Finite Group Databasebeta

← Group #10696147

Character table — Group #10696147

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order12222234444666444466121212121212121288881212242424242424242444881212121224242424444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ922222222222222-2-2-2-222-2-22222-2-20000-2-200000000000000000000000022-2-20000
χ1022222222222222-2-2-2-222-2-22222-2-20000-2-2000000000000000000000000-2-2220000
χ112222222-2-2-2-222222-2-22222-2-2-2-2-2-22i2i−2i−2i2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ122222222-2-2-2-222222-2-22222-2-2-2-2-2-2−2i−2i2i2i2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ132222222-2-2-2-2222-2-22222-2-2-2-2-2-2220000-220000000000000000000022-2-200000000
χ142222222-2-2-2-2222-2-22222-2-2-2-2-2-2220000-2200000000000000000000-2-22200000000
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ19222222-1-2-2-2-2-1-1-122-2-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii0000−i3−i3i3i333−3−3000000000000
χ20222222-1-2-2-2-2-1-1-122-2-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii0000i3i3−i3−i3−3−333000000000000
χ21222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i0000−i3−i3i3i3−3−333000000000000
χ22222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i0000i3i3−i3−i333−3−3000000000000
χ232222-2-222-2-222222-22-2-2-22222-2-2220000-2-200000000000000000000000000002-200
χ242222-2-222-2-222222-22-2-2-22222-2-2220000-2-20000000000000000000000000000-2200
χ252222-2-222-2-22222-22-22-2-2-2-222-2-2-2-2000022000000002-2002-22-20000000000000000
χ262222-2-222-2-22222-22-22-2-2-2-222-2-2-2-200002200000000-2200-22-220000000000000000
χ272222-2-22-222-22222-2-22-2-222-2-222-2-20000-220000000000000000000000000000002-2
χ282222-2-22-222-22222-2-22-2-222-2-222-2-20000-22000000000000000000000000000000-22
χ292222-2-22-222-2222-222-2-2-2-2-2-2-2222200002-200000000002-200002-22-2000000000000
χ302222-2-22-222-2222-222-2-2-2-2-2-2-2222200002-20000000000-220000-22-22000000000000
χ312222-2-2-12-2-22-1-1-1-22-221111-1-111110000-1-133−3−333−3−32-200-11-113−3−33000000000000
χ322222-2-2-12-2-22-1-1-1-22-221111-1-111110000-1-133−3−333−3−3-22001-11-1−333−3000000000000
χ332222-2-2-12-2-22-1-1-1-22-221111-1-111110000-1-1−3−333−3−3332-200-11-11−333−3000000000000
χ342222-2-2-12-2-22-1-1-1-22-221111-1-111110000-1-1−3−333−3−333-22001-11-13−3−33000000000000
χ352222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-10000-11−i3−i3i3i3i3i3−i3−i3002-2−i3i3i3−i3-11-11000000000000
χ362222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-10000-11−i3−i3i3i3i3i3−i3−i300-22i3−i3−i3i31-11-1000000000000
χ372222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-10000-11i3i3−i3−i3−i3−i3i3i3002-2i3−i3−i3i3-11-11000000000000
χ382222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-10000-11i3i3−i3−i3−i3−i3i3i300-22−i3i3i3−i31-11-1000000000000
χ39444444-24444-2-2-2-4-4-4-4-2-222-2-2-2-22200002200000000000000000000000000000000
χ40444444-2-4-4-4-4-2-2-2-4-444-2-2222222-2-200002-200000000000000000000000000000000
χ414444-4-4-24-4-44-2-2-24-44-422-2-2-2-222-2-200002200000000000000000000000000000000
χ424444-4-4-2-444-4-2-2-24-4-4422-2-222-2-22200002-200000000000000000000000000000000
χ4344-4-44-4400004-4-400004-4000000000000000000000000000000000000000022−220000
χ4444-4-44-4400004-4-400004-40000000000000000000000000000000000000000−22220000
χ4544-4-4-44400004-4-40000-440000000000000000000000000000000000000022−22000000
χ4644-4-4-44400004-4-40000-4400000000000000000000000000000000000000−2222000000
χ474-44-4004400-4-44-4000000004-400002-22-2002-22-22-22-2000000000000000000000000
χ484-44-4004400-4-44-4000000004-40000-22-2200-22-22-22-22000000000000000000000000
χ494-44-4004-4004-44-400000000-4400002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ504-44-4004-4004-44-400000000-440000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ514-44-400-2400-42-2200000023−23-220023−232-22-200−1+31−3−1−31+3−1+31−3−1−31+3000000000000000000000000
χ524-44-400-2400-42-2200000023−23-220023−23-22-22001−3−1+31+3−1−31−3−1+31+3−1−3000000000000000000000000
χ534-44-400-2400-42-22000000−2323-2200−23232-22-200−1−31+3−1+31−3−1−31+3−1+31−3000000000000000000000000
χ544-44-400-2400-42-22000000−2323-2200−2323-22-22001+3−1−31−3−1+31+3−1−31−3−1+3000000000000000000000000
χ554-44-400-2-40042-2200000023−232-200−23232i−2i−2i2i00ζ4+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+ζ22000000000000000000000000
χ564-44-400-2-40042-2200000023−232-200−2323−2i2i2i−2i00−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−ζ22000000000000000000000000
χ574-44-400-2-40042-22000000−23232-20023−232i−2i−2i2i00−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+ζ22000000000000000000000000
χ584-44-400-2-40042-22000000−23232-20023−23−2i2i2i−2i00ζ4−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−ζ22000000000000000000000000
χ594-4-4400404i−4i0-4-4400000000004i−4i00000000000000000000000000002i−2i2-200000000
χ604-4-4400404i−4i0-4-4400000000004i−4i0000000000000000000000000000−2i2i-2200000000
χ614-4-440040−4i4i0-4-440000000000−4i4i00000000000000000000000000002i−2i-2200000000
χ624-4-440040−4i4i0-4-440000000000−4i4i0000000000000000000000000000−2i2i2-200000000
χ6388-8-88-8-40000-4440000-440000000000000000000000000000000000000000000000
χ6488-8-8-88-40000-44400004-40000000000000000000000000000000000000000000000
χ658-8-8800-408i−8i044-40000000000−4i4i0000000000000000000000000000000000000000
χ668-8-8800-40−8i8i044-400000000004i−4i0000000000000000000000000000000000000000

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