Finite Group Databasebeta

← Group #10696130

Character table — Group #10696130

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order122222344446664444661212121212121212888812122424242424242424246688121224242424444488882488
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
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ922222222222222-2-2-2-22222-2-222-2-20000-2-200000000000000000000000022-2-20000
χ1022222222222222-2-2-2-22222-2-222-2-20000-2-2000000000000000000000000-2-2220000
χ112222222-2-2-2-222222-2-222-2-222-2-2-2-22i2i−2i−2i-222i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ122222222-2-2-2-222222-2-222-2-222-2-2-2-2−2i−2i2i2i-22−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ132222222-2-2-2-2222-2-22222-2-2-2-2-2-22200002-20000000000000000000022-2-200000000
χ142222222-2-2-2-2222-2-22222-2-2-2-2-2-22200002-200000000000000000000-2-22200000000
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-11111000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-1000000000000
χ19222222-1-2-2-2-2-1-1-122-2-2-1-111-1-111112i2i−2i−2i1-1−i−i−i−iiiii00−i3i300−i3i333−3−3000000000000
χ20222222-1-2-2-2-2-1-1-122-2-2-1-111-1-111112i2i−2i−2i1-1−i−i−i−iiiii00i3−i300i3−i3−3−333000000000000
χ21222222-1-2-2-2-2-1-1-122-2-2-1-111-1-11111−2i−2i2i2i1-1iiii−i−i−i−i00−i3i300−i3i3−3−333000000000000
χ22222222-1-2-2-2-2-1-1-122-2-2-1-111-1-11111−2i−2i2i2i1-1iiii−i−i−i−i00i3−i300i3−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
χ252222-2-222-2-22222-22-22-2-222-2-2-2-2-2-2000022000000002-22200-2-20000000000000000
χ262222-2-222-2-22222-22-22-2-222-2-2-2-2-2-200002200000000-22-2-200220000000000000000
χ272222-2-22-222-22222-2-22-2-2-2-22222-2-200002-20000000000000000000000000000002-2
χ282222-2-22-222-22222-2-22-2-2-2-22222-2-200002-2000000000000000000000000000000-22
χ292222-2-22-222-2222-222-2-2-2-2-2-2-222220000-220000000000002-2002-22-2000000000000
χ302222-2-22-222-2222-222-2-2-2-2-2-2-222220000-22000000000000-2200-22-22000000000000
χ312222-2-2-12-2-22-1-1-1-22-2211-1-11111110000-1-133−3−333−3−32-2-1-100113−3−33000000000000
χ322222-2-2-12-2-22-1-1-1-22-2211-1-11111110000-1-133−3−333−3−3-221100-1-1−333−3000000000000
χ332222-2-2-12-2-22-1-1-1-22-2211-1-11111110000-1-1−3−333−3−3332-2-1-10011−333−3000000000000
χ342222-2-2-12-2-22-1-1-1-22-2211-1-11111110000-1-1−3−333−3−333-221100-1-13−3−33000000000000
χ352222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-100001-1−i3−i3i3i3i3i3−i3−i300−i3i32-2i3−i3-11-11000000000000
χ362222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-100001-1−i3−i3i3i3i3i3−i3−i300i3−i3-22−i3i31-11-1000000000000
χ372222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-100001-1i3i3−i3−i3−i3−i3i3i300−i3i3-22i3−i31-11-1000000000000
χ382222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-100001-1i3i3−i3−i3−i3−i3i3i300i3−i32-2−i3i3-11-11000000000000
χ39444444-24444-2-2-2-4-4-4-4-2-2-2-222-2-22200002200000000000000000000000000000000
χ40444444-2-4-4-4-4-2-2-2-4-444-2-2222222-2-20000-2200000000000000000000000000000000
χ414444-4-4-24-4-44-2-2-24-44-422-2-2-2-222-2-200002200000000000000000000000000000000
χ424444-4-4-2-444-4-2-2-24-4-442222-2-2-2-2220000-2200000000000000000000000000000000
χ4344-4-4004400-44-4-40000004-40000002-22-2002-22-22-22-2000000000000000000000000
χ4444-4-4004400-44-4-40000004-4000000-22-2200-22-22-22-22000000000000000000000000
χ4544-4-4004-40044-4-4000000-440000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4644-4-4004-40044-4-4000000-44000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4744-4-400-2400-4-222000000-2223−230023−232-22-200−1+31−3−1−31+3−1+31−3−1−31+3000000000000000000000000
χ4844-4-400-2400-4-222000000-2223−230023−23-22-22001−3−1+31+3−1−31−3−1+31+3−1−3000000000000000000000000
χ4944-4-400-2400-4-222000000-22−232300−23232-22-200−1−31+3−1+31−3−1−31+3−1+31−3000000000000000000000000
χ5044-4-400-2400-4-222000000-22−232300−2323-22-22001+3−1−31−3−1+31+3−1−31−3−1+3000000000000000000000000
χ5144-4-400-2-4004-2220000002-223−2300−23232i−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
χ5244-4-400-2-4004-2220000002-223−2300−2323−2i2i2i−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
χ5344-4-400-2-4004-2220000002-2−23230023−232i−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
χ5444-4-400-2-4004-2220000002-2−23230023−23−2i2i2i−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
χ554-44-400404i−4i0-44-400000000004i−4i00000000000000000000000000002-22i−2i00000000
χ564-44-400404i−4i0-44-400000000004i−4i0000000000000000000000000000-22−2i2i00000000
χ574-44-40040−4i4i0-44-40000000000−4i4i00000000000000000000000000002-2−2i2i00000000
χ584-44-40040−4i4i0-44-40000000000−4i4i0000000000000000000000000000-222i−2i00000000
χ594-4-444-440000-4-4400004-4000000000000000000000000000000000000000022−220000
χ604-4-444-440000-4-4400004-40000000000000000000000000000000000000000−22220000
χ614-4-44-4440000-4-440000-440000000000000000000000000000000000000022−22000000
χ624-4-44-4440000-4-440000-4400000000000000000000000000000000000000−2222000000
χ638-88-800-408i−8i04-440000000000−4i4i0000000000000000000000000000000000000000
χ648-88-800-40−8i8i04-4400000000004i−4i0000000000000000000000000000000000000000
χ658-8-888-8-4000044-40000-440000000000000000000000000000000000000000000000
χ668-8-88-88-4000044-400004-40000000000000000000000000000000000000000000000

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