Finite Group Databasebeta

← Group #10696587

Character table — Group #10696587

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order122222344666444446612121212121212128888121224242424242424242466881212242424244444224488
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
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
χ9222222222222-2-22-2-222-2-222-2-2-2-20000-22000000002-22200-2-200000000000000
χ10222222222222-2-22-2-222-2-222-2-2-2-20000-2200000000-22-2-2002200000000000000
χ112222222-2-22222-2-22-222-2-2-2-222-2-200002-20000000000000000000000002-20000
χ122222222-2-22222-2-22-222-2-2-2-222-2-200002-2000000000000000000000000-220000
χ132222222-2-2222-22-2-222222-2-2-2-2220000-2-20000000000000000000022-2-2000000
χ142222222-2-2222-22-2-222222-2-2-2-2220000-2-200000000000000000000-2-222000000
χ15222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10000000000
χ16222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-21111110000000000
χ17222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-111110000000000
χ18222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-10000000000
χ19222222-122-1-1-1-2-22-2-2-1-111-1-1111100001-13333−3−3−3−32-2-1-1001133−3−30000000000
χ20222222-122-1-1-1-2-22-2-2-1-111-1-1111100001-13333−3−3−3−3-221100-1-1−3−3330000000000
χ21222222-122-1-1-1-2-22-2-2-1-111-1-1111100001-1−3−3−3−333332-2-1-10011−3−3330000000000
χ22222222-122-1-1-1-2-22-2-2-1-111-1-1111100001-1−3−3−3−33333-221100-1-133−3−30000000000
χ232222-2-22222222-2-2-22-2-2-2-222-2-22200002-200000000000000000000000000002-2
χ242222-2-22222222-2-2-22-2-2-2-222-2-22200002-20000000000000000000000000000-22
χ252222-2-2222222-22-22-2-2-2222222-2-20000-2-2000000000000000000000000002-200
χ262222-2-2222222-22-22-2-2-2222222-2-20000-2-200000000000000000000000000-2200
χ272222-2-22-2-2222222-2-2-2-222-2-2-2-2-2-20000220000000000002i−2i002i−2i2i−2i0000000000
χ282222-2-22-2-2222222-2-2-2-222-2-2-2-2-2-2000022000000000000−2i2i00−2i2i−2i2i0000000000
χ292222-2-22-2-2222-2-2222-2-2-2-2-2-2222222-2-2-2222-2-222-2-20000000000000000000000
χ302222-2-22-2-2222-2-2222-2-2-2-2-2-22222-2-222-22-2-222-2-2220000000000000000000000
χ312222-2-2-1-2-2-1-1-1222-2-211-1-11111110000-1-133−3−3−3−33300−i3i32i−2i−i3i3−ii−ii0000000000
χ322222-2-2-1-2-2-1-1-1222-2-211-1-11111110000-1-133−3−3−3−33300i3−i3−2i2ii3−i3i−ii−i0000000000
χ332222-2-2-1-2-2-1-1-1222-2-211-1-11111110000-1-1−3−33333−3−300−i3i3−2i2i−i3i3i−ii−i0000000000
χ342222-2-2-1-2-2-1-1-1222-2-211-1-11111110000-1-1−3−33333−3−300i3−i32i−2ii3−i3−ii−ii0000000000
χ352222-2-2-1-2-2-1-1-1-2-2222111111-1-1-1-122-2-21-1-1-111-1-11100−i3i300i3−i3−i3i3i3−i30000000000
χ362222-2-2-1-2-2-1-1-1-2-2222111111-1-1-1-122-2-21-1-1-111-1-11100i3−i300−i3i3i3−i3−i3i30000000000
χ372222-2-2-1-2-2-1-1-1-2-2222111111-1-1-1-1-2-2221-111-1-111-1-100−i3i300i3−i3i3−i3−i3i30000000000
χ382222-2-2-1-2-2-1-1-1-2-2222111111-1-1-1-1-2-2221-111-1-111-1-100i3−i300−i3i3−i3i3i3−i30000000000
χ39444444-2-4-4-2-2-24-4-44-4-2-22222-2-2220000-22000000000000000000000000000000
χ40444444-2-4-4-2-2-2-44-4-44-2-2-2-22222-2-2000022000000000000000000000000000000
χ414444-4-4-244-2-2-24-4-4-442222-2-222-2-20000-22000000000000000000000000000000
χ424444-4-4-244-2-2-2-44-44-422-2-2-2-2-2-222000022000000000000000000000000000000
χ4344-4-44-44004-4-4000004-4000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ4444-4-44-44004-4-4000004-400000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ4544-4-44-4-200-22200000-2223−23000023−232i−2i2i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ4644-4-44-4-200-22200000-2223−23000023−23−2i2i−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ4744-4-44-4-200-22200000-22−23230000−23232i−2i2i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ4844-4-44-4-200-22200000-22−23230000−2323−2i2i−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ4944-4-4-444004-4-400000-44000000002i−2i−2i2i002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ5044-4-4-444004-4-400000-4400000000−2i2i2i−2i00−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ5144-4-4-44-200-222000002-223−230000−23232i−2i−2i2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ5244-4-4-44-200-222000002-223−230000−2323−2i2i2i−2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ5344-4-4-44-200-222000002-2−2323000023−232i−2i−2i2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ5444-4-4-44-200-222000002-2−2323000023−23−2i2i2i−2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ554-4-440044-4-4-440000000004-40000000000000000000000000000002-22-2000000
χ564-4-440044-4-4-440000000004-4000000000000000000000000000000-22-22000000
χ574-4-44004-44-4-44000000000-440000000000000000000000000000002-2-22000000
χ584-4-44004-44-4-44000000000-44000000000000000000000000000000-222-2000000
χ598-88-800800-88-8000000000000000000000000000000000000000000000000000
χ608-88-800-4004-440000000000043−4300000000000000000000000000000000000000
χ618-88-800-4004-4400000000000−434300000000000000000000000000000000000000
χ628-8-8800-48-844-4000000000-440000000000000000000000000000000000000000
χ638-8-8800-4-8844-40000000004-40000000000000000000000000000000000000000

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