Finite Group Databasebeta

← Group #10696859

Character table — Group #10696859

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order12222234466644444661212121212121212888812122424242424242424448812121212242424248888444488
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-111-1-1-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-1-1111
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-11-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-111
χ9222222222222-2-2-2-222222-2-2-2-2-2-200002-2000000002-20022-2-200000000000000
χ10222222222222-2-2-2-222222-2-2-2-2-2-200002-200000000-2200-2-22200000000000000
χ112222222-2-222222-2-2-222-2-222-2-2-2-20000-2200000000002i−2i00002i2i−2i−2i0000000000
χ122222222-2-222222-2-2-222-2-222-2-2-2-20000-220000000000−2i2i0000−2i−2i2i2i0000000000
χ132222222-2-2222-2-222-222-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000
χ142222222-2-2222-2-222-222-2-2-2-22222-2-222-2-2-2-2-2-222220000000000000000000000
χ15222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ16222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ17222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-111110000000000
χ18222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-10000000000
χ19222222-122-1-1-1-2-2-2-22-1-1-1-11111110000-1133−3−333−3−32-200-1-1113−33−30000000000
χ20222222-122-1-1-1-2-2-2-22-1-1-1-11111110000-1133−3−333−3−3-220011-1-1−33−330000000000
χ21222222-122-1-1-1-2-2-2-22-1-1-1-11111110000-11−3−333−3−3332-200-1-111−33−330000000000
χ22222222-122-1-1-1-2-2-2-22-1-1-1-11111110000-11−3−333−3−333-220011-1-13−33−30000000000
χ23222222-1-2-2-1-1-122-2-2-2-1-111-1-1111100001-133−3−3−3−333002i−2i−i3i3−i3i3−i−iii0000000000
χ24222222-1-2-2-1-1-122-2-2-2-1-111-1-1111100001-133−3−3−3−33300−2i2ii3−i3i3−i3ii−i−i0000000000
χ25222222-1-2-2-1-1-122-2-2-2-1-111-1-1111100001-1−3−33333−3−3002i−2ii3−i3i3−i3−i−iii0000000000
χ26222222-1-2-2-1-1-122-2-2-2-1-111-1-1111100001-1−3−33333−3−300−2i2i−i3i3−i3i3ii−i−i0000000000
χ27222222-1-2-2-1-1-1-2-222-2-1-11111-1-1-1-122-2-211-1-1-1-111110000−i3i3i3−i3−i3i3i3−i30000000000
χ28222222-1-2-2-1-1-1-2-222-2-1-11111-1-1-1-122-2-211-1-1-1-111110000i3−i3−i3i3i3−i3−i3i30000000000
χ29222222-1-2-2-1-1-1-2-222-2-1-11111-1-1-1-1-2-222111111-1-1-1-10000−i3i3i3−i3i3−i3−i3i30000000000
χ30222222-1-2-2-1-1-1-2-222-2-1-11111-1-1-1-1-2-222111111-1-1-1-10000i3−i3−i3i3−i3i3i3−i30000000000
χ312222-2-22222222-22-2-2-2-2222222-2-20000-2-2000000000000000000000000200-200
χ322222-2-22222222-22-2-2-2-2222222-2-20000-2-2000000000000000000000000-200200
χ332222-2-2222222-22-22-2-2-222-2-2-2-2220000-2200000000000000000000000000002-2
χ342222-2-2222222-22-22-2-2-222-2-2-2-2220000-220000000000000000000000000000-22
χ352222-2-22-2-22222-2-222-2-2-2-222-2-22200002-20000000000000000000022-2-2000000
χ362222-2-22-2-22222-2-222-2-2-2-222-2-22200002-200000000000000000000-2-222000000
χ372222-2-22-2-2222-222-22-2-2-2-2-2-222-2-200002200000000000000000000000002-2000
χ382222-2-22-2-2222-222-22-2-2-2-2-2-222-2-20000220000000000000000000000000-22000
χ394444-4-4-244-2-2-24-44-4-422-2-2-2-2-2-222000022000000000000000000000000000000
χ404444-4-4-244-2-2-2-44-44-422-2-22222-2-200002-2000000000000000000000000000000
χ414444-4-4-2-4-4-2-2-24-4-4442222-2-222-2-20000-22000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-2-444-44222222-2-2220000-2-2000000000000000000000000000000
χ4344-4-44-4400-44-4000004-4000000000022−2200000022−2222−220000000000000000000000
χ4444-4-44-4400-44-4000004-40000000000−2222000000−2222−22220000000000000000000000
χ4544-4-44-4-2002-2200000-22000023−2323−230022−220000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000000000
χ4644-4-44-4-2002-2200000-22000023−2323−2300−2222000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000000000
χ4744-4-44-4-2002-2200000-220000−2323−23230022−220000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000
χ4844-4-44-4-2002-2200000-220000−2323−232300−2222000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000000000
χ4944-4-4-44400-44-400000-440000000022−22000022−2222−2200000000000000000000000000
χ5044-4-4-44400-44-400000-4400000000−22220000−2222−222200000000000000000000000000
χ5144-4-4-44-2002-22000002-2000023−23−232322−2200002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000
χ5244-4-4-44-2002-22000002-2000023−23−2323−22220000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000
χ5344-4-4-44-2002-22000002-20000−232323−2322−2200002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000
χ5444-4-4-44-2002-22000002-20000−232323−23−22220000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300000000000000000000000000
χ554-4-440044-44-4-400000004-4000000000000000000000000000000002i−2i2i−2i000000
χ564-4-440044-44-4-400000004-400000000000000000000000000000000−2i2i−2i2i000000
χ574-4-44004-444-4-40000000-44000000000000000000000000000000002i−2i−2i2i000000
χ584-4-44004-444-4-40000000-4400000000000000000000000000000000−2i2i2i−2i000000
χ598-88-800800-8-88000000000000000000000000000000000000000000000000000
χ608-88-800-40044-400000000043−430000000000000000000000000000000000000000
χ618-88-800-40044-4000000000−43430000000000000000000000000000000000000000
χ628-8-8800-48-8-4440000000-44000000000000000000000000000000000000000000
χ638-8-8800-4-88-44400000004-4000000000000000000000000000000000000000000

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