Finite Group Databasebeta

← Group #72220468

Character table — Group #72220468

Order 6912.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122448888999916161818242424243232363648484848484848484848545454547272727272727272969696969696108108108108108108108108108108144144144144144144144144144144144144216216216216216216288288
order124424883612122244612243612122424883661212122424242444444444661212612242424244488888888246121212121224242424888888612
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1
χ3111111-1-11111111111111111-1-1-1-1111111-1-1-1-111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111-1-11111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1111111
χ511-1-1-11i−i11-1-111-1-1-11-1111-1-1i−ii−i1-111-1-1ii−i−i-1-111ii−i−i11-1-1-11ii−i−i1-1iiii−i−i−i−i1-1-1ii−i−i1ii−i−ii−i11-1-11-1
χ611-1-1-11i−i11-1-111-1-1-11-1111-1-1i−ii−i1-111-1-1ii−i−i-1-111−i−iii11-1-1-11ii−i−i1-1−i−i−i−iiiii-11-1−i−iii1ii−i−ii−i-1-111-11
χ711-1-1-11−ii11-1-111-1-1-11-1111-1-1−ii−ii1-111-1-1−i−iii-1-111ii−i−i11-1-1-11−i−iii1-1iiii−i−i−i−i-11-1ii−i−i1−i−iii−ii-1-111-11
χ811-1-1-11−ii11-1-111-1-1-11-1111-1-1−ii−ii1-111-1-1−i−iii-1-111−i−iii11-1-1-11−i−iii1-1−i−i−i−iiiii1-1-1−i−iii1−i−iii−ii11-1-11-1
χ922222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1-1-1220000000000-10000-1-1-1-1-122000000
χ10222222222222-2-2-2-222-2-2-1-1-1-122-2-2-1-1-1-1-1-1-1-1-1-1000000001111-1-1-1-1-1-100−i2−i2i2i2−i2−i2i2i200100001111100−i2i2−i2i200
χ11222222222222-2-2-2-222-2-2-1-1-1-122-2-2-1-1-1-1-1-1-1-1-1-1000000001111-1-1-1-1-1-100i2i2−i2−i2i2i2−i2−i200100001111100i2−i2i2−i200
χ12222222-2-2222222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1111122220000-1-1-1-1-1-11111220000000000-10000-11111-2-2000000
χ13222222-2-22222-2-2-2-222-2-2-1-1-1-1-2-222-1-1-1-1-1-11111000000001111-1-1111100−i2−i2i2i2−i2−i2i2i200100001-1-1-1-100i2−i2i2−i200
χ14222222-2-22222-2-2-2-222-2-2-1-1-1-1-2-222-1-1-1-1-1-11111000000001111-1-1111100i2i2−i2−i2i2i2−i2−i200100001-1-1-1-100−i2i2−i2i200
χ152222-2-20022222222-2-2-2-2222200002-22-2220000222200002222-2-20000-2-20000000000-20000-2000000000000
χ162222-2-20022222222-2-2-2-2-1-1-1-10000-11-11-1-1−i3i3−i3i322220000-1-1-1-111−i3i3−i3i3-2-20000000000100001−i3i3−i3i300000000
χ172222-2-20022222222-2-2-2-2-1-1-1-10000-11-11-1-1i3−i3i3−i322220000-1-1-1-111i3−i3i3−i3-2-20000000000100001i3−i3i3−i300000000
χ1822-2-22-20022-2-222-2-22-22-222-2-20000222-2-2-20000-2-222000022-2-22-20000-22000000000020000-2000000000000
χ1922-2-22-20022-2-222-2-22-22-2-1-1110000-1-1-11113−3−33-2-2220000-1-111-113−3−33-220000000000-1000013−3−3300000000
χ2022-2-22-20022-2-222-2-22-22-2-1-1110000-1-1-1111−333−3-2-2220000-1-111-11−333−3-220000000000-100001−333−300000000
χ2122-2-2-222i−2i22-2-222-2-2-22-22-1-1112i−2i2i−2i-11-1-111−i−iii-2-2220000-1-1111-1−i−iii2-2000000000010000-1−i−iii2i−2i000000
χ2222-2-2-222i−2i22-2-2-2-222-222-2-1-1112i−2i−2i2i-11-1-111−i−iii0000000011-1-11-1−i−iii0022−2−2−2−22200-100001ii−i−i00−i2i2i2−i200
χ2322-2-2-222i−2i22-2-2-2-222-222-2-1-1112i−2i−2i2i-11-1-111−i−iii0000000011-1-11-1−i−iii00−2−22222−2−200-100001ii−i−i00i2−i2−i2i200
χ2422-2-2-22−2i2i22-2-222-2-2-22-22-1-111−2i2i−2i2i-11-1-111ii−i−i-2-2220000-1-1111-1ii−i−i2-2000000000010000-1ii−i−i−2i2i000000
χ2522-2-2-22−2i2i22-2-2-2-222-222-2-1-111−2i2i2i−2i-11-1-111ii−i−i0000000011-1-11-1ii−i−i0022−2−2−2−22200-100001−i−iii00i2−i2−i2i200
χ2622-2-2-22−2i2i22-2-2-2-222-222-2-1-111−2i2i2i−2i-11-1-111ii−i−i0000000011-1-11-1ii−i−i00−2−22222−2−200-100001−i−iii00−i2i2i2−i200
χ272-22i−2i00002-22i−2i2-22i−2i00002-22i−2i000020-202i−2i00002i−2i2-21+i−1−i1−i−1+i2-22i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0001+i−1−i1−i−1+i0000000000000
χ282-22i−2i00002-22i−2i2-22i−2i00002-22i−2i000020-202i−2i00002i−2i2-2−1−i1+i−1+i1−i2-22i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000−1−i1+i−1+i1−i0000000000000
χ292-2−2i2i00002-2−2i2i2-2−2i2i00002-2−2i2i000020-20−2i2i0000−2i2i2-21−i−1+i1+i−1−i2-2−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0001−i−1+i1+i−1−i0000000000000
χ302-2−2i2i00002-2−2i2i2-2−2i2i00002-2−2i2i000020-20−2i2i0000−2i2i2-2−1+i1−i−1−i1+i2-2−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000−1+i1−i−1−i1+i0000000000000
χ3133333333333333333333000033330000000000-1-1-1-111110000000000-1-1-1-1-1-1-1-1-1-1110111100000-1-1-1-1-1-111
χ3233333333333333333333000033330000000000-1-1-1-1-1-1-1-10000000000-1-111111111-1-10-1-1-1-100000-1-11111-1-1
χ33333333-3-33333333333330000-3-3-3-30000000000-1-1-1-111110000000000-1-1-1-1-1-1-1-1-1-1-1-10111100000111111-1-1
χ34333333-3-33333333333330000-3-3-3-30000000000-1-1-1-1-1-1-1-10000000000-1-111111111110-1-1-1-10000011-1-1-1-111
χ3533-3-3-333i−3i33-3-333-3-3-33-3300003i−3i3i−3i000000000011-1-1ii−i−i0000000000-11−i−i−i−iiiii1-10ii−i−i00000−ii-1-1111-1
χ3633-3-3-333i−3i33-3-333-3-3-33-3300003i−3i3i−3i000000000011-1-1−i−iii0000000000-11iiii−i−i−i−i-110−i−iii00000−ii11-1-1-11
χ3733-3-3-33−3i3i33-3-333-3-3-33-330000−3i3i−3i3i000000000011-1-1ii−i−i0000000000-11−i−i−i−iiiii-110ii−i−i00000i−i11-1-1-11
χ3833-3-3-33−3i3i33-3-333-3-3-33-330000−3i3i−3i3i000000000011-1-1−i−iii0000000000-11iiii−i−i−i−i1-10−i−iii00000i−i-1-1111-1
χ39444444444444-4-4-4-444-4-4111144-4-4111111111100000000-1-1-1-1111111000000000000-10000-1-1-1-1-100000000
χ40444444-4-44444-4-4-4-444-4-41111-4-444111111-1-1-1-100000000-1-1-1-111-1-1-1-1000000000000-10000-1111100000000
χ414444-4-4004444-4-4-4-4-4-444111100001-11-111−i3i3−i3i300000000-1-1-1-1-1-1−i3i3−i3i3000000000000100001i3−i3i3−i300000000
χ424444-4-4004444-4-4-4-4-4-444111100001-11-111i3−i3i3−i300000000-1-1-1-1-1-1i3−i3i3−i3000000000000100001−i3i3−i3i300000000
χ434444-4-4004444-4-4-4-4-4-444-2-2-2-20000-22-22-2-20000000000002222220000000000000000-20000-2000000000000
χ4444-4-44-40044-4-4-4-4444-4-4411-1-10000111-1-1-13−3−3300000000-1-1111-13−3−33000000000000-100001−333−300000000
χ4544-4-44-40044-4-4-4-4444-4-4411-1-10000111-1-1-1−333−300000000-1-1111-1−333−3000000000000-1000013−3−3300000000
χ4644-4-44-40044-4-4-4-4444-4-44-2-2220000-2-2-222200000000000022-2-2-22000000000000000020000-2000000000000
χ4744-4-4-444i−4i44-4-4-4-444-444-411-1-14i−4i−4i4i1-111-1-1ii−i−i00000000-1-111-11ii−i−i00000000000010000-1−i−iii00000000
χ4844-4-4-44−4i4i44-4-4-4-444-444-411-1-1−4i4i4i−4i1-111-1-1−i−iii00000000-1-111-11−i−iii00000000000010000-1ii−i−i00000000
χ494-44i−4i00004-44i−4i4-44i−4i0000-22−2i2i0000-2020−2i2i00004i−4i4-40000-22−2i2i000000000000000000000000000000000000
χ504-44i−4i00004-44i−4i-44−4i4i0000-22−2i2i0000-2020−2i2i0000000000002-22i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ514-44i−4i00004-44i−4i-44−4i4i0000-22−2i2i0000-2020−2i2i0000000000002-22i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ524-4−4i4i00004-4−4i4i4-4−4i4i0000-222i−2i0000-20202i−2i0000−4i4i4-40000-222i−2i000000000000000000000000000000000000
χ534-4−4i4i00004-4−4i4i-444i−4i0000-222i−2i0000-20202i−2i0000000000002-2−2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ544-4−4i4i00004-4−4i4i-444i−4i0000-222i−2i0000-20202i−2i0000000000002-2−2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ556666-6-60066666666-6-6-6-6000000000000000000-2-2-2-200000000000000220000000000000000000000000000
χ5666-6-66-60066-6-666-6-66-66-600000000000000000022-2-2000000000000002-20000000000000000000000000000
χ576-66i−6i00006-66i−6i6-66i−6i0000000000000000000000−2i2i-221+i−1−i1−i−1+i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0001+i−1−i1−i−1+i0000000000000
χ586-66i−6i00006-66i−6i6-66i−6i0000000000000000000000−2i2i-22−1−i1+i−1+i1−i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000−1−i1+i−1+i1−i0000000000000
χ596-6−6i6i00006-6−6i6i6-6−6i6i00000000000000000000002i−2i-221−i−1+i1+i−1−i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0001−i−1+i1+i−1−i0000000000000
χ606-6−6i6i00006-6−6i6i6-6−6i6i00000000000000000000002i−2i-22−1+i1−i−1−i1+i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000−1+i1−i−1−i1+i0000000000000
χ6188888888-1-1-1-10000-1-1002222-1-100-12-12-1-12222000022220000-1-1-1-1-1-10000000000220-1-1-1-100000000000-1-1
χ6288888888-1-1-1-10000-1-1002222-1-100-12-12-1-122220000-2-2-2-20000-1-1-1-1-1-10000000000-2-2011110000000000011
χ63888888-8-8-1-1-1-10000-1-10022221100-12-12-1-1-2-2-2-2000022220000-1-111110000000000-2-20-1-1-1-10000000000011
χ64888888-8-8-1-1-1-10000-1-10022221100-12-12-1-1-2-2-2-20000-2-2-2-20000-1-111110000000000220111100000000000-1-1
χ6588-8-8-888i−8i-1-11100001-10022-2-2−ii00-1-2-12112i2i−2i−2i00002i2i−2i−2i00001-1−i−iii00000000002-20−i−iii00000000000-11
χ6688-8-8-888i−8i-1-11100001-10022-2-2−ii00-1-2-12112i2i−2i−2i0000−2i−2i2i2i00001-1−i−iii0000000000-220ii−i−i000000000001-1
χ6788-8-8-88−8i8i-1-11100001-10022-2-2i−i00-1-2-1211−2i−2i2i2i00002i2i−2i−2i00001-1ii−i−i0000000000-220−i−iii000000000001-1
χ6888-8-8-88−8i8i-1-11100001-10022-2-2i−i00-1-2-1211−2i−2i2i2i0000−2i−2i2i2i00001-1ii−i−i00000000002-20ii−i−i00000000000-11
χ698-88i−8i00008-88i−8i-88−8i8i00002-22i−2i000020-202i−2i000000000000-22−2i2i000000000000000000000000000000000000
χ708-8−8i8i00008-8−8i8i-888i−8i00002-2−2i2i000020-20−2i2i000000000000-222i−2i000000000000000000000000000000000000
χ711616161616161616-2-2-2-20000-2-200-2-2-2-2-2-2001-21-211-2-2-2-2000000000000111111000000000000000000000000000000
χ72161616161616-16-16-2-2-2-20000-2-200-2-2-2-222001-21-211222200000000000011-1-1-1-1000000000000000000000000000000
χ7316161616-16-1600-2-2-2-20000220044440000-2-4-2-4-2-20000000000000000220000000000000000000000000000000000
χ7416161616-16-1600-2-2-2-200002200-2-2-2-20000121211−2i32i3−2i32i3000000000000-1-1i3−i3i3−i3000000000000000000000000000000
χ7516161616-16-1600-2-2-2-200002200-2-2-2-200001212112i3−2i32i3−2i3000000000000-1-1−i3i3−i3i3000000000000000000000000000000
χ761616-16-1616-1600-2-2220000-220044-4-40000-24-2-4220000000000000000-220000000000000000000000000000000000
χ771616-16-1616-1600-2-2220000-2200-2-22200001-212-1-123−23−23230000000000001-1−333−3000000000000000000000000000000
χ781616-16-1616-1600-2-2220000-2200-2-22200001-212-1-1−232323−230000000000001-13−3−33000000000000000000000000000000
χ791616-16-16-161616i−16i-2-22200002-200-2-222−2i2i00121-2-1-1−2i−2i2i2i000000000000-11ii−i−i000000000000000000000000000000
χ801616-16-16-1616−16i16i-2-22200002-200-2-2222i−2i00121-2-1-12i2i−2i−2i000000000000-11−i−iii000000000000000000000000000000
χ8116-1616i−16i0000-22−2i2i000000004-44i−4i0000-2020−2i2i000000002+2i−2−2i2−2i−2+2i00000000000000000000000−1−i1+i−1+i1−i0000000000000
χ8216-1616i−16i0000-22−2i2i000000004-44i−4i0000-2020−2i2i00000000−2−2i2+2i−2+2i2−2i000000000000000000000001+i−1−i1−i−1+i0000000000000
χ8316-16−16i16i0000-222i−2i000000004-4−4i4i0000-20202i−2i000000002−2i−2+2i2+2i−2−2i00000000000000000000000−1+i1−i−1−i1+i0000000000000
χ8416-16−16i16i0000-222i−2i000000004-4−4i4i0000-20202i−2i00000000−2+2i2−2i−2−2i2+2i000000000000000000000001−i−1+i1+i−1−i0000000000000
χ8532-3232i−32i0000-44−4i4i00000000-44−4i4i000020-202i−2i0000000000000000000000000000000000000000000000000000
χ8632-32−32i32i0000-444i−4i00000000-444i−4i000020-20−2i2i0000000000000000000000000000000000000000000000000000

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