Finite Group Databasebeta

← Group #13139205

Character table — Group #13139205

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order1244234612126881233661212121224242244366612121212242424242444444444661212612242424242424224468812121212121212121224242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1111111111-11-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-11-11-1-1-1-1-1-1-1-11111-1-1-1-1-11-11
χ511111111111-1-1111111111-1-1111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1
χ611111111111-1-1111111111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ711111111111-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-11-1111111-1-1-1-1-11111-11-11
χ811111111111-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-11-1-111-1-1-1-1-1111111111-11-1
χ911-1-1-1111-1-1-1i−i11111-1-1-1-1i−i11-1-11-11-111-1-1ii−i−i-11ii−i−iii−i−i11-1-1-11i−iii−i−i11-1-1-1i−iii−i−i1ii−i−iii−i−i11-1-1
χ1011-1-1-1111-1-1-1i−i11111-1-1-1-1i−i11-1-11-11-111-1-1ii−i−i-11−i−iii−i−iii11-1-1-11i−iii−i−i-1-111-1i−i−i−iii1−i−iiiii−i−i-1-111
χ1111-1-1-1111-1-1-1i−i11111-1-1-1-1i−i-1-1111-11-111-1-1ii−i−i1-1ii−i−i−i−iii-1-111-11i−iii−i−i1-1-111−iiii−i−i-1−i−iii−i−iii1-1-11
χ1211-1-1-1111-1-1-1i−i11111-1-1-1-1i−i-1-1111-11-111-1-1ii−i−i1-1−i−iiiii−i−i-1-111-11i−iii−i−i-111-11−ii−i−iii-1ii−i−i−i−iii-111-1
χ1311-1-1-1111-1-1-1−ii11111-1-1-1-1−ii11-1-11-11-111-1-1−i−iii-11ii−i−iii−i−i11-1-1-11−ii−i−iii-1-111-1−iiii−i−i1ii−i−i−i−iii-1-111
χ1411-1-1-1111-1-1-1−ii11111-1-1-1-1−ii11-1-11-11-111-1-1−i−iii-11−i−iii−i−iii11-1-1-11−ii−i−iii11-1-1-1−ii−i−iii1−i−iii−i−iii11-1-1
χ1511-1-1-1111-1-1-1−ii11111-1-1-1-1−ii-1-1111-11-111-1-1−i−iii1-1ii−i−i−i−iii-1-111-11−ii−i−iii-111-11i−iii−i−i-1−i−iiiii−i−i-111-1
χ1611-1-1-1111-1-1-1−ii11111-1-1-1-1−ii-1-1111-11-111-1-1−i−iii1-1−i−iiiii−i−i-1-111-11−ii−i−iii1-1-111i−i−i−iii-1ii−i−iii−i−i1-1-11
χ17222222222222222-12-122-1-1222222-1-1-122-1-1-1-1-1-1-12200000000-1-1-1-1-1-122-1-1-1-10000-1220000-10000-1-1-1-10000
χ18222222222222222-12-122-1-122-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-2000000001111-1-122-1-1-1-100001-2-200001000011110000
χ1922222222222222-12-12-1-122220000-12-1-1-12-1-1222200000022220000-1-1-1-1-1-1-1-1020200000000-1-1-1-100000-10-1
χ2022222222222222-12-12-1-122220000-12-1-1-12-1-12222000000-2-2-2-20000-1-1-1-1-1-1-1-10-20-200000000111100000101
χ2122222222222-2-222-12-122-1-1-2-22222-1-1-122-1-1-111112200000000-1-1-1-1-1-1-2-211110000-1-2-20000-1000011110000
χ2222222222222-2-222-12-122-1-1-2-2-2-2-2-2-1-1-122-1-1-11111-2-2000000001111-1-1-2-211110000122000010000-1-1-1-10000
χ2322222222222-2-22-12-12-1-122-2-20000-12-1-1-12-1-1-2-2-2-200000022220000-1-11111110-20-200000000-1-1-1-100000101
χ2422222222222-2-22-12-12-1-122-2-20000-12-1-1-12-1-1-2-2-2-2000000-2-2-2-20000-1-1111111020200000000111100000-10-1
χ252222-22-2222-200-2222222220022222-22-2-2-2220000-2-2000000002222-2-20000000000-2000000-2000000000000
χ262222-22-2222-200-22222222200-2-2-2-22-22-2-2-22200002200000000-2-2-2-2-2-2000000000020000002000000000000
χ272222-22-2222-200-22-12-122-1-1002222-11-1-2-21-1-1−i3i3−i3i3-2-200000000-1-1-1-11100−i3i3−i3i30000100000010000−i3i3−i3i30000
χ282222-22-2222-200-22-12-122-1-1002222-11-1-2-21-1-1i3−i3i3−i3-2-200000000-1-1-1-11100i3−i3i3−i30000100000010000i3−i3i3−i30000
χ292222-22-2222-200-22-12-122-1-100-2-2-2-2-11-1-2-21-1-1−i3i3−i3i3220000000011111100−i3i3−i3i30000-1000000-10000i3−i3i3−i30000
χ302222-22-2222-200-22-12-122-1-100-2-2-2-2-11-1-2-21-1-1i3−i3i3−i3220000000011111100i3−i3i3−i30000-1000000-10000−i3i3−i3i30000
χ3122-2-222-22-2-2200-22222-2-2-2-20022-2-22222-2-2-2-200002-20000000022-2-22-200000000002000000-2000000000000
χ3222-2-222-22-2-2200-22222-2-2-2-200-2-2222222-2-2-2-20000-2200000000-2-2222-20000000000-20000002000000000000
χ3322-2-222-22-2-2200-22-12-1-2-2110022-2-2-1-1-12-21113−3−332-200000000-1-111-11003−3−330000-1000000100003−3−330000
χ3422-2-222-22-2-2200-22-12-1-2-2110022-2-2-1-1-12-2111−333−32-200000000-1-111-1100−333−30000-100000010000−333−30000
χ3522-2-222-22-2-2200-22-12-1-2-21100-2-222-1-1-12-21113−3−33-220000000011-1-1-11003−3−3300001000000-10000−333−30000
χ3622-2-222-22-2-2200-22-12-1-2-21100-2-222-1-1-12-2111−333−3-220000000011-1-1-1100−333−300001000000-100003−3−330000
χ3722-2-2-2222-2-2-22i−2i22-12-1-2-2112i−2i22-2-2-11-1-22-111−i−iii-2200000000-1-1111-12i−2i−i−iii000012i−2i0000-10000−i−iii0000
χ3822-2-2-2222-2-2-22i−2i22-12-1-2-2112i−2i-2-222-11-1-22-111−i−iii2-20000000011-1-11-12i−2i−i−iii0000-1−2i2i000010000ii−i−i0000
χ3922-2-2-2222-2-2-22i−2i2-12-1211-2-22i−2i0000-1-2-11-12112i2i−2i−2i0000002i2i−2i−2i00001-1−ii−i−iii020-200000000−i−iii00000-101
χ4022-2-2-2222-2-2-22i−2i2-12-1211-2-22i−2i0000-1-2-11-12112i2i−2i−2i000000−2i−2i2i2i00001-1−ii−i−iii0-20200000000ii−i−i0000010-1
χ4122-2-2-2222-2-2-2−2i2i22-12-1-2-211−2i2i22-2-2-11-1-22-111ii−i−i-2200000000-1-1111-1−2i2iii−i−i00001−2i2i0000-10000ii−i−i0000
χ4222-2-2-2222-2-2-2−2i2i22-12-1-2-211−2i2i-2-222-11-1-22-111ii−i−i2-20000000011-1-11-1−2i2iii−i−i0000-12i−2i000010000−i−iii0000
χ4322-2-2-2222-2-2-2−2i2i2-12-1211-2-2−2i2i0000-1-2-11-1211−2i−2i2i2i0000002i2i−2i−2i00001-1i−iii−i−i0-20200000000−i−iii0000010-1
χ4422-2-2-2222-2-2-2−2i2i2-12-1211-2-2−2i2i0000-1-2-11-1211−2i−2i2i2i000000−2i−2i2i2i00001-1i−iii−i−i020-200000000ii−i−i00000-101
χ452-22i−2i020-22i−2i000022-2-22i−2i2i−2i002-22i−2i20-20002i−2i0000001+i−1−i1−i−1+i1+i−1−i1−i−1+i2-22i−2i0000000000000001+i−1−i1−i−1+i01+i−1−i1−i−1+i00000000
χ462-22i−2i020-22i−2i000022-2-22i−2i2i−2i002-22i−2i20-20002i−2i000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i2-22i−2i000000000000000−1−i1+i−1+i1−i0−1−i1+i−1+i1−i00000000
χ472-22i−2i020-22i−2i000022-2-22i−2i2i−2i00-22−2i2i20-20002i−2i0000001+i−1−i1−i−1+i−1−i1+i−1+i1−i-22−2i2i0000000000000001+i−1−i1−i−1+i0−1−i1+i−1+i1−i00000000
χ482-22i−2i020-22i−2i000022-2-22i−2i2i−2i00-22−2i2i20-20002i−2i000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i-22−2i2i000000000000000−1−i1+i−1+i1−i01+i−1−i1−i−1+i00000000
χ492-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i002-2−2i2i20-2000−2i2i0000001−i−1+i1+i−1−i1−i−1+i1+i−1−i2-2−2i2i0000000000000001−i−1+i1+i−1−i01−i−1+i1+i−1−i00000000
χ502-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i002-2−2i2i20-2000−2i2i000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i2-2−2i2i000000000000000−1+i1−i−1−i1+i0−1+i1−i−1−i1+i00000000
χ512-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i00-222i−2i20-2000−2i2i0000001−i−1+i1+i−1−i−1+i1−i−1−i1+i-222i−2i0000000000000001−i−1+i1+i−1−i0−1+i1−i−1−i1+i00000000
χ522-2−2i2i020-2−2i2i000022-2-2−2i2i−2i2i00-222i−2i20-2000−2i2i000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i-222i−2i000000000000000−1+i1−i−1−i1+i01−i−1+i1+i−1−i00000000
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−2i2i004-44i−4i-202000−2i2i00000000000000-22−2i2i00000000000000000000000000000000
χ644-44i−4i040-44i−4i00004-2-424i−4i−2i2i00-44−4i4i-202000−2i2i000000000000002-22i−2i00000000000000000000000000000000
χ654-44i−4i040-44i−4i0000-242-4−2i2i4i−4i000000-202000−2i2i00000000002+2i−2−2i2−2i−2+2i000000000000000000000000−1−i1+i−1+i1−i00000000
χ664-44i−4i040-44i−4i0000-242-4−2i2i4i−4i000000-202000−2i2i0000000000−2−2i2+2i−2+2i2−2i0000000000000000000000001+i−1−i1−i−1+i00000000
χ674-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i004-4−4i4i-2020002i−2i00000000000000-222i−2i00000000000000000000000000000000
χ684-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i00-444i−4i-2020002i−2i000000000000002-2−2i2i00000000000000000000000000000000
χ694-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i000000-2020002i−2i00000000002−2i−2+2i2+2i−2−2i000000000000000000000000−1+i1−i−1−i1+i00000000
χ704-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i000000-2020002i−2i0000000000−2+2i2−2i−2−2i2+2i0000000000000000000000001−i−1+i1+i−1−i00000000
χ7166666-36-3-3-3-366-300000000-3-3000000000000000000222200000000000000002020000-1-1-1-1000000000-10-10
χ7266666-36-3-3-3-366-300000000-3-3000000000000000000-2-2-2-20000000000000000-20-2000011110000000001010
χ7366666-36-3-3-3-3-6-6-3000000003300000000000000000022220000000000000000-20-20000-1-1-1-10000000001010
χ7466666-36-3-3-3-3-6-6-30000000033000000000000000000-2-2-2-2000000000000000020200001111000000000-10-10
χ7566-6-6-6-36-33336i−6i-300000000−3i3i0000000000000000002i2i−2i−2i000000000000000020-20000−i−iii000000000-1010
χ7666-6-6-6-36-33336i−6i-300000000−3i3i000000000000000000−2i−2i2i2i0000000000000000-2020000ii−i−i00000000010-10
χ7766-6-6-6-36-3333−6i6i-3000000003i−3i0000000000000000002i2i−2i−2i0000000000000000-2020000−i−iii00000000010-10
χ7866-6-6-6-36-3333−6i6i-3000000003i−3i000000000000000000−2i−2i2i2i000000000000000020-20000ii−i−i000000000-1010
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−12i0-606−6i6i000000000000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000000000000−1−i1+i−1+i1−i0000000000000
χ8412-1212i−12i0-606−6i6i00000000000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000000001+i−1−i1−i−1+i0000000000000
χ8512-12−12i12i0-6066i−6i000000000000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000000−1+i1−i−1−i1+i0000000000000
χ8612-12−12i12i0-6066i−6i00000000000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000000001−i−1+i1+i−1−i0000000000000

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