Finite Group Databasebeta

← Group #10695880

Character table — Group #10695880

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888888888888888816161616161624242424484848484848
order12222222344666121212122444666612121212688888888122424242424242424242424242424242488242424242222444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-1
χ411111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ51111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-11-11-1-1
χ61111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-111
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
χ9222222222-2-2222-2-2-2-22-2-2-22222-2-2-2-2200000000-20000000000000000000000000000002i−2i
χ10222222222-2-2222-2-2-2-22-2-2-22222-2-2-2-2200000000-2000000000000000000000000000000−2i2i
χ1122222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ1222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-111111111-2-211110000000000
χ1322222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-22222-111111111-1-1-1-1-1-1-1-1-2-211110000000000
χ1422222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1111111111111111122-1-1-1-10000000000
χ15222222-2-22222222222-22-2-222-2-222-2-2-200000000-20000000000000000000000000020-2000
χ16222222-2-22222222222-22-2-222-2-222-2-2-200000000-200000000000000000000000000-202000
χ17222222-2-22-2-2222-2-2-2-2-2-22222-2-2-2-222-2000022-2-22000000002222-2-2-2-20000000000000000
χ18222222-2-22-2-2222-2-2-2-2-2-22222-2-2-2-222-20000-2-222200000000-2-2-2-222220000000000000000
χ19222222-2-2-1-2-2-1-1-11111-2-222-1-11111-1-11000022-2-2-13333−3−3−3−3-1-1-1-111110033−3−30000000000
χ20222222-2-2-1-2-2-1-1-11111-2-222-1-11111-1-11000022-2-2-1−3−3−3−33333-1-1-1-1111100−3−3330000000000
χ21222222-2-2-1-2-2-1-1-11111-2-222-1-11111-1-110000-2-222-13333−3−3−3−31111-1-1-1-100−3−3330000000000
χ22222222-2-2-1-2-2-1-1-11111-2-222-1-11111-1-110000-2-222-1−3−3−3−333331111-1-1-1-10033−3−30000000000
χ232222-2-2222222222222-2-22-2-2-222-2-222-200000000-200000000000000000000000000020-200
χ242222-2-2222222222222-2-22-2-2-222-2-222-200000000-2000000000000000000000000000-20200
χ252222-2-2222-2-2222-2-2-2-2-22-22-2-22222-2-2-222-2-20000222-2-222-2-2000000000000000000000000
χ262222-2-2222-2-2222-2-2-2-2-22-22-2-22222-2-2-2-2-22200002-2-222-2-222000000000000000000000000
χ272222-2-222-1-2-2-1-1-11111-22-2211-1-1-1-111122-2-20000-1-1-111-1-11133−3−333−3−3003−33−30000000000
χ282222-2-222-1-2-2-1-1-11111-22-2211-1-1-1-111122-2-20000-1-1-111-1-111−3−333−3−33300−33−330000000000
χ292222-2-222-1-2-2-1-1-11111-22-2211-1-1-1-1111-2-2220000-111-1-111-1-133−3−333−3−300−33−330000000000
χ302222-2-222-1-2-2-1-1-11111-22-2211-1-1-1-1111-2-2220000-111-1-111-1-1−3−333−3−333003−33−30000000000
χ312222-2-2-2-222222222222-2-22-2-2-2-2-2-2-2-2200000000200000000000000002-22-2-220000000000
χ322222-2-2-2-222222222222-2-22-2-2-2-2-2-2-2-220000000020000000000000000-22-222-20000000000
χ332222-2-2-2-22-2-2222-2-2-2-2222-2-2-2-2-22222200000000-2000000000000000000000022-2-2000000
χ342222-2-2-2-22-2-2222-2-2-2-2222-2-2-2-2-22222200000000-20000000000000000000000-2-222000000
χ352222-2-2-2-2-122-1-1-1-1-1-1-12-2-2211111111-100000000-133−3−3−3−33333−3−3−3−333-221-1-110000000000
χ362222-2-2-2-2-122-1-1-1-1-1-1-12-2-2211111111-100000000-133−3−3−3−333−3−33333−3−32-2-111-10000000000
χ372222-2-2-2-2-122-1-1-1-1-1-1-12-2-2211111111-100000000-1−3−33333−3−333−3−3−3−3332-2-111-10000000000
χ382222-2-2-2-2-122-1-1-1-1-1-1-12-2-2211111111-100000000-1−3−33333−3−3−3−33333−3−3-221-1-110000000000
χ3944444444-2-4-4-2-2-222224-4-4-4-2-2-2-22222-200000000200000000000000000000000000000000
χ40444444-4-4-244-2-2-2-2-2-2-2-44-4-4-2-222-2-222200000000200000000000000000000000000000000
χ414444-4-444-244-2-2-2-2-2-2-2-4-44-422-2-222-2-2200000000200000000000000000000000000000000
χ424444-4-4-4-4-2-4-4-2-2-22222444-42222-2-2-2-2-200000000200000000000000000000000000000000
χ4344-4-4004-44004-4-400000000004-40000000−2i22i20000000−2i22i200−2i22i2000000000000000000000000
χ4444-4-4004-44004-4-400000000004-400000002i2−2i200000002i2−2i2002i2−2i2000000000000000000000000
χ4544-4-4004-4-200-2222323−23−23000000-220023−23000−2i22i200000i6−i6i2−i2i6−i6i2−i2000000000000000000000000
χ4644-4-4004-4-200-2222323−23−23000000-220023−230002i2−2i200000−i6i6−i2i2−i6i6−i2i2000000000000000000000000
χ4744-4-4004-4-200-222−23−232323000000-2200−2323000−2i22i200000−i6i6i2−i2−i6i6i2−i2000000000000000000000000
χ4844-4-4004-4-200-222−23−232323000000-2200−23230002i2−2i200000i6−i6−i2i2i6−i6−i2i2000000000000000000000000
χ4944-4-400-444004-4-40000000000-4400000−2i22i20000000−2i22i2002i2−2i200000000000000000000000000
χ5044-4-400-444004-4-40000000000-44000002i2−2i200000002i2−2i200−2i22i200000000000000000000000000
χ5144-4-400-44-200-2222323−23−230000002-200−23230−2i22i20000000i2−i2i6−i6−i2i2−i6i6000000000000000000000000
χ5244-4-400-44-200-2222323−23−230000002-200−232302i2−2i20000000−i2i2−i6i6i2−i2i6−i6000000000000000000000000
χ5344-4-400-44-200-222−23−2323230000002-20023−230−2i22i20000000i2−i2−i6i6−i2i2i6−i6000000000000000000000000
χ5444-4-400-44-200-222−23−2323230000002-20023−2302i2−2i20000000−i2i2i6−i6i2−i2−i6i6000000000000000000000000
χ554-44-44-400400-44-4000000004-40000000000000−2i22i20000000000000−2i22i2−2i22i20000000000000000
χ564-44-44-400400-44-4000000004-400000000000002i2−2i200000000000002i2−2i22i2−2i20000000000000000
χ574-44-44-400-2002-2223−2323−230000-220023−23000000000−2i22i2000000000i6−i6i6−i6i2−i2i2−i20000000000000000
χ584-44-44-400-2002-2223−2323−230000-220023−230000000002i2−2i2000000000−i6i6−i6i6−i2i2−i2i20000000000000000
χ594-44-44-400-2002-22−2323−23230000-2200−2323000000000−2i22i2000000000−i6i6−i6i6i2−i2i2−i20000000000000000
χ604-44-44-400-2002-22−2323−23230000-2200−23230000000002i2−2i2000000000i6−i6i6−i6−i2i2−i2i20000000000000000
χ614-44-4-4400400-44-400000000-4400000000000−2i22i200000000000−2i22i22i2−2i200000000000000000000
χ624-44-4-4400400-44-400000000-44000000000002i2−2i2000000000002i2−2i2−2i22i200000000000000000000
χ634-44-4-4400-2002-2223−2323−2300002-200−23230000000−2i22i200000000000i2−i2−i2i2i6−i6−i6i60000000000000000
χ644-44-4-4400-2002-2223−2323−2300002-200−232300000002i2−2i200000000000−i2i2i2−i2−i6i6i6−i60000000000000000
χ654-44-4-4400-2002-22−2323−232300002-20023−230000000−2i22i200000000000i2−i2−i2i2−i6i6i6−i60000000000000000
χ664-44-4-4400-2002-22−2323−232300002-20023−2300000002i2−2i200000000000−i2i2i2−i2i6−i6−i6i60000000000000000
χ674-4-44000044-4-4-444-4-44000000000000000000000000000000000000000000002-22-2000000
χ684-4-44000044-4-4-444-4-4400000000000000000000000000000000000000000000-22-22000000
χ694-4-4400004-44-4-44-444-4000000000000000000000000000000000000000000002-2-22000000
χ704-4-4400004-44-4-44-444-400000000000000000000000000000000000000000000-222-2000000
χ718-8-880000-48-844-4-444-4000000000000000000000000000000000000000000000000000000
χ728-8-880000-4-8844-44-4-44000000000000000000000000000000000000000000000000000000

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