Finite Group Databasebeta

← Group #10691016

Character table — Group #10691016

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12222234444446661212121244466888812121212121288888812122424242424242424242424242424242444448824242424444444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ91111-1-11-1-111-1-1111111111-1-1-1ii−i−i-1-1-1-1-1-1i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-1-11ii−i−iii−i−i1-1
χ101111-1-11-1-111-1-1111111111-1-1-1ii−i−i-1-1-1-1-1-1i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-1111-111-1-11-1−i−iii−i−iii-11
χ111111-1-11-1-111-1-1111111111-1-1-1ii−i−i-1-1-1-1-1-1i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii11-1-1-11-1-111-11−i−iiiii−i−i-11
χ121111-1-11-1-111-1-1111111111-1-1-1ii−i−i-1-1-1-1-1-1i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-1111-1ii−i−i−i−iii1-1
χ131111-1-11-1-111-1-1111111111-1-1-1−i−iii-1-1-1-1-1-1−iiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-1-111-11ii−i−i−i−iii-11
χ141111-1-11-1-111-1-1111111111-1-1-1−i−iii-1-1-1-1-1-1−iiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-1111-1−i−iiiii−i−i1-1
χ151111-1-11-1-111-1-1111111111-1-1-1−i−iii-1-1-1-1-1-1−ii−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-1-11−i−iii−i−iii1-1
χ161111-1-11-1-111-1-1111111111-1-1-1−i−iii-1-1-1-1-1-1−ii−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-1111-111-1-11-1ii−i−iii−i−i-11
χ17222222222-2-2-2-2222-2-2-2-2-22-222000022-2-2-2-20000002-2000000000000000000000000000000002i−2i2i−2i00
χ18222222222-2-2-2-2222-2-2-2-2-22-222000022-2-2-2-20000002-200000000000000000000000000000000−2i2i−2i2i00
χ192222222-2-222-2-22222222-2-22220000-2-222-2-2000000-2-2000000000000000022-2-20000002-20000000000
χ202222222-2-222-2-22222222-2-22220000-2-222-2-2000000-2-20000000000000000-2-222000000-220000000000
χ212222222-2-2-2-222222-2-2-2-22-2-2222222-2-2-2-222-2-20000-2222-2-222-2-2000000000000000000000000000000
χ222222222-2-2-2-222222-2-2-2-22-2-222-2-2-2-2-2-2-2-222220000-22-2-222-2-222000000000000000000000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ25222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ26222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ27222222-1-2-2-2-222-1-1-111112-2-2-1-122221111-1-1-2-200001-1-1-111-1-11133−3−333−3−30000003−33−3000000000000
χ28222222-1-2-2-2-222-1-1-111112-2-2-1-122221111-1-1-2-200001-1-1-111-1-111−3−333−3−333000000−33−33000000000000
χ29222222-1-2-2-2-222-1-1-111112-2-2-1-1-2-2-2-21111-1-12200001-111-1-111-1-133−3−333−3−3000000−33−33000000000000
χ30222222-1-2-2-2-222-1-1-111112-2-2-1-1-2-2-2-21111-1-12200001-111-1-111-1-1−3−333−3−3330000003−33−3000000000000
χ312222-2-222222222222222-2-2-2-2-2000022-2-222000000-2-200000000000000002222000000-2-20000000000
χ322222-2-222222222222222-2-2-2-2-2000022-2-222000000-2-20000000000000000-2-2-2-2000000220000000000
χ332222-2-2222-2-2-2-2222-2-2-2-22-22-2-22i2i−2i−2i2222-2-2−2i2i0000-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ342222-2-2222-2-2-2-2222-2-2-2-22-22-2-2−2i−2i2i2i2222-2-22i−2i0000-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ352222-2-22-2-2-2-222222-2-2-2-2-222-2-20000-2-222220000002-2000000000000000000000000000000002-2-2200
χ362222-2-22-2-2-2-222222-2-2-2-2-222-2-20000-2-222220000002-200000000000000000000000000000000-222-200
χ372222-2-2-122-2-2-2-2-1-1-111112-22112i2i−2i−2i-1-1-1-111−2i2i00001-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000−333−3000000000000
χ382222-2-2-122-2-2-2-2-1-1-111112-22112i2i−2i−2i-1-1-1-111−2i2i00001-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000003−3−33000000000000
χ392222-2-2-122-2-2-2-2-1-1-111112-2211−2i−2i2i2i-1-1-1-1112i−2i00001-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000003−3−33000000000000
χ402222-2-2-122-2-2-2-2-1-1-111112-2211−2i−2i2i2i-1-1-1-1112i−2i00001-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000−333−3000000000000
χ412222-2-2-1-2-222-2-2-1-1-1-1-1-1-122-2112i2i−2i−2i1111112i−2i2i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii00002-2-1-111000000000000
χ422222-2-2-1-2-222-2-2-1-1-1-1-1-1-122-2112i2i−2i−2i1111112i−2i−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-1000000000000
χ432222-2-2-1-2-222-2-2-1-1-1-1-1-1-122-211−2i−2i2i2i111111−2i2i2i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-1000000000000
χ442222-2-2-1-2-222-2-2-1-1-1-1-1-1-122-211−2i−2i2i2i111111−2i2i−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i00002-2-1-111000000000000
χ452-22-20022i−2i2-22i−2i2-2-222-2-20000000002i−2i002i−2i001+i−1−i1−i−1+i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22i−2i000000001+i−1−i1−i−1+i000000
χ462-22-20022i−2i2-22i−2i2-2-222-2-20000000002i−2i002i−2i001+i−1−i1−i−1+i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i00000000−1−i1+i−1+i1−i000000
χ472-22-20022i−2i2-22i−2i2-2-222-2-20000000002i−2i002i−2i00−1−i1+i−1+i1−i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22i−2i00000000−1−i1+i−1+i1−i000000
χ482-22-20022i−2i2-22i−2i2-2-222-2-20000000002i−2i002i−2i00−1−i1+i−1+i1−i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i000000001+i−1−i1−i−1+i000000
χ492-22-2002−2i2i2-2−2i2i2-2-222-2-2000000000−2i2i00−2i2i001−i−1+i1+i−1−i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2−2i2i000000001−i−1+i1+i−1−i000000
χ502-22-2002−2i2i2-2−2i2i2-2-222-2-2000000000−2i2i00−2i2i001−i−1+i1+i−1−i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i00000000−1+i1−i−1−i1+i000000
χ512-22-2002−2i2i2-2−2i2i2-2-222-2-2000000000−2i2i00−2i2i00−1+i1−i−1−i1+i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2−2i2i00000000−1+i1−i−1−i1+i000000
χ522-22-2002−2i2i2-2−2i2i2-2-222-2-2000000000−2i2i00−2i2i00−1+i1−i−1−i1+i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i000000001−i−1+i1+i−1−i000000
χ53444444-244-4-4-4-4-2-2-22222-44-4-2-20000-2-22222000000-2200000000000000000000000000000000000000
χ54444444-2-4-444-4-4-2-2-2-2-2-2-2-4-44-2-2000022-2-2220000002200000000000000000000000000000000000000
χ554444-4-4-2444444-2-2-2-2-2-2-2-4-4-4220000-2-222-2-20000002200000000000000000000000000000000000000
χ564444-4-4-2-4-4-4-444-2-2-22222-44422000022-2-2-2-2000000-2200000000000000000000000000000000000000
χ574-44-40044i−4i-44−4i4i4-4-4-4-4440000000004i−4i00−4i4i0000000000000000000000000000000000000000000000
χ584-44-4004−4i4i-444i−4i4-4-4-4-444000000000−4i4i004i−4i0000000000000000000000000000000000000000000000
χ594-44-400-24i−4i4-44i−4i-222-2-222000000000−2i2i00−2i2i002+2i−2−2i2−2i−2+2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000
χ604-44-400-24i−4i4-44i−4i-222-2-222000000000−2i2i00−2i2i00−2−2i2+2i−2+2i2−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000
χ614-44-400-24i−4i-44−4i4i-22222-2-2000000000−2i2i002i−2i0000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000
χ624-44-400-24i−4i-44−4i4i-22222-2-2000000000−2i2i002i−2i0000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000
χ634-44-400-2−4i4i4-4−4i4i-222-2-2220000000002i−2i002i−2i002−2i−2+2i2+2i−2−2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000
χ644-44-400-2−4i4i4-4−4i4i-222-2-2220000000002i−2i002i−2i00−2+2i2−2i−2−2i2+2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000
χ654-44-400-2−4i4i-444i−4i-22222-2-20000000002i−2i00−2i2i0000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000
χ664-44-400-2−4i4i-444i−4i-22222-2-20000000002i−2i00−2i2i0000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000
χ674-4-444-44000000-44-400000004-4−2i22i2−2i22i200000000000000−2i22i200−2i22i200000000000000000000000000000000
χ684-4-444-44000000-44-400000004-42i2−2i22i2−2i2000000000000002i2−2i2002i2−2i200000000000000000000000000000000
χ694-4-444-4-20000002-2223−2323−23000-22−2i22i2−2i22i20023−230000000000i2−i2i6−i6i2−i2i6−i6000000000000000000000000000000
χ704-4-444-4-20000002-2223−2323−23000-222i2−2i22i2−2i20023−230000000000−i2i2−i6i6−i2i2−i6i6000000000000000000000000000000
χ714-4-444-4-20000002-22−2323−2323000-22−2i22i2−2i22i200−23230000000000i2−i2−i6i6i2−i2−i6i6000000000000000000000000000000
χ724-4-444-4-20000002-22−2323−2323000-222i2−2i22i2−2i200−23230000000000−i2i2i6−i6−i2i2i6−i6000000000000000000000000000000
χ734-4-44-444000000-44-40000000-4422−22−22220000000000000022−2200−222200000000000000000000000000000000
χ744-4-44-444000000-44-40000000-44−222222−2200000000000000−22220022−2200000000000000000000000000000000
χ754-4-44-44-20000002-2223−2323−230002-222−22−222200−23230000000000−22−662−26−6000000000000000000000000000000
χ764-4-44-44-20000002-2223−2323−230002-2−222222−2200−232300000000002−26−6−22−66000000000000000000000000000000
χ774-4-44-44-20000002-22−2323−23230002-222−22−22220023−230000000000−226−62−2−66000000000000000000000000000000
χ784-4-44-44-20000002-22−2323−23230002-2−222222−220023−2300000000002−2−66−226−6000000000000000000000000000000
χ7988-8-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

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