Finite Group Databasebeta

← Group #10699165

Character table — Group #10699165

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888888888888888881616161616164848484848484848
order122234444666121212122444412121212121212126888888881224242424242424242424242424242424441212121244888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1
χ41111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ5111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111
χ6111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-111
χ92222222222222222-2-2-22-222-2-222-2-2-200000000-2000000000000000000000000200-200
χ102222222222222222-2-2-22-222-2-222-2-2-200000000-2000000000000000000000000-200200
χ112222222-2-222222222-2-2-22-2-2-2-2-2-2-2-222i2i−2i−2i000022i2i2i2i−2i−2i−2i−2i0000000000000000000000
χ122222222-2-222222222-2-2-22-2-2-2-2-2-2-2-22−2i−2i2i2i00002−2i−2i−2i−2i2i2i2i2i0000000000000000000000
χ132222222-2-22222222-222-2-2-2-222-2-222-200000000-200000000000000000000000000002i−2i
χ142222222-2-22222222-222-2-2-2-222-2-222-200000000-20000000000000000000000000000−2i2i
χ1522222-2-222222-2-2-2-22-22-2-222-2-2-2-222200000000-200000000000000000000002-2000000
χ1622222-2-222222-2-2-2-22-22-2-222-2-2-2-222200000000-20000000000000000000000-22000000
χ1722222-2-222222-2-2-2-2-22-2-222222-2-2-2-2-200000000200000000000000002-222-2-200000000
χ1822222-2-222222-2-2-2-2-22-2-222222-2-2-2-2-20000000020000000000000000-22-2-22200000000
χ1922222-2-2-2-2222-2-2-2-222-22-2-2-22222-2-2200000000-200000000000000000000000002i−2i000
χ2022222-2-2-2-2222-2-2-2-222-22-2-2-22222-2-2200000000-20000000000000000000000000−2i2i000
χ2122222-2-2-2-2222-2-2-2-2-2-2222-2-2-2-22222-2000022-2-22000000002222-2-2-2-200000000000000
χ2222222-2-2-2-2222-2-2-2-2-2-2222-2-2-2-22222-20000-2-222200000000-2-2-2-2222200000000000000
χ232222-12222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000
χ242222-12222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-111111111-2-2111100000000
χ252222-12222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-2-2-2-22222-111111111-1-1-1-1-1-1-1-1-2-2111100000000
χ262222-12222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1111111111111111122-1-1-1-100000000
χ272222-122-2-2-1-1-1-1-1-1-12-2-2-2211111111-12i2i−2i−2i0000-1−i−i−i−iiiii33−3−333−3−300−i3i3−i3i300000000
χ282222-122-2-2-1-1-1-1-1-1-12-2-2-2211111111-12i2i−2i−2i0000-1−i−i−i−iiiii−3−333−3−33300i3−i3i3−i300000000
χ292222-122-2-2-1-1-1-1-1-1-12-2-2-2211111111-1−2i−2i2i2i0000-1iiii−i−i−i−i33−3−333−3−300i3−i3i3−i300000000
χ302222-122-2-2-1-1-1-1-1-1-12-2-2-2211111111-1−2i−2i2i2i0000-1iiii−i−i−i−i−3−333−3−33300−i3i3−i3i300000000
χ312222-1-2-222-1-1-11111-22-2-22-1-1-1-11111100000000-133−3−333−3−333−3−3−3−3332-2-1-11100000000
χ322222-1-2-222-1-1-11111-22-2-22-1-1-1-11111100000000-133−3−333−3−3−3−33333−3−3-2211-1-100000000
χ332222-1-2-222-1-1-11111-22-2-22-1-1-1-11111100000000-1−3−333−3−33333−3−3−3−333-2211-1-100000000
χ342222-1-2-222-1-1-11111-22-2-22-1-1-1-11111100000000-1−3−333−3−333−3−33333−3−32-2-1-11100000000
χ352222-1-2-2-2-2-1-1-11111-2-22221111-1-1-1-11000022-2-2-1−i3−i3i3i3i3i3−i3−i3-1-1-1-1111100−i3i3i3−i300000000
χ362222-1-2-2-2-2-1-1-11111-2-22221111-1-1-1-11000022-2-2-1i3i3−i3−i3−i3−i3i3i3-1-1-1-1111100i3−i3−i3i300000000
χ372222-1-2-2-2-2-1-1-11111-2-22221111-1-1-1-110000-2-222-1−i3−i3i3i3i3i3−i3−i31111-1-1-1-100i3−i3−i3i300000000
χ382222-1-2-2-2-2-1-1-11111-2-22221111-1-1-1-110000-2-222-1i3i3−i3−i3−i3−i3i3i31111-1-1-1-100−i3i3i3−i300000000
χ394444-24444-2-2-2-2-2-2-2-4-4-44-4-2-222-2-2222000000002000000000000000000000000000000
χ404444-244-4-4-2-2-2-2-2-2-2-444-4-422-2-222-2-22000000002000000000000000000000000000000
χ414444-2-4-444-2-2-222224-44-4-4-2-22222-2-2-2000000002000000000000000000000000000000
χ424444-2-4-4-4-4-2-2-2222244-44-422-2-2-2-222-2000000002000000000000000000000000000000
χ4344-4-44004-4-44-40000000004-400000002-22-2000002-22-22-22-20000000000000000000000
χ4444-4-44004-4-44-40000000004-40000000-22-2200000-22-22-22-220000000000000000000000
χ4544-4-4400-44-44-4000000000-4400000002i−2i−2i2i000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ4644-4-4400-44-44-4000000000-440000000−2i2i2i−2i00000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ4744-4-4-2004-42-222323−23−2300000-220023−230002-22-200000−1+31−3−1−31+3−1+31−3−1−31+30000000000000000000000
χ4844-4-4-2004-42-222323−23−2300000-220023−23000-22-22000001−3−1+31+3−1−31−3−1+31+3−1−30000000000000000000000
χ4944-4-4-2004-42-22−23−23232300000-2200−23230002-22-200000−1−31+3−1+31−3−1−31+3−1+31−30000000000000000000000
χ5044-4-4-2004-42-22−23−23232300000-2200−2323000-22-22000001+3−1−31−3−1+31+3−1−31−3−1+30000000000000000000000
χ5144-4-4-200-442-222323−23−23000002-200−23230002i−2i−2i2i00000ζ2+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
χ5244-4-4-200-442-222323−23−23000002-200−2323000−2i2i2i−2i00000−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
χ5344-4-4-200-442-22−23−232323000002-20023−230002i−2i−2i2i00000−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
χ5444-4-4-200-442-22−23−232323000002-20023−23000−2i2i2i−2i00000ζ2−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
χ554-4-4444i−4i00-4-444i−4i4i−4i0000000000000000002-22i−2i0000000002-22-22i−2i2i−2i00000000000000
χ564-4-4444i−4i00-4-444i−4i4i−4i000000000000000000-22−2i2i000000000-22-22−2i2i−2i2i00000000000000
χ574-4-444−4i4i00-4-44−4i4i−4i4i0000000000000000002-2−2i2i0000000002-22-2−2i2i−2i2i00000000000000
χ584-4-444−4i4i00-4-44−4i4i−4i4i000000000000000000-222i−2i000000000-22-222i−2i2i−2i00000000000000
χ594-4-44-24i−4i0022-2−2i2i−2i2i0000000−2i32i30023−23000002-22i−2i000000000−1+31−3−1−31+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000
χ604-4-44-24i−4i0022-2−2i2i−2i2i0000000−2i32i30023−2300000-22−2i2i0000000001−3−1+31+3−1−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000
χ614-4-44-24i−4i0022-2−2i2i−2i2i00000002i3−2i300−2323000002-22i−2i000000000−1−31+3−1+31−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000
χ624-4-44-24i−4i0022-2−2i2i−2i2i00000002i3−2i300−232300000-22−2i2i0000000001+3−1−31−3−1+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000
χ634-4-44-2−4i4i0022-22i−2i2i−2i0000000−2i32i300−2323000002-2−2i2i000000000−1−31+3−1+31−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000
χ644-4-44-2−4i4i0022-22i−2i2i−2i0000000−2i32i300−232300000-222i−2i0000000001+3−1−31−3−1+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000
χ654-4-44-2−4i4i0022-22i−2i2i−2i00000002i3−2i30023−23000002-2−2i2i000000000−1+31−3−1−31+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000
χ664-4-44-2−4i4i0022-22i−2i2i−2i00000002i3−2i30023−2300000-222i−2i0000000001−3−1+31+3−1−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000
χ678-88-8800008-8-8000000000000000000000000000000000000000000000000000000000
χ688-88-8-40000-444−4i34i34i3−4i300000000000000000000000000000000000000000000000000000
χ698-88-8-40000-4444i3−4i3−4i34i300000000000000000000000000000000000000000000000000000

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