Finite Group Databasebeta

← Group #72220457

Character table — Group #72220457

Order 6912.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122448888999916161818242424243232363648484848484848484848545454547272727272727272969696969696108108108108108108108108108108144144144144144144144144144144144144216216216216216216288288
order124424243612122244612243612126122436666121212121244444444661212666121212448888888866688121212121212124488882424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111-1-1-1-1-1-1
χ3111111-1-11111111111111111-1-1-1-111-1-111-1-1111111111111111-1-11-1-111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ4111111-1-11111111111111111-1-1-1-111-1-111-1-1111111-1-1-1-111111-1-11-1-111-1-1-1-1-1-1-1-11-1-111-1-1-1-11-1-1-1-1111111
χ511-1-1-111-111-1-111-1-1-11-1111-1-11-11-11-11111-1-1-1-111-1-1ii−i−i11-1-1-1111-1-11-1iiii−i−i−i−i-111i−iii−i−i1-1-11-1ii−i−ii−i
χ611-1-1-111-111-1-111-1-1-11-1111-1-11-11-11-11111-1-1-1-111-1-1−i−iii11-1-1-1111-1-11-1−i−i−i−iiiii-111−ii−i−iii1-1-11-1−i−iii−ii
χ711-1-1-11-1111-1-111-1-1-11-1111-1-1-11-111-1-1-11111-1-111-1-1ii−i−i11-1-1-1-1-11111-1iiii−i−i−i−i-1-1-1−iiii−i−i111-11−i−iii−ii
χ811-1-1-11-1111-1-111-1-1-11-1111-1-1-11-111-1-1-11111-1-111-1-1−i−iii11-1-1-1-1-11111-1−i−i−i−iiiii-1-1-1i−i−i−iii111-11ii−i−ii−i
χ922222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1-1-12200000000-1-1-1000000-1-1-122000000
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−i2i2i211100000011100−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−i211100000011100i2−i2i2−i200
χ12222222-2-2222222222222-1-1-1-1-2-2-2-2-1-111-1-111-1-122220000-1-1-1-1-111-1112200000000-111000000-111-2-2000000
χ13222222-2-22222-2-2-2-222-2-2-1-1-1-1-2-222-1-111-1-111-1-1000000001111-111-11100−i2−i2i2i2−i2−i2i2i21-1-10000001-1-100i2−i2i2−i200
χ14222222-2-22222-2-2-2-222-2-2-1-1-1-1-2-222-1-111-1-111-1-1000000001111-111-11100i2i2−i2−i2i2i2−i2−i21-1-10000001-1-100−i2i2−i2i200
χ152222-2-20022222222-2-2-2-2222200002-2002-20022222200002222-200-200-2-200000000-200000000-20000000000
χ162222-2-20022222222-2-2-2-2-1-1-1-10000-11−i3i3-11−i3i3-1-122220000-1-1-1-11−i3i31−i3i3-2-2000000001−i3i30000001−i3i300000000
χ172222-2-20022222222-2-2-2-2-1-1-1-10000-11i3−i3-11i3−i3-1-122220000-1-1-1-11i3−i31i3−i3-2-2000000001i3−i30000001i3−i300000000
χ1822-2-22-20022-2-222-2-22-22-222-2-2000022002-200-2-222-2-2000022-2-2200-200-2200000000200000000-20000000000
χ1922-2-22-20022-2-222-2-22-22-2-1-1110000-1-1−i3i3-11i3−i31122-2-20000-1-111-1−i3i31i3−i3-2200000000-1−i3i30000001i3−i300000000
χ2022-2-22-20022-2-222-2-22-22-2-1-1110000-1-1i3−i3-11−i3i31122-2-20000-1-111-1i3−i31−i3i3-2200000000-1i3−i30000001−i3i300000000
χ2122-2-2-222-222-2-222-2-2-22-22-1-1112-22-2-11-1-1-1-1111122-2-20000-1-1111-1-1-1112-2000000001-1-1000000-1112-2000000
χ2222-2-2-222-222-2-2-2-222-222-2-1-1112-2-22-11-1-1-1-111110000000011-1-11-1-1-1110022−2−2−2−222-1110000001-1-1002−2−2200
χ2322-2-2-222-222-2-2-2-222-222-2-1-1112-2-22-11-1-1-1-111110000000011-1-11-1-1-11100−2−22222−2−2-1110000001-1-100−222−200
χ2422-2-2-22-2222-2-222-2-2-22-22-1-111-22-22-1111-1-1-1-11122-2-20000-1-111111-1-1-12-200000000111000000-1-1-1-22000000
χ2522-2-2-22-2222-2-2-2-222-222-2-1-111-222-2-1111-1-1-1-1110000000011-1-1111-1-1-10022−2−2−2−222-1-1-100000011100−222−200
χ2622-2-2-22-2222-2-2-2-222-222-2-1-111-222-2-1111-1-1-1-1110000000011-1-1111-1-1-100−2−22222−2−2-1-1-1000000111002−2−2200
χ272-22i−2i00002-22i−2i2-22i−2i00002-22i−2i00002000-20002i−2i2-22i−2i1+i−1−i1−i−1+i2-22i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000001+i−1−i1−i−1+i00000000000
χ282-22i−2i00002-22i−2i2-22i−2i00002-22i−2i00002000-20002i−2i2-22i−2i−1−i1+i−1+i1−i2-22i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000−1−i1+i−1+i1−i00000000000
χ292-2−2i2i00002-2−2i2i2-2−2i2i00002-2−2i2i00002000-2000−2i2i2-2−2i2i1−i−1+i1+i−1−i2-2−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000001−i−1+i1+i−1−i00000000000
χ302-2−2i2i00002-2−2i2i2-2−2i2i00002-2−2i2i00002000-2000−2i2i2-2−2i2i−1+i1−i−1−i1+i2-2−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000−1+i1−i−1−i1+i00000000000
χ3133333333333333333333000033330000000000-1-1-1-111110000000000-1-1-1-1-1-1-1-1-1-1000111111000-1-1-1-1-1-111
χ3233333333333333333333000033330000000000-1-1-1-1-1-1-1-10000000000-1-111111111000-1-1-1-1-1-1000-1-11111-1-1
χ33333333-3-33333333333330000-3-3-3-30000000000-1-1-1-111110000000000-1-1-1-1-1-1-1-1-1-1000-1-11111000111111-1-1
χ34333333-3-33333333333330000-3-3-3-30000000000-1-1-1-1-1-1-1-10000000000-1-11111111100011-1-1-1-100011-1-1-1-111
χ3533-3-3-333-333-3-333-3-3-33-3300003-33-30000000000-1-111ii−i−i0000000000-11−i−i−i−iiiii000i−iii−i−i000-11−i−iiii−i
χ3633-3-3-333-333-3-333-3-3-33-3300003-33-30000000000-1-111−i−iii0000000000-11iiii−i−i−i−i000−ii−i−iii000-11ii−i−i−ii
χ3733-3-3-33-3333-3-333-3-3-33-330000-33-330000000000-1-111ii−i−i0000000000-11−i−i−i−iiiii000−iiii−i−i0001-1ii−i−i−ii
χ3833-3-3-33-3333-3-333-3-3-33-330000-33-330000000000-1-111−i−iii0000000000-11iiii−i−i−i−i000i−i−i−iii0001-1−i−iiii−i
χ39444444444444-4-4-4-444-4-4111144-4-4111111111100000000-1-1-1-11111110000000000-1-1-1000000-1-1-100000000
χ40444444-4-44444-4-4-4-444-4-41111-4-44411-1-111-1-11100000000-1-1-1-11-1-11-1-10000000000-111000000-11100000000
χ414444-4-4004444-4-4-4-4-4-444111100001-1−i3i31-1−i3i31100000000-1-1-1-1-1−i3i3-1−i3i300000000001i3−i30000001i3−i300000000
χ424444-4-4004444-4-4-4-4-4-444111100001-1i3−i31-1i3−i31100000000-1-1-1-1-1i3−i3-1i3−i300000000001−i3i30000001−i3i300000000
χ434444-4-4004444-4-4-4-4-4-444-2-2-2-20000-2200-2200-2-20000000022222002000000000000-200000000-20000000000
χ4444-4-44-40044-4-4-4-4444-4-4411-1-1000011−i3i31-1i3−i3-1-100000000-1-1111−i3i3-1i3−i30000000000-1i3−i30000001−i3i300000000
χ4544-4-44-40044-4-4-4-4444-4-4411-1-1000011i3−i31-1−i3i3-1-100000000-1-1111i3−i3-1−i3i30000000000-1−i3i30000001i3−i300000000
χ4644-4-44-40044-4-4-4-4444-4-44-2-2220000-2-200-2200220000000022-2-2-2002000000000000200000000-20000000000
χ4744-4-4-444-444-4-4-4-444-444-411-1-14-4-441-11111-1-1-1-100000000-1-111-1111-1-100000000001-1-1000000-11100000000
χ4844-4-4-44-4444-4-4-4-444-444-411-1-1-444-41-1-1-11111-1-100000000-1-111-1-1-11110000000000111000000-1-1-100000000
χ494-44i−4i00004-44i−4i4-44i−4i0000-22−2i2i0000-20002000−2i2i4-44i−4i0000-22−2i2i000000000000000000000000000000000000
χ504-44i−4i00004-44i−4i-44−4i4i0000-22−2i2i0000-20002000−2i2i000000002-22i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ514-44i−4i00004-44i−4i-44−4i4i0000-22−2i2i0000-20002000−2i2i000000002-22i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ524-4−4i4i00004-4−4i4i4-4−4i4i0000-222i−2i0000-200020002i−2i4-4−4i4i0000-222i−2i000000000000000000000000000000000000
χ534-4−4i4i00004-4−4i4i-444i−4i0000-222i−2i0000-200020002i−2i000000002-2−2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ544-4−4i4i00004-4−4i4i-444i−4i0000-222i−2i0000-200020002i−2i000000002-2−2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ556666-6-60066666666-6-6-6-6000000000000000000-2-2-2-200000000000000220000000000000000000000000000
χ5666-6-66-60066-6-666-6-66-66-6000000000000000000-2-222000000000000002-20000000000000000000000000000
χ576-66i−6i00006-66i−6i6-66i−6i0000000000000000000000-22−2i2i1+i−1−i1−i−1+i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000001+i−1−i1−i−1+i00000000000
χ586-66i−6i00006-66i−6i6-66i−6i0000000000000000000000-22−2i2i−1−i1+i−1+i1−i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000−1−i1+i−1+i1−i00000000000
χ596-6−6i6i00006-6−6i6i6-6−6i6i0000000000000000000000-222i−2i1−i−1+i1+i−1−i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000001−i−1+i1+i−1−i00000000000
χ606-6−6i6i00006-6−6i6i6-6−6i6i0000000000000000000000-222i−2i−1+i1−i−1−i1+i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000−1+i1−i−1−i1+i00000000000
χ6188888888-1-1-1-10000-1-1002222-1-100-1222-1222-1-1000022220000-1-1-1-1-1-1000000000000022-1-1-1-1000000000-1-1
χ6288888888-1-1-1-10000-1-1002222-1-100-1222-1222-1-10000-2-2-2-20000-1-1-1-1-1-10000000000000-2-2111100000000011
χ63888888-8-8-1-1-1-10000-1-10022221100-12-2-2-12-2-2-1-1000022220000-111-1110000000000000-2-2-1-1-1-100000000011
χ64888888-8-8-1-1-1-10000-1-10022221100-12-2-2-12-2-2-1-10000-2-2-2-20000-111-1110000000000000221111000000000-1-1
χ6588-8-8-888-8-1-11100001-10022-2-2-1100-1-222-12-2-21100002i2i−2i−2i00001-1-1-11100000000000002i−2i−i−iii000000000−ii
χ6688-8-8-888-8-1-11100001-10022-2-2-1100-1-222-12-2-2110000−2i−2i2i2i00001-1-1-1110000000000000−2i2iii−i−i000000000i−i
χ6788-8-8-88-88-1-11100001-10022-2-21-100-1-2-2-2-12221100002i2i−2i−2i0000111-1-1-10000000000000−2i2i−i−iii000000000i−i
χ6888-8-8-88-88-1-11100001-10022-2-21-100-1-2-2-2-1222110000−2i−2i2i2i0000111-1-1-100000000000002i−2iii−i−i000000000−ii
χ698-88i−8i00008-88i−8i-88−8i8i00002-22i−2i00002000-20002i−2i00000000-22−2i2i000000000000000000000000000000000000
χ708-8−8i8i00008-8−8i8i-888i−8i00002-2−2i2i00002000-2000−2i2i00000000-222i−2i000000000000000000000000000000000000
χ711616161616161616-2-2-2-20000-2-200-2-2-2-2-2-2001-2-2-21-2-2-211000000000000111111000000000000000000000000000000
χ72161616161616-16-16-2-2-2-20000-2-200-2-2-2-222001-2221-222110000000000001-1-11-1-1000000000000000000000000000000
χ7316161616-16-1600-2-2-2-20000220044440000-2-400-2-400-2-2000000000000200200000000000000000000000000000000
χ7416161616-16-1600-2-2-2-200002200-2-2-2-2000012−2i32i312−2i32i311000000000000-1i3−i3-1i3−i3000000000000000000000000000000
χ7516161616-16-1600-2-2-2-200002200-2-2-2-20000122i3−2i3122i3−2i311000000000000-1−i3i3-1−i3i3000000000000000000000000000000
χ761616-16-1616-1600-2-2220000-220044-4-40000-2400-2-40022000000000000-200200000000000000000000000000000000
χ771616-16-1616-1600-2-2220000-2200-2-22200001-2−2i32i3122i3−2i3-1-10000000000001i3−i3-1−i3i3000000000000000000000000000000
χ781616-16-1616-1600-2-2220000-2200-2-22200001-22i3−2i312−2i32i3-1-10000000000001−i3i3-1i3−i3000000000000000000000000000000
χ791616-16-16-161616-16-2-22200002-200-2-222-220012-2-21-222-1-1000000000000-1111-1-1000000000000000000000000000000
χ801616-16-16-1616-1616-2-22200002-200-2-2222-20012221-2-2-2-1-1000000000000-1-1-1111000000000000000000000000000000
χ8116-1616i−16i0000-22−2i2i000000004-44i−4i0000-20002000−2i2i00002+2i−2−2i2−2i−2+2i0000000000000000000000000−1−i1+i−1+i1−i00000000000
χ8216-1616i−16i0000-22−2i2i000000004-44i−4i0000-20002000−2i2i0000−2−2i2+2i−2+2i2−2i00000000000000000000000001+i−1−i1−i−1+i00000000000
χ8316-16−16i16i0000-222i−2i000000004-4−4i4i0000-200020002i−2i00002−2i−2+2i2+2i−2−2i0000000000000000000000000−1+i1−i−1−i1+i00000000000
χ8416-16−16i16i0000-222i−2i000000004-4−4i4i0000-200020002i−2i0000−2+2i2−2i−2−2i2+2i00000000000000000000000001−i−1+i1+i−1−i00000000000
χ8532-3232i−32i0000-44−4i4i00000000-44−4i4i00002000-20002i−2i000000000000000000000000000000000000000000000000
χ8632-32−32i32i0000-444i−4i00000000-444i−4i00002000-2000−2i2i000000000000000000000000000000000000000000000000

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