Finite Group Databasebeta

← Group #10696728

Character table — Group #10696728

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888888888888888816161616161624242424484848484848
order122234444446661212121224441212121212121212688888888122424242424242424242424242424242488242424248888244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-1
χ411111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111
χ51111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-11-1-1-1
χ61111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ922222222-2-222222222-2-22-222-2-222-2-2-200000000-200000000000000000000000000020-200
χ1022222222-2-222222222-2-22-222-2-222-2-2-200000000-2000000000000000000000000000-20200
χ112222222-222-2222-2-2-2-2-2-2-2222-2-2-2-222-222-2-2000022222-2-2-2-2000000000000000000000000
χ122222222-222-2222-2-2-2-2-2-2-2222-2-2-2-222-2-2-22200002-2-2-2-22222000000000000000000000000
χ132222222-2-2-2-2222-2-2-2-222-2-22222-2-2-2-2200000000-200000000000000000000002i2i−2i−2i000000
χ142222222-2-2-2-2222-2-2-2-222-2-22222-2-2-2-2200000000-20000000000000000000000−2i−2i2i2i000000
χ1522222-2-222222222222-22-2-2-2-222-2-222-200000000-20000000000000000000000000020-2000
χ1622222-2-222222222222-22-2-2-2-222-2-222-200000000-200000000000000000000000000-202000
χ1722222-2-22-2-2222222222-2-22-2-2-2-2-2-2-2-2200000000200000000000000002-222-2-20000000000
χ1822222-2-22-2-2222222222-2-22-2-2-2-2-2-2-2-220000000020000000000000000-22-2-2220000000000
χ1922222-2-2-222-2222-2-2-2-22-22-2-2-2-2-22222200000000-20000000000000000000000000000002-2
χ2022222-2-2-222-2222-2-2-2-22-22-2-2-2-2-22222200000000-2000000000000000000000000000000-22
χ2122222-2-2-2-2-2-2222-2-2-2-2-2222-2-22222-2-2-2000022-2-22000000002222-2-2-2-20000000000000000
χ2222222-2-2-2-2-2-2222-2-2-2-2-2222-2-22222-2-2-20000-2-222200000000-2-2-2-222220000000000000000
χ232222-1222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ242222-1222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-111111111-2-211110000000000
χ252222-1222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-22222-111111111-1-1-1-1-1-1-1-1-2-211110000000000
χ262222-1222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1111111111111111122-1-1-1-10000000000
χ272222-122-222-2-1-1-11111-2-2-22-1-11111-1-1122-2-20000-1-1-1-1-1111133−3−333−3−3003−33−30000000000
χ282222-122-222-2-1-1-11111-2-2-22-1-11111-1-1122-2-20000-1-1-1-1-11111−3−333−3−33300−33−330000000000
χ292222-122-222-2-1-1-11111-2-2-22-1-11111-1-11-2-2220000-11111-1-1-1-133−3−333−3−300−33−330000000000
χ302222-122-222-2-1-1-11111-2-2-22-1-11111-1-11-2-2220000-11111-1-1-1-1−3−333−3−333003−33−30000000000
χ312222-1-2-22-2-22-1-1-1-1-1-1-12-2-2211111111-100000000-133−3−333−3−333−3−3−3−3332-2-1-1110000000000
χ322222-1-2-22-2-22-1-1-1-1-1-1-12-2-2211111111-100000000-133−3−333−3−3−3−33333−3−3-2211-1-10000000000
χ332222-1-2-22-2-22-1-1-1-1-1-1-12-2-2211111111-100000000-1−3−333−3−33333−3−3−3−333-2211-1-10000000000
χ342222-1-2-22-2-22-1-1-1-1-1-1-12-2-2211111111-100000000-1−3−333−3−333−3−33333−3−32-2-1-1110000000000
χ352222-1-2-2-2-2-2-2-1-1-11111-222211-1-1-1-1111000022-2-2-133−3−3−3−333-1-1-1-1111100−333−30000000000
χ362222-1-2-2-2-2-2-2-1-1-11111-222211-1-1-1-1111000022-2-2-1−3−33333−3−3-1-1-1-11111003−3−330000000000
χ372222-1-2-2-2-2-2-2-1-1-11111-222211-1-1-1-11110000-2-222-133−3−3−3−3331111-1-1-1-1003−3−330000000000
χ382222-1-2-2-2-2-2-2-1-1-11111-222211-1-1-1-11110000-2-222-1−3−33333−3−31111-1-1-1-100−333−30000000000
χ394444-2444-4-44-2-2-2-2-2-2-2-4-44-4-2-222-2-222200000000200000000000000000000000000000000
χ404444-244-4-4-4-4-2-2-2222244-4-4-2-2-2-22222-200000000200000000000000000000000000000000
χ414444-2-4-44444-2-2-2-2-2-2-2-44-4-422-2-222-2-2200000000200000000000000000000000000000000
χ424444-2-4-4-444-4-2-2-222224-44-42222-2-2-2-2-200000000200000000000000000000000000000000
χ4344-4-440004-404-4-4000000000000004-4000002-22-20000000002-22-22-22-20000000000000000
χ4444-4-440004-404-4-4000000000000004-400000-22-22000000000-22-22-22-220000000000000000
χ4544-4-44000-4404-4-400000000000000-44000002-2-220000000002-22-2-22-220000000000000000
χ4644-4-44000-4404-4-400000000000000-4400000-222-2000000000-22-222-22-20000000000000000
χ4744-4-4-20004-40-22223−2323−2300000023−2300-22000002-22-2000000000−1+31−3−1−31+3−1+31−3−1−31+30000000000000000
χ4844-4-4-20004-40-22223−2323−2300000023−2300-2200000-22-220000000001−3−1+31+3−1−31−3−1+31+3−1−30000000000000000
χ4944-4-4-20004-40-222−2323−2323000000−232300-22000002-22-2000000000−1−31+3−1+31−3−1−31+3−1+31−30000000000000000
χ5044-4-4-20004-40-222−2323−2323000000−232300-2200000-22-220000000001+3−1−31−3−1+31+3−1−31−3−1+30000000000000000
χ5144-4-4-2000-440-22223−2323−23000000−2323002-2000002-2-22000000000−1−31+3−1+31−31+3−1−31−3−1+30000000000000000
χ5244-4-4-2000-440-22223−2323−23000000−2323002-200000-222-20000000001+3−1−31−3−1+3−1−31+3−1+31−30000000000000000
χ5344-4-4-2000-440-222−2323−232300000023−23002-2000002-2-22000000000−1+31−3−1−31+31−3−1+31+3−1−30000000000000000
χ5444-4-4-2000-440-222−2323−232300000023−23002-200000-222-20000000001−3−1+31+3−1−3−1+31−3−1−31+30000000000000000
χ554-44-444-40000-44-4000000004-4000000000−2i22i2000000000−2i22i2−2i22i2000000000000000000000000
χ564-44-444-40000-44-4000000004-40000000002i2−2i20000000002i2−2i22i2−2i2000000000000000000000000
χ574-44-44-440000-44-400000000-440000000−2i22i20000000−2i22i2−2i22i20000000000000000000000000000
χ584-44-44-440000-44-400000000-4400000002i2−2i200000002i2−2i22i2−2i20000000000000000000000000000
χ594-44-4-24-400002-2223−23−23230000-220023−2300000−2i22i200000i6−i6−i6i6i2−i2i2−i2000000000000000000000000
χ604-44-4-24-400002-2223−23−23230000-220023−23000002i2−2i200000−i6i6i6−i6−i2i2−i2i2000000000000000000000000
χ614-44-4-24-400002-22−232323−230000-2200−232300000−2i22i200000−i6i6i6−i6i2−i2i2−i2000000000000000000000000
χ624-44-4-24-400002-22−232323−230000-2200−2323000002i2−2i200000i6−i6−i6i6−i2i2−i2i2000000000000000000000000
χ634-44-4-2-4400002-2223−23−232300002-200−2323000−2i22i20000000i2−i2i2−i2−i6i6i6−i6000000000000000000000000
χ644-44-4-2-4400002-2223−23−232300002-200−23230002i2−2i20000000−i2i2−i2i2i6−i6−i6i6000000000000000000000000
χ654-44-4-2-4400002-22−232323−2300002-20023−23000−2i22i20000000i2−i2i2−i2i6−i6−i6i6000000000000000000000000
χ664-44-4-2-4400002-22−232323−2300002-20023−230002i2−2i20000000−i2i2−i2i2−i6i6i6−i6000000000000000000000000
χ674-4-44400400-4-4-4444-4-4000000000000000000000000000000000000000000002i−2i2i−2i000000
χ684-4-44400400-4-4-4444-4-400000000000000000000000000000000000000000000−2i2i−2i2i000000
χ694-4-44400-4004-4-44-4-444000000000000000000000000000000000000000000002-2-22000000
χ704-4-44400-4004-4-44-4-44400000000000000000000000000000000000000000000-222-2000000
χ718-8-88-400800-844-4-4-444000000000000000000000000000000000000000000000000000000
χ728-8-88-400-800844-444-4-4000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).