Finite Group Databasebeta

← Group #13139206

Character table — Group #13139206

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order1244234612126881233661212121224243666121212122424242422446612126122424242424242244444468812121212121212121224242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-11-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11
χ511111111111-1-1111111111-1-111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ611111111111-1-1111111111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-1111111111-1-1-1-1-1-1-1-1
χ711111111111-1-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11-1-1-111-111-1-1-1-1-1111111111-11-1
χ811111111111-1-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1111-1-1-1111111-1-1-1-1-11111-11-11
χ911-1-1-1111-1-1-1i−i11111-1-1-1-1i−i1-11-111-1-1ii−i−i1-11-111-1-1-11i−iii−i−i1-1-11i−ii−i-1i−iii−i−i1ii−i−iii−i−i1-1-11
χ1011-1-1-1111-1-1-1i−i11111-1-1-1-1i−i1-11-111-1-1ii−i−i1-11-111-1-1-11i−iii−i−i-111-1−ii−ii-1i−i−i−iii1−i−iiiii−i−i-111-1
χ1111-1-1-1111-1-1-1i−i11111-1-1-1-1i−i1-11-111-1-1ii−i−i-11-11-1-111-11i−iii−i−i11-1-1i−i−ii1−iiii−i−i-1−i−iii−i−iii11-1-1
χ1211-1-1-1111-1-1-1i−i11111-1-1-1-1i−i1-11-111-1-1ii−i−i-11-11-1-111-11i−iii−i−i-1-111−iii−i1−ii−i−iii-1ii−i−i−i−iii-1-111
χ1311-1-1-1111-1-1-1−ii11111-1-1-1-1−ii1-11-111-1-1−i−iii1-11-111-1-1-11−ii−i−iii1-1-11−ii−ii-1−ii−i−iii1−i−iii−i−iii1-1-11
χ1411-1-1-1111-1-1-1−ii11111-1-1-1-1−ii1-11-111-1-1−i−iii1-11-111-1-1-11−ii−i−iii-111-1i−ii−i-1−iiii−i−i1ii−i−i−i−iii-111-1
χ1511-1-1-1111-1-1-1−ii11111-1-1-1-1−ii1-11-111-1-1−i−iii-11-11-1-111-11−ii−i−iii11-1-1−iii−i1i−i−i−iii-1ii−i−iii−i−i11-1-1
χ1611-1-1-1111-1-1-1−ii11111-1-1-1-1−ii1-11-111-1-1−i−iii-11-11-1-111-11−ii−i−iii-1-111i−i−ii1i−iii−i−i-1−i−iiiii−i−i-1-111
χ17222222222222222-12-122-1-122-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-100000000-1220000-10000-1-1-1-10000
χ18222222222222222-12-122-1-122-1-1-122-1-1-1-1-1-1-1-2-2-2-21111-1-122-1-1-1-1000000001-2-200001000011110000
χ1922222222222222-12-12-1-12222-12-1-1-12-1-1222200000000-1-1-1-1-1-1-1-10202002200000000-1-1-1-100000-10-1
χ2022222222222222-12-12-1-12222-12-1-1-12-1-1222200000000-1-1-1-1-1-1-1-10-20-200-2-200000000111100000101
χ2122222222222-2-222-12-122-1-1-2-2-1-1-122-1-1-111112222-1-1-1-1-1-1-2-2111100000000-1-2-20000-1000011110000
χ2222222222222-2-222-12-122-1-1-2-2-1-1-122-1-1-11111-2-2-2-21111-1-1-2-2111100000000122000010000-1-1-1-10000
χ2322222222222-2-22-12-12-1-122-2-2-12-1-1-12-1-1-2-2-2-200000000-1-1111111020200-2-200000000111100000-10-1
χ2422222222222-2-22-12-12-1-122-2-2-12-1-1-12-1-1-2-2-2-200000000-1-11111110-20-2002200000000-1-1-1-100000101
χ252222-22-2222-200-222222222002-22-2-2-22200002-2-222222-2-200000000000000-2000000-2000000000000
χ262222-22-2222-200-222222222002-22-2-2-2220000-222-2-2-2-2-2-2-20000000000000020000002000000000000
χ272222-22-2222-200-22-12-122-1-100-11-1-2-21-1-1−i3i3−i3i32-2-22-1-1-1-11100−i3i3−i3i300000000100000010000−i3i3−i3i30000
χ282222-22-2222-200-22-12-122-1-100-11-1-2-21-1-1−i3i3−i3i3-222-211111100−i3i3−i3i300000000-1000000-10000i3−i3i3−i30000
χ292222-22-2222-200-22-12-122-1-100-11-1-2-21-1-1i3−i3i3−i32-2-22-1-1-1-11100i3−i3i3−i300000000100000010000i3−i3i3−i30000
χ302222-22-2222-200-22-12-122-1-100-11-1-2-21-1-1i3−i3i3−i3-222-211111100i3−i3i3−i300000000-1000000-10000−i3i3−i3i30000
χ3122-2-222-22-2-2200-22222-2-2-2-2002222-2-2-2-2000022-2-222-2-22-2000000000000002000000-2000000000000
χ3222-2-222-22-2-2200-22222-2-2-2-2002222-2-2-2-20000-2-222-2-2222-200000000000000-20000002000000000000
χ3322-2-222-22-2-2200-22-12-1-2-21100-1-1-12-21113−3−3322-2-2-1-111-11003−3−3300000000-1000000100003−3−330000
χ3422-2-222-22-2-2200-22-12-1-2-21100-1-1-12-21113−3−33-2-22211-1-1-11003−3−33000000001000000-10000−333−30000
χ3522-2-222-22-2-2200-22-12-1-2-21100-1-1-12-2111−333−322-2-2-1-111-1100−333−300000000-100000010000−333−30000
χ3622-2-222-22-2-2200-22-12-1-2-21100-1-1-12-2111−333−3-2-22211-1-1-1100−333−3000000001000000-100003−3−330000
χ3722-2-2-2222-2-2-22i−2i22-12-1-2-2112i−2i-11-1-22-111−i−iii2-22-2-1-1111-12i−2i−i−iii0000000012i−2i0000-10000−i−iii0000
χ3822-2-2-2222-2-2-22i−2i22-12-1-2-2112i−2i-11-1-22-111−i−iii-22-2211-1-11-12i−2i−i−iii00000000-1−2i2i000010000ii−i−i0000
χ3922-2-2-2222-2-2-22i−2i2-12-1211-2-22i−2i-1-2-11-12112i2i−2i−2i000000001-1−ii−i−iii020-200−2i2i00000000ii−i−i00000-101
χ4022-2-2-2222-2-2-22i−2i2-12-1211-2-22i−2i-1-2-11-12112i2i−2i−2i000000001-1−ii−i−iii0-202002i−2i00000000−i−iii0000010-1
χ4122-2-2-2222-2-2-2−2i2i22-12-1-2-211−2i2i-11-1-22-111ii−i−i2-22-2-1-1111-1−2i2iii−i−i000000001−2i2i0000-10000ii−i−i0000
χ4222-2-2-2222-2-2-2−2i2i22-12-1-2-211−2i2i-11-1-22-111ii−i−i-22-2211-1-11-1−2i2iii−i−i00000000-12i−2i000010000−i−iii0000
χ4322-2-2-2222-2-2-2−2i2i2-12-1211-2-2−2i2i-1-2-11-1211−2i−2i2i2i000000001-1i−iii−i−i020-2002i−2i00000000−i−iii00000-101
χ4422-2-2-2222-2-2-2−2i2i2-12-1211-2-2−2i2i-1-2-11-1211−2i−2i2i2i000000001-1i−iii−i−i0-20200−2i2i00000000ii−i−i0000010-1
χ4544444444444444-2-2-2-2-2-2-2-2441-21-2-2-211-2-2-2-20000000011-2-211110000000000000000000000000000
χ4644444444444-4-44-2-2-2-2-2-2-2-2-4-41-21-2-2-2112222000000001122-1-1-1-10000000000000000000000000000
χ474444-44-4444-400-4-24-24-2-24400-2-4-222-4-2-2000000000000220000000000000000000000000000000000
χ484444-44-4444-400-4-2-2-2-2-2-2-2-20012122211−2i32i3−2i32i300000000-1-100i3−i3i3−i30000000000000000000000000000
χ494444-44-4444-400-4-2-2-2-2-2-2-2-200121222112i3−2i32i3−2i300000000-1-100−i3i3−i3i30000000000000000000000000000
χ5044-4-444-44-4-4400-4-24-2422-4-400-24-2-22-422000000000000-220000000000000000000000000000000000
χ5144-4-444-44-4-4400-4-2-2-2-22222001-21-222-1-123−23−2323000000001-100−333−30000000000000000000000000000
χ5244-4-444-44-4-4400-4-2-2-2-22222001-21-222-1-1−232323−23000000001-1003−3−330000000000000000000000000000
χ5344-4-4-4444-4-4-44i−4i4-2-2-2-222224i−4i1212-2-2-1-1−2i−2i2i2i00000000-11−2i2iii−i−i0000000000000000000000000000
χ5444-4-4-4444-4-4-4−4i4i4-2-2-2-22222−4i4i1212-2-2-1-12i2i−2i−2i00000000-112i−2i−i−iii0000000000000000000000000000
χ554-44i−4i040-44i−4i000044-4-44i−4i4i−4i0040-40004i−4i000000000000000000000000000000000000000000000000
χ564-44i−4i040-44i−4i00004-2-424i−4i−2i2i00-202000−2i2i00000000−2i32i323−23000000000000000000000000000000000000
χ574-44i−4i040-44i−4i00004-2-424i−4i−2i2i00-202000−2i2i000000002i3−2i3−2323000000000000000000000000000000000000
χ584-44i−4i040-44i−4i0000-242-4−2i2i4i−4i00-202000−2i2i000000000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000
χ594-44i−4i040-44i−4i0000-242-4−2i2i4i−4i00-202000−2i2i000000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000
χ604-4−4i4i040-4−4i4i000044-4-4−4i4i−4i4i0040-4000−4i4i000000000000000000000000000000000000000000000000
χ614-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i00-2020002i−2i00000000−2i32i3−2323000000000000000000000000000000000000
χ624-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i00-2020002i−2i000000002i3−2i323−23000000000000000000000000000000000000
χ634-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i00-2020002i−2i000000000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000
χ644-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i00-2020002i−2i000000000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000
χ6566666-36-3-3-3-366-300000000-3-3000000000000000000000000000020202200000-1-1-1-1000000000-10-10
χ6666666-36-3-3-3-366-300000000-3-30000000000000000000000000000-20-20-2-20000011110000000001010
χ6766666-36-3-3-3-3-6-6-3000000003300000000000000000000000000002020-2-2000001111000000000-10-10
χ6866666-36-3-3-3-3-6-6-300000000330000000000000000000000000000-20-202200000-1-1-1-10000000001010
χ6966-6-6-6-36-33336i−6i-300000000−3i3i000000000000000000000000000020-202i−2i00000−i−iii000000000-1010
χ7066-6-6-6-36-33336i−6i-300000000−3i3i0000000000000000000000000000-2020−2i2i00000ii−i−i00000000010-10
χ7166-6-6-6-36-3333−6i6i-3000000003i−3i000000000000000000000000000020-20−2i2i00000ii−i−i000000000-1010
χ7266-6-6-6-36-3333−6i6i-3000000003i−3i0000000000000000000000000000-20202i−2i00000−i−iii00000000010-10
χ738-88i−8i080-88i−8i0000-4-444−4i4i−4i4i0020-20002i−2i000000000000000000000000000000000000000000000000
χ748-8−8i8i080-8−8i8i0000-4-4444i−4i4i−4i0020-2000−2i2i000000000000000000000000000000000000000000000000
χ7512121212-12-6-12-6-6-66006000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-1212-6-12-666-6006000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212i−12i0-606−6i6i00000000000000000000000000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000
χ7812-1212i−12i0-606−6i6i00000000000000000000000000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000
χ7912-12−12i12i0-6066i−6i00000000000000000000000000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000
χ8012-12−12i12i0-6066i−6i00000000000000000000000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.