Finite Group Databasebeta

← Group #10696755

Character table — Group #10696755

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888888888888888881616161616164848484848484848
order1222344446661212121224444121212121212121268888888812242424242424242424242424242424242466121222448888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ5111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1111-1-1
χ92222222222222222-22-2-2-22222-2-2-2-2-200000000-2000000000000000000000000002-200
χ102222222222222222-22-2-2-22222-2-2-2-2-200000000-200000000000000000000000000-2200
χ112222222-2-222222222-2-2-22-2-2-2-2-2-2-2-2200000000200000000000000000000000000002-2
χ122222222-2-222222222-2-2-22-2-2-2-2-2-2-2-220000000020000000000000000000000000000-22
χ132222222-2-22222222-2-222-2-2-2-2-22222-2000022-2-2-2000000002222-2-2-2-200000000000000
χ142222222-2-22222222-2-222-2-2-2-2-22222-20000-2-222-200000000-2-2-2-2222200000000000000
χ1522222-2-222222-2-2-2-22-2-22-222-2-2-2-222200000000-20000000000000000000000020-20000
χ1622222-2-222222-2-2-2-22-2-22-222-2-2-2-222200000000-200000000000000000000000-2020000
χ1722222-2-222222-2-2-2-2-2-22-2222-2-222-2-2-200000000200000000000000002-222-2-200000000
χ1822222-2-222222-2-2-2-2-2-22-2222-2-222-2-2-20000000020000000000000000-22-2-22200000000
χ1922222-2-2-2-2222-2-2-2-2222-2-2-2-22222-2-222i2i−2i−2i0000-22i2i2i2i−2i−2i−2i−2i0000000000000000000000
χ2022222-2-2-2-2222-2-2-2-2222-2-2-2-22222-2-22−2i−2i2i2i0000-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000
χ2122222-2-2-2-2222-2-2-2-2-22-222-2-222-2-222-2000000002000000000000000000000020-200000
χ2222222-2-2-2-2222-2-2-2-2-22-222-2-222-2-222-20000000020000000000000000000000-20200000
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
χ272222-122-2-2-1-1-1-1-1-1-1-2-222-21111-1-1-1-11000022-2-21−i3−i3i3i3−i3−i3i3i3-1-1-1-1111100−i3i3−i3i300000000
χ282222-122-2-2-1-1-1-1-1-1-1-2-222-21111-1-1-1-11000022-2-21i3i3−i3−i3i3i3−i3−i3-1-1-1-1111100i3−i3i3−i300000000
χ292222-122-2-2-1-1-1-1-1-1-1-2-222-21111-1-1-1-110000-2-2221−i3−i3i3i3−i3−i3i3i31111-1-1-1-100i3−i3i3−i300000000
χ302222-122-2-2-1-1-1-1-1-1-1-2-222-21111-1-1-1-110000-2-2221i3i3−i3−i3i3i3−i3−i31111-1-1-1-100−i3i3−i3i300000000
χ312222-1-2-222-1-1-11111-2-22-22-1-111-1-111100000000-133−3−3−3−33333−3−333−3−32-2-1-11100000000
χ322222-1-2-222-1-1-11111-2-22-22-1-111-1-111100000000-133−3−3−3−333−3−333−3−333-2211-1-100000000
χ332222-1-2-222-1-1-11111-2-22-22-1-111-1-111100000000-1−3−33333−3−333−3−333−3−3-2211-1-100000000
χ342222-1-2-222-1-1-11111-2-22-22-1-111-1-111100000000-1−3−33333−3−3−3−333−3−3332-2-1-11100000000
χ352222-1-2-2-2-2-1-1-11111222-2-211-1-1-1-111-12i2i−2i−2i00001−i−i−i−iiiii33−3−3−3−33300−i3i3i3−i300000000
χ362222-1-2-2-2-2-1-1-11111222-2-211-1-1-1-111-12i2i−2i−2i00001−i−i−i−iiiii−3−33333−3−300i3−i3−i3i300000000
χ372222-1-2-2-2-2-1-1-11111222-2-211-1-1-1-111-1−2i−2i2i2i00001iiii−i−i−i−i33−3−3−3−33300i3−i3−i3i300000000
χ382222-1-2-2-2-2-1-1-11111222-2-211-1-1-1-111-1−2i−2i2i2i00001iiii−i−i−i−i−3−33333−3−300−i3i3i3−i300000000
χ394444-24444-2-2-2-2-2-2-2-44-4-4-4-2-2-2-222222000000002000000000000000000000000000000
χ404444-244-4-4-2-2-2-2-2-2-24-4-4-4422222222-200000000-2000000000000000000000000000000
χ414444-2-4-444-2-2-222224-4-44-4-2-22222-2-2-2000000002000000000000000000000000000000
χ424444-2-4-4-4-4-2-2-22222-44-44422-2-222-2-2200000000-2000000000000000000000000000000
χ4344-4-444i−4i004-4-44i4i−4i−4i000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ4444-4-444i−4i004-4-44i4i−4i−4i00000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ4544-4-44−4i4i004-4-4−4i−4i4i4i00000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ4644-4-44−4i4i004-4-4−4i−4i4i4i000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ4744-4-4-24i−4i00-222−2i−2i2i2i000000000−2i32i323−2302ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ50000000000000000000000
χ4844-4-4-24i−4i00-222−2i−2i2i2i000000000−2i32i323−230−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000002ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ50000000000000000000000
χ4944-4-4-24i−4i00-222−2i−2i2i2i0000000002i3−2i3−232302ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ130000000000000000000000
χ5044-4-4-24i−4i00-222−2i−2i2i2i0000000002i3−2i3−23230−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000002ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ130000000000000000000000
χ5144-4-4-2−4i4i00-2222i2i−2i−2i000000000−2i32i3−23230−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000002ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ230000000000000000000000
χ5244-4-4-2−4i4i00-2222i2i−2i−2i000000000−2i32i3−232302ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ230000000000000000000000
χ5344-4-4-2−4i4i00-2222i2i−2i−2i0000000002i3−2i323−230−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000002ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ70000000000000000000000
χ5444-4-4-2−4i4i00-2222i2i−2i−2i0000000002i3−2i323−2302ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ70000000000000000000000
χ554-4-444004-4-44-40000000004-4000000000002-22-20000000002-22-22-22-200000000000000
χ564-4-444004-4-44-40000000004-400000000000-22-22000000000-22-22-22-2200000000000000
χ574-4-44400-44-44-4000000000-44000000000002-2-220000000002-22-2-22-2200000000000000
χ584-4-44400-44-44-4000000000-4400000000000-222-2000000000-22-222-22-200000000000000
χ594-4-44-2004-42-2223−2323−2300000-2223−230000000002-22-2000000000−1−31+3−1+31−3−1−31+3−1+31−300000000000000
χ604-4-44-2004-42-2223−2323−2300000-2223−23000000000-22-220000000001+3−1−31−3−1+31+3−1−31−3−1+300000000000000
χ614-4-44-2004-42-22−2323−232300000-22−23230000000002-22-2000000000−1+31−3−1−31+3−1+31−3−1−31+300000000000000
χ624-4-44-2004-42-22−2323−232300000-22−2323000000000-22-220000000001−3−1+31+3−1−31−3−1+31+3−1−300000000000000
χ634-4-44-200-442-2223−2323−23000002-2−23230000000002-2-22000000000−1−31+3−1+31−31+3−1−31−3−1+300000000000000
χ644-4-44-200-442-2223−2323−23000002-2−2323000000000-222-20000000001+3−1−31−3−1+3−1−31+3−1+31−300000000000000
χ654-4-44-200-442-22−2323−2323000002-223−230000000002-2-22000000000−1+31−3−1−31+31−3−1+31+3−1−300000000000000
χ664-4-44-200-442-22−2323−2323000002-223−23000000000-222-20000000001−3−1+31+3−1−3−1+31−3−1−31+300000000000000
χ678-88-880000-8-88000000000000000000000000000000000000000000000000000000000
χ688-88-8-4000044-4−4i34i34i3−4i300000000000000000000000000000000000000000000000000000
χ698-88-8-4000044-44i3−4i3−4i34i300000000000000000000000000000000000000000000000000000

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