Finite Group Databasebeta

← Group #10692489

Character table — Group #10692489

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order12222234466644444661212121212121212444488881212242424242424242444448812121212242424242244442488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1
χ91111-1-11-1-111111-11-1-1-111-1-111-1-1i−ii−iii−i−i1-1iiii−i−i−i−iii−i−i1-1ii−i−i11-1-11-11-1i−i1-1i−i
χ101111-1-11-1-111111-11-1-1-111-1-111-1-1i−ii−iii−i−i1-1iiii−i−i−i−i−i−iii1-1ii−i−i11-1-1-11-11−ii-11−ii
χ111111-1-11-1-111111-11-1-1-111-1-111-1-1i−ii−i−i−iii1-1−i−i−i−iiiiiii−i−i-11ii−i−i-1-1111-11-1i−i-11−ii
χ121111-1-11-1-111111-11-1-1-111-1-111-1-1i−ii−i−i−iii1-1−i−i−i−iiiii−i−iii-11ii−i−i-1-111-11-11−ii1-1i−i
χ131111-1-11-1-111111-11-1-1-111-1-111-1-1−ii−iiii−i−i1-1iiii−i−i−i−iii−i−i-11−i−iii-1-111-11-11i−i1-1−ii
χ141111-1-11-1-111111-11-1-1-111-1-111-1-1−ii−iiii−i−i1-1iiii−i−i−i−i−i−iii-11−i−iii-1-1111-11-1−ii-11i−i
χ151111-1-11-1-111111-11-1-1-111-1-111-1-1−ii−ii−i−iii1-1−i−i−i−iiiiiii−i−i1-1−i−iii11-1-1-11-11i−i-11i−i
χ161111-1-11-1-111111-11-1-1-111-1-111-1-1−ii−ii−i−iii1-1−i−i−i−iiiii−i−iii1-1−i−iii11-1-11-11-1−ii1-1−ii
χ17222222222222-22-2-2-222-2-2-2-2-2-222000000002-200000000222200000000000000-2-20000
χ18222222222222-22-2-2-222-2-2-2-2-2-222000000002-200000000-2-2-2-200000000000000220000
χ192222222-2-22222-2-2-222222-2-2-2-2-2-222-2-20000-22000000000000002-22-200000000000000
χ202222222-2-22222-2-2-222222-2-2-2-2-2-2-2-2220000-2200000000000000-22-2200000000000000
χ212222222-2-2222-2-222-222-2-22222-2-200000000-2-2000000000000000000000022-2-2000000
χ222222222-2-2222-2-222-222-2-22222-2-200000000-2-20000000000000000000000-2-222000000
χ23222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-10000000000
χ24222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-2-1-1-1-111110000000000
χ25222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-2111111110000000000
χ26222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-10000000000
χ27222222-1-2-2-1-1-12-2-2-22-1-1-1-111111122-2-200001-133−3−333−3−3000000-11-113−33−30000000000
χ28222222-1-2-2-1-1-12-2-2-22-1-1-1-111111122-2-200001-1−3−333−3−333000000-11-11−33−330000000000
χ29222222-1-2-2-1-1-12-2-2-22-1-1-1-1111111-2-22200001-133−3−333−3−30000001-11-1−33−330000000000
χ30222222-1-2-2-1-1-12-2-2-22-1-1-1-1111111-2-22200001-1−3−333−3−3330000001-11-13−33−30000000000
χ312222-2-22222222-22-2-2-2-22222-2-2222i−2i−2i2i0000-2-2000000000000002i−2i−2i2i00000000000000
χ322222-2-22222222-22-2-2-2-22222-2-222−2i2i2i−2i0000-2-200000000000000−2i2i2i−2i00000000000000
χ332222-2-2222222-2-2-222-2-2-2-2-2-2222200000000-2200000000000000000000002-2-22000000
χ342222-2-2222222-2-2-222-2-2-2-2-2-2222200000000-220000000000000000000000-222-2000000
χ352222-2-22-2-2222-222-22-2-2-2-222-2-2-2-20000000022000000002i2i−2i−2i00000000000000−2i2i0000
χ362222-2-22-2-2222-222-22-2-2-2-222-2-2-2-2000000002200000000−2i−2i2i2i000000000000002i−2i0000
χ372222-2-2-122-1-1-12-22-2-211-1-1-1-111-1-12i−2i−2i2i000011−i3−i3i3i3i3i3−i3−i3000000−iii−i−333−30000000000
χ382222-2-2-122-1-1-12-22-2-211-1-1-1-111-1-12i−2i−2i2i000011i3i3−i3−i3−i3−i3i3i3000000−iii−i3−3−330000000000
χ392222-2-2-122-1-1-12-22-2-211-1-1-1-111-1-1−2i2i2i−2i000011−i3−i3i3i3i3i3−i3−i3000000i−i−ii3−3−330000000000
χ402222-2-2-122-1-1-12-22-2-211-1-1-1-111-1-1−2i2i2i−2i000011i3i3−i3−i3−i3−i3i3i3000000i−i−ii−333−30000000000
χ412222-2-2-1-2-2-1-1-122-22-211-1-111-1-1112i−2i2i−2i2i2i−2i−2i-11−i−i−i−iiiii00002-2−i−iii-1-1110000000000
χ422222-2-2-1-2-2-1-1-122-22-211-1-111-1-1112i−2i2i−2i−2i−2i2i2i-11iiii−i−i−i−i0000-22−i−iii11-1-10000000000
χ432222-2-2-1-2-2-1-1-122-22-211-1-111-1-111−2i2i−2i2i2i2i−2i−2i-11−i−i−i−iiiii0000-22ii−i−i11-1-10000000000
χ442222-2-2-1-2-2-1-1-122-22-211-1-111-1-111−2i2i−2i2i−2i−2i2i2i-11iiii−i−i−i−i00002-2ii−i−i-1-1110000000000
χ45444444-244-2-2-2-44-4-4-4-2-2222222-2-200000000-2200000000000000000000000000000000
χ46444444-2-4-4-2-2-2-4-444-4-2-222-2-2-2-222000000002200000000000000000000000000000000
χ474444-4-4-244-2-2-2-4-4-444222222-2-2-2-2000000002-200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-2-444-442222-2-2222200000000-2-200000000000000000000000000000000
χ4944-4-40044i−4i4-4-400000000000004i−4i0000000000000000002+2i−2−2i2−2i−2+2i00000000000000000000
χ5044-4-40044i−4i4-4-400000000000004i−4i000000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000
χ5144-4-4004−4i4i4-4-40000000000000−4i4i0000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000
χ5244-4-4004−4i4i4-4-40000000000000−4i4i000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000
χ534-44-44-4400-44-4000004-40000000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ544-44-44-4400-44-4000004-4000000000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ554-44-44-4-2002-2200000-220023−2323−230000002i−2i2i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ564-44-44-4-2002-2200000-220023−2323−23000000−2i2i−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ574-44-44-4-2002-2200000-2200−2323−23230000002i−2i2i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ584-44-44-4-2002-2200000-2200−2323−2323000000−2i2i−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ594-44-4-44400-44-400000-440000000000002-2-22002-22-2-22-22000000000000000000000000
χ604-44-4-44400-44-400000-44000000000000-222-200-22-222-22-2000000000000000000000000
χ614-44-4-44-2002-22000002-20023−23−23230000002-2-2200−1+31−3−1−31+31−3−1+31+3−1−3000000000000000000000000
χ624-44-4-44-2002-22000002-20023−23−2323000000-222-2001−3−1+31+3−1−3−1+31−3−1−31+3000000000000000000000000
χ634-44-4-44-2002-22000002-200−232323−230000002-2-2200−1−31+3−1+31−31+3−1−31−3−1+3000000000000000000000000
χ644-44-4-44-2002-22000002-200−232323−23000000-222-2001+3−1−31−3−1+3−1−31+3−1+31−3000000000000000000000000
χ6588-8-800-48i−8i-4440000000000000−4i4i000000000000000000000000000000000000000000
χ6688-8-800-4−8i8i-44400000000000004i−4i000000000000000000000000000000000000000000
χ678-8-8800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-8-8800-40044-4000000043−43000000000000000000000000000000000000000000000000
χ698-8-8800-40044-40000000−4343000000000000000000000000000000000000000000000000

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