Finite Group Databasebeta

← Group #10692472

Character table — Group #10692472

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order122222344666444446612121212121212122244888812122424242424242424444466881212242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1
χ91111-1-11-1-111111-1-11-1-111-1-1-1-1-1-11-11-1ii−i−i11iiii−i−i−i−iii−i−i1-1i−i1-1ii−i−ii−ii−ii−i1-11-1
χ101111-1-11-1-111111-1-11-1-111-1-1-1-1-1-11-11-1ii−i−i11iiii−i−i−i−i−i−iii1-1i−i1-1ii−i−i−ii−ii−ii-11-11
χ111111-1-11-1-111111-1-11-1-111-1-1-1-1-1-11-11-1−i−iii11−i−i−i−iiiiiii−i−i1-1−ii1-1−i−iiii−ii−ii−i-11-11
χ121111-1-11-1-111111-1-11-1-111-1-1-1-1-1-11-11-1−i−iii11−i−i−i−iiiii−i−iii1-1−ii1-1−i−iii−ii−ii−ii1-11-1
χ131111-1-11-1-111111-1-11-1-111-1-1-1-1-1-1-11-11ii−i−i11iiii−i−i−i−iii−i−i-11−ii-11−i−iii−iii−i−ii1-1-11
χ141111-1-11-1-111111-1-11-1-111-1-1-1-1-1-1-11-11ii−i−i11iiii−i−i−i−i−i−iii-11−ii-11−i−iiii−i−iii−i-111-1
χ151111-1-11-1-111111-1-11-1-111-1-1-1-1-1-1-11-11−i−iii11−i−i−i−iiiiiii−i−i-11i−i-11ii−i−i−iii−i−ii-111-1
χ161111-1-11-1-111111-1-11-1-111-1-1-1-1-1-1-11-11−i−iii11−i−i−i−iiiii−i−iii-11i−i-11ii−i−ii−i−iii−i1-1-11
χ172222222222222-2-2-2-222-2-2-2-222-2-2000000002-2000000002222000000000000-2-2000000
χ182222222222222-2-2-2-222-2-2-2-222-2-2000000002-200000000-2-2-2-200000000000022000000
χ192222222-2-2222-22-22-22222-2-2-2-22200000000-2-200000000000000000000002200-2-20000
χ202222222-2-2222-22-22-22222-2-2-2-22200000000-2-20000000000000000000000-2-200220000
χ212222222-2-2222-2-22-2222-2-222-2-2-2-222-2-20000-220000000000002200-2-200000000000000
χ222222222-2-2222-2-22-2222-2-222-2-2-2-2-2-2220000-22000000000000-2-2002200000000000000
χ23222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000-1-122-1-1-1-1-1-10000000000
χ24222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-1-1-2-2-1-111110000000000
χ25222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000011-2-21111110000000000
χ26222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000112211-1-1-1-10000000000
χ27222222-1-2-2-1-1-1-2-22-22-1-111-1-1111122-2-200001-133−3−333−3−30000-1-100113−33−30000000000
χ28222222-1-2-2-1-1-1-2-22-22-1-111-1-1111122-2-200001-1−3−333−3−3330000-1-10011−33−330000000000
χ29222222-1-2-2-1-1-1-2-22-22-1-111-1-11111-2-22200001-133−3−333−3−300001100-1-1−33−330000000000
χ30222222-1-2-2-1-1-1-2-22-22-1-111-1-11111-2-22200001-1−3−333−3−33300001100-1-13−33−30000000000
χ312222-2-2222222-222-2-2-2-2222222-2-200000000-2-200000000000000000000002i−2i00−2i2i0000
χ322222-2-2222222-222-2-2-2-2222222-2-200000000-2-20000000000000000000000−2i2i002i−2i0000
χ332222-2-2222222-2-2-222-2-2-2-2-2-222222-2-220000-220000000000002-200-2200000000000000
χ342222-2-2222222-2-2-222-2-2-2-2-2-22222-222-20000-22000000000000-22002-200000000000000
χ352222-2-22-2-22222-222-2-2-2-2-222-2-222000000002-2000000002i2i−2i−2i000000000000−2i2i000000
χ362222-2-22-2-22222-222-2-2-2-2-222-2-222000000002-200000000−2i−2i2i2i0000000000002i−2i000000
χ372222-2-2-122-1-1-1-2-2-222111111-1-1-1-12-2-2200001-1−i3−i3i3i3i3i3−i3−i30000-11001-1−i3i3i3−i30000000000
χ382222-2-2-122-1-1-1-2-2-222111111-1-1-1-12-2-2200001-1i3i3−i3−i3−i3−i3i3i30000-11001-1i3−i3−i3i30000000000
χ392222-2-2-122-1-1-1-2-2-222111111-1-1-1-1-222-200001-1−i3−i3i3i3i3i3−i3−i300001-100-11i3−i3−i3i30000000000
χ402222-2-2-122-1-1-1-2-2-222111111-1-1-1-1-222-200001-1i3i3−i3−i3−i3−i3i3i300001-100-11−i3i3i3−i30000000000
χ412222-2-2-1-2-2-1-1-122-2-2211-1-11111112-22-22i2i−2i−2i-1-1−i−i−i−iiiii0000-112i−2i-11−i−iii0000000000
χ422222-2-2-1-2-2-1-1-122-2-2211-1-11111112-22-2−2i−2i2i2i-1-1iiii−i−i−i−i0000-11−2i2i-11ii−i−i0000000000
χ432222-2-2-1-2-2-1-1-122-2-2211-1-1111111-22-222i2i−2i−2i-1-1−i−i−i−iiiii00001-1−2i2i1-1ii−i−i0000000000
χ442222-2-2-1-2-2-1-1-122-2-2211-1-1111111-22-22−2i−2i2i2i-1-1iiii−i−i−i−i00001-12i−2i1-1−i−iii0000000000
χ45444444-244-2-2-24-4-4-4-4-2-22222-2-22200000000-2200000000000000000000000000000000
χ46444444-2-4-4-2-2-2-44-44-4-2-2-2-22222-2-2000000002200000000000000000000000000000000
χ474444-4-4-244-2-2-2-444-4-422-2-2-2-2-2-222000000002200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-24-444-42222-2-222-2-200000000-2200000000000000000000000000000000
χ4944-4-44-44004-4-4000004-40000000000002-22-2002-22-22-22-2000000000000000000000000
χ5044-4-44-44004-4-4000004-4000000000000-22-2200-22-22-22-22000000000000000000000000
χ5144-4-44-4-200-22200000-2223−23000023−2300002-22-200−1+31−3−1−31+3−1+31−3−1−31+3000000000000000000000000
χ5244-4-44-4-200-22200000-2223−23000023−230000-22-22001−3−1+31+3−1−31−3−1+31+3−1−3000000000000000000000000
χ5344-4-44-4-200-22200000-22−23230000−232300002-22-200−1−31+3−1+31−3−1−31+3−1+31−3000000000000000000000000
χ5444-4-44-4-200-22200000-22−23230000−23230000-22-22001+3−1−31−3−1+31+3−1−31−3−1+3000000000000000000000000
χ5544-4-4-444004-4-400000-440000000000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5644-4-4-444004-4-400000-44000000000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5744-4-4-44-200-222000002-223−230000−232300002i−2i−2i2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ5844-4-4-44-200-222000002-223−230000−23230000−2i2i2i−2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ5944-4-4-44-200-222000002-2−2323000023−2300002i−2i−2i2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ6044-4-4-44-200-222000002-2−2323000023−230000−2i2i2i−2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ614-44-40044i−4i-44-4000000000004i−4i000000000000000000002+2i−2−2i2−2i−2+2i00000000000000000000
χ624-44-40044i−4i-44-4000000000004i−4i00000000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000
χ634-44-4004−4i4i-44-400000000000−4i4i000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000
χ644-44-4004−4i4i-44-400000000000−4i4i00000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000
χ658-88-800-48i−8i4-4400000000000−4i4i00000000000000000000000000000000000000000000
χ668-88-800-4−8i8i4-44000000000004i−4i00000000000000000000000000000000000000000000
χ678-8-8800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-8-8800-40044-4000000000−4i34i30000000000000000000000000000000000000000000000
χ698-8-8800-40044-40000000004i3−4i30000000000000000000000000000000000000000000000

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