333−3000000000000000000000000
χ6044-4-444-44-4-4400-4-2-2-2-222220000001-21-222-1-1−232323−23000000000000001-1003−3−33000000000000000000000000
χ6144-4-4-4444-4-4-44i−4i4-2-2-2-222224i−4i00001212-2-2-1-1−2i−2i2i2i00000000000000-11−2i2iii−i−i000000000000000000000000
χ6244-4-4-4444-4-4-4−4i4i4-2-2-2-22222−4i4i00001212-2-2-1-12i2i−2i−2i00000000000000-112i−2i−i−iii000000000000000000000000
χ634-44i−4i040-44i−4i00004-2-424i−4i−2i2i004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13-202000−2i2i00000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ644-44i−4i040-44i−4i00004-2-424i−4i−2i2i00−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13-202000−2i2i000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ654-44i−4i040-44i−4i0000-242-4−2i2i4i−4i000000-202000−2i2i00002+2i−2−2i2−2i−2+2i0000000000000000000000000000−1−i1+i−1+i1−i0000000000
χ664-44i−4i040-44i−4i0000-242-4−2i2i4i−4i000000-202000−2i2i0000−2−2i2+2i−2+2i2−2i00000000000000000000000000001+i−1−i1−i−1+i0000000000
χ674-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i00−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23-2020002i−2i000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ684-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23-2020002i−2i00000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ694-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i000000-2020002i−2i00002−2i−2+2i2+2i−2−2i0000000000000000000000000000−1+i1−i−1−i1+i0000000000
χ704-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i000000-2020002i−2i0000−2+2i2−2i−2−2i2+2i00000000000000000000000000001−i−1+i1+i−1−i0000000000
χ7166666-36-3-3-3-366-300000000-3-30000000000000000000000222200000000000000000022000000-1-1-1-10000-1-1
χ7266666-36-3-3-3-366-300000000-3-30000000000000000000000-2-2-2-2000000000000000000-2-20000001111000011
χ7366666-36-3-3-3-3-6-6-3000000003300000000000000000000002222000000000000000000-2-2000000-1-1-1-1000011
χ7466666-36-3-3-3-3-6-6-300000000330000000000000000000000-2-2-2-20000000000000000002200000011110000-1-1
χ7566-6-6-6-36-33336i−6i-300000000−3i3i000000000000000000000022-2-20000000000000000002i−2i000000-1-1110000−ii
χ7666-6-6-6-36-33336i−6i-300000000−3i3i0000000000000000000000-2-222000000000000000000−2i2i00000011-1-10000i−i
χ7766-6-6-6-36-3333−6i6i-3000000003i−3i000000000000000000000022-2-2000000000000000000−2i2i000000-1-1110000i−i
χ7866-6-6-6-36-3333−6i6i-3000000003i−3i0000000000000000000000-2-2220000000000000000002i−2i00000011-1-10000−ii
χ798-88i−8i080-88i−8i0000-4-444−4i4i−4i4i00000020-20002i−2i00000000000000000000000000000000000000000000000000
χ808-8−8i8i080-8−8i8i0000-4-4444i−4i4i−4i00000020-2000−2i2i00000000000000000000000000000000000000000000000000
χ8112121212-12-6-12-6-6-66006000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-1212-6-12-666-6006000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212i−12i0-606−6i6i00000000000000000000000000000000000022−22−2i22i200000000000000000000000000−22i2−i2000000
χ8412-1212i−12i0-606−6i6i000000000000000000000000000000000000−22222i2−2i2000000000000000000000000002−2−i2i2000000
χ8512-12−12i12i0-6066i−6i00000000000000000000000000000000000022−222i2−2i200000000000000000000000000−22−i2i2000000
χ8612-12−12i12i0-6066i−6i000000000000000000000000000000000000−2222−2i22i2000000000000000000000000002−2i2−i2000000

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