Finite Group Databasebeta

← Group #10692480

Character table — Group #10692480

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881616161616161616161616162424242424242424242424244848
order12222234466644444444466121212121212121244121212121212121212128888242424242424242444444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ91111-1-11-1-11111-11ii−i−i1-1-1-111-1-111-1-1i−i1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-11-11-1i−ii−iii−i−i1-1
χ101111-1-11-1-11111-11ii−i−i1-1-1-111-1-111-1-1i−i1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-1-11-11−ii−ii−i−iii-11
χ111111-1-11-1-11111-11ii−i−i1-1-1-111-1-111-1-1i−i1-1iiii−i−i−i−i−ii-11−i−iii-1-1111-11-1i−ii−i−i−iii-11
χ121111-1-11-1-11111-11ii−i−i1-1-1-111-1-111-1-1i−i1-1iiii−i−i−i−i−ii-11−i−iii-1-111-11-11−ii−iiii−i−i1-1
χ131111-1-11-1-11111-11−i−iii1-1-1-111-1-111-1-1−ii1-1−i−i−i−iiiiii−i-11ii−i−i-1-1111-11-1−ii−iiii−i−i-11
χ141111-1-11-1-11111-11−i−iii1-1-1-111-1-111-1-1−ii1-1−i−i−i−iiiiii−i-11ii−i−i-1-111-11-11i−ii−i−i−iii1-1
χ151111-1-11-1-11111-11−i−iii1-1-1-111-1-111-1-1−ii1-1−i−i−i−iiiii−ii1-1−i−iii11-1-11-11-1−ii−ii−i−iii1-1
χ161111-1-11-1-11111-11−i−iii1-1-1-111-1-111-1-1−ii1-1−i−i−i−iiiii−ii1-1−i−iii11-1-1-11-11i−ii−iii−i−i-11
χ172222222222222-2-22222-2-2222222-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-2-2-222-2-22200000000000000000000000000
χ192222222-2-2222-22-200002-222-2-2-2-222-2-200-220000000000000000000022-2-20000000000
χ202222222-2-2222-22-200002-222-2-2-2-222-2-200-2200000000000000000000-2-2220000000000
χ212222222-2-2222-2-220000-2222-2-2-2-2-2-222002-200000000000000000000000022-2-2000000
χ222222222-2-2222-2-220000-2222-2-2-2-2-2-222002-2000000000000000000000000-2-222000000
χ23222222-122-1-1-1222222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ24222222-122-1-1-1222222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ25222222-122-1-1-1222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ26222222-122-1-1-1222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ27222222-122-1-1-12-2-22222-2-2-1-1-1-1-1-11111-2-211-1-111-1-11100003−33−33−33−300000000000000
χ28222222-122-1-1-12-2-22222-2-2-1-1-1-1-1-11111-2-211-1-111-1-1110000−33−33−33−3300000000000000
χ29222222-122-1-1-12-2-2-2-2-2-2-2-2-1-1-1-1-1-11111221111-1-111-1-100003−33−3−33−3300000000000000
χ30222222-122-1-1-12-2-2-2-2-2-2-2-2-1-1-1-1-1-11111221111-1-111-1-10000−33−333−33−300000000000000
χ312222-2-2222222-2220000-2-2-2-2-2-222-2-2-2-200220000000000000000000000002i−2i−2i2i000000
χ322222-2-2222222-2220000-2-2-2-2-2-222-2-2-2-20022000000000000000000000000−2i2i2i−2i000000
χ332222-2-2222222-2-2-2000022-2-2-2-222222200-2-2000000000000000000002-2-220000000000
χ342222-2-2222222-2-2-2000022-2-2-2-222222200-2-200000000000000000000-222-20000000000
χ352222-2-22-2-222222-22i2i−2i−2i-22-2-222-2-2-2-222−2i2i-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-2-222222-2−2i−2i2i2i-22-2-222-2-2-2-2222i−2i-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-1-2-2-1-1-122-22i2i−2i−2i-2211-1-11111-1-1−2i2i1-1−i−iiiii−i−i0000−i3i3i3−i3−333−300000000000000
χ382222-2-2-1-2-2-1-1-122-22i2i−2i−2i-2211-1-11111-1-1−2i2i1-1−i−iiiii−i−i0000i3−i3−i3i33−3−3300000000000000
χ392222-2-2-1-2-2-1-1-122-2−2i−2i2i2i-2211-1-11111-1-12i−2i1-1ii−i−i−i−iii0000−i3i3i3−i33−3−3300000000000000
χ402222-2-2-1-2-2-1-1-122-2−2i−2i2i2i-2211-1-11111-1-12i−2i1-1ii−i−i−i−iii0000i3−i3−i3i3−333−300000000000000
χ412222-2-2-1-2-2-1-1-12-222i2i−2i−2i2-211-1-111-1-1112i−2i-11−i−i−i−iiiii2i−2i2-2−i−iii-1-11100000000000000
χ422222-2-2-1-2-2-1-1-12-222i2i−2i−2i2-211-1-111-1-1112i−2i-11−i−i−i−iiiii−2i2i-22ii−i−i11-1-100000000000000
χ432222-2-2-1-2-2-1-1-12-22−2i−2i2i2i2-211-1-111-1-111−2i2i-11iiii−i−i−i−i2i−2i-22−i−iii11-1-100000000000000
χ442222-2-2-1-2-2-1-1-12-22−2i−2i2i2i2-211-1-111-1-111−2i2i-11iiii−i−i−i−i−2i2i2-2ii−i−i-1-11100000000000000
χ45444444-2-4-4-2-2-2-44-400004-4-2-22222-2-222002-20000000000000000000000000000000000
χ46444444-2-4-4-2-2-2-4-440000-44-2-2222222-2-200-220000000000000000000000000000000000
χ474444-4-4-244-2-2-2-4440000-4-42222-2-2222200-2-20000000000000000000000000000000000
χ484444-4-4-244-2-2-2-4-4-40000442222-2-2-2-2-2-200220000000000000000000000000000000000
χ4944-4-44-44004-4-40000000004-400000000000000000000000000000000000000002-22-200
χ5044-4-44-44004-4-40000000004-40000000000000000000000000000000000000000-22-2200
χ5144-4-4-444004-4-4000000000-4400000000000000000000000000000000000000002i−2i−2i2i00
χ5244-4-4-444004-4-4000000000-440000000000000000000000000000000000000000−2i2i2i−2i00
χ534-4-440044i−4i-44-40002+2i−2−2i2−2i−2+2i0000004i−4i000000002+2i−2−2i002−2i−2+2i0000000000000000000000000000
χ544-4-440044i−4i-44-4000−2−2i2+2i−2+2i2−2i0000004i−4i00000000−2−2i2+2i00−2+2i2−2i0000000000000000000000000000
χ554-4-44004−4i4i-44-40002−2i−2+2i2+2i−2−2i000000−4i4i000000002−2i−2+2i002+2i−2−2i0000000000000000000000000000
χ564-4-44004−4i4i-44-4000−2+2i2−2i−2−2i2+2i000000−4i4i00000000−2+2i2−2i00−2−2i2+2i0000000000000000000000000000
χ574-4-4400-24i−4i2-220002+2i−2−2i2−2i−2+2i000000−2i2i23−23−2i32i30000−1−i1+i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−1+i1−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000000000000000
χ584-4-4400-24i−4i2-220002+2i−2−2i2−2i−2+2i000000−2i2i−23232i3−2i30000−1−i1+iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−1+i1−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000000000000000
χ594-4-4400-24i−4i2-22000−2−2i2+2i−2+2i2−2i000000−2i2i23−23−2i32i300001+i−1−iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ111−i−1+iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000000000000000
χ604-4-4400-24i−4i2-22000−2−2i2+2i−2+2i2−2i000000−2i2i−23232i3−2i300001+i−1−i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ111−i−1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000000000000000
χ614-4-4400-2−4i4i2-220002−2i−2+2i2+2i−2−2i0000002i−2i23−232i3−2i30000−1+i1−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−1−i1+iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000000000000000
χ624-4-4400-2−4i4i2-220002−2i−2+2i2+2i−2−2i0000002i−2i−2323−2i32i30000−1+i1−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−1−i1+i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000000000000000
χ634-4-4400-2−4i4i2-22000−2+2i2−2i−2−2i2+2i0000002i−2i23−232i3−2i300001−i−1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ111+i−1−i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000000000000000
χ644-4-4400-2−4i4i2-22000−2+2i2−2i−2−2i2+2i0000002i−2i−2323−2i32i300001−i−1+iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ111+i−1−iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000000000000000
χ6588-8-88-8-400-444000000000-440000000000000000000000000000000000000000000000
χ6688-8-8-88-400-4440000000004-40000000000000000000000000000000000000000000000
χ678-88-800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-88-800-40044-40000000000043−4300000000000000000000000000000000000000000000
χ698-88-800-40044-400000000000−434300000000000000000000000000000000000000000000

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