Finite Group Databasebeta

← Group #10698113

Character table — Group #10698113

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888888888888888816161616161624242424484848484848
order12222222344666121212122444666612121212444444446121212121212121212121212121212121288242424244444244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ5111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-11-11-1-1
χ6111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ9222222222-2-2222-2-2-2-22-2-2-22222-2-2-2-2000000002-2000000000000000000000022-2-2000000
χ10222222222-2-2222-2-2-2-22-2-2-22222-2-2-2-2000000002-20000000000000000000000-2-222000000
χ1122222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ1222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-211110000000000
χ1322222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-211110000000000
χ1422222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-10000000000
χ15222222-2-22222222222-22-2-222-2-222-2-200000000-2-20000000000000000000000000020-2000
χ16222222-2-22222222222-22-2-222-2-222-2-200000000-2-200000000000000000000000000-202000
χ17222222-2-22-2-2222-2-2-2-2-2-22222-2-2-2-22222-2-20000-222222-2-2-2-2000000000000000000000000
χ18222222-2-22-2-2222-2-2-2-2-2-22222-2-2-2-222-2-2220000-22-2-2-2-22222000000000000000000000000
χ19222222-2-2-1-2-2-1-1-11111-2-222-1-11111-1-122-2-200001-1-1-1-1-111113333−3−3−3−30033−3−30000000000
χ20222222-2-2-1-2-2-1-1-11111-2-222-1-11111-1-122-2-200001-1-1-1-1-11111−3−3−3−3333300−3−3330000000000
χ21222222-2-2-1-2-2-1-1-11111-2-222-1-11111-1-1-2-22200001-11111-1-1-1-13333−3−3−3−300−3−3330000000000
χ22222222-2-2-1-2-2-1-1-11111-2-222-1-11111-1-1-2-22200001-11111-1-1-1-1−3−3−3−333330033−3−30000000000
χ232222-2-2222222222222-2-22-2-2-222-2-22200000000-2-200000000000000000000000000020-200
χ242222-2-2222222222222-2-22-2-2-222-2-22200000000-2-2000000000000000000000000000-20200
χ252222-2-2222-2-2222-2-2-2-2-22-22-2-22222-2-2000022-2-2-220000000022-2-222-2-20000000000000000
χ262222-2-2222-2-2222-2-2-2-2-22-22-2-22222-2-20000-2-222-2200000000-2-222-2-2220000000000000000
χ272222-2-222-1-2-2-1-1-11111-22-2211-1-1-1-111000022-2-21-133−3−333−3−3-1-111-1-111003−33−30000000000
χ282222-2-222-1-2-2-1-1-11111-22-2211-1-1-1-111000022-2-21-1−3−333−3−333-1-111-1-11100−33−330000000000
χ292222-2-222-1-2-2-1-1-11111-22-2211-1-1-1-1110000-2-2221-133−3−333−3−311-1-111-1-100−33−330000000000
χ302222-2-222-1-2-2-1-1-11111-22-2211-1-1-1-1110000-2-2221-1−3−333−3−33311-1-111-1-1003−33−30000000000
χ312222-2-2-2-222222222222-2-22-2-2-2-2-2-2-2-2000000002200000000000000002-22-2-220000000000
χ322222-2-2-2-222222222222-2-22-2-2-2-2-2-2-2-200000000220000000000000000-22-222-20000000000
χ332222-2-2-2-22-2-2222-2-2-2-2222-2-2-2-2-22222000000002-20000000000000000000000000000002i−2i
χ342222-2-2-2-22-2-2222-2-2-2-2222-2-2-2-2-22222000000002-2000000000000000000000000000000−2i2i
χ352222-2-2-2-2-122-1-1-1-1-1-1-12-2-221111111100000000-1-133−3−3−3−33333−3−3−3−333-221-1-110000000000
χ362222-2-2-2-2-122-1-1-1-1-1-1-12-2-221111111100000000-1-133−3−3−3−333−3−33333−3−32-2-111-10000000000
χ372222-2-2-2-2-122-1-1-1-1-1-1-12-2-221111111100000000-1-1−3−33333−3−333−3−3−3−3332-2-111-10000000000
χ382222-2-2-2-2-122-1-1-1-1-1-1-12-2-221111111100000000-1-1−3−33333−3−3−3−33333−3−3-221-1-110000000000
χ3944444444-2-4-4-2-2-222224-4-4-4-2-2-2-2222200000000-2200000000000000000000000000000000
χ40444444-4-4-244-2-2-2-2-2-2-2-44-4-4-2-222-2-222000000002200000000000000000000000000000000
χ414444-4-444-244-2-2-2-2-2-2-2-4-44-422-2-222-2-2000000002200000000000000000000000000000000
χ424444-4-4-4-4-2-4-4-2-2-22222444-42222-2-2-2-200000000-2200000000000000000000000000000000
χ4344-4-44-4004004-4-4000000004-400000000002-22-200000000002-22-22-22-20000000000000000
χ4444-4-44-4004004-4-4000000004-40000000000-22-220000000000-22-22-22-220000000000000000
χ4544-4-44-400-200-2222323−23−230000-220023−230000002-22-20000000000−1+31−3−1+31−3−1−31+3−1−31+30000000000000000
χ4644-4-44-400-200-2222323−23−230000-220023−23000000-22-2200000000001−3−1+31−3−1+31+3−1−31+3−1−30000000000000000
χ4744-4-44-400-200-222−23−2323230000-2200−23230000002-22-20000000000−1−31+3−1−31+3−1+31−3−1+31−30000000000000000
χ4844-4-44-400-200-222−23−2323230000-2200−2323000000-22-2200000000001+3−1−31+3−1−31−3−1+31−3−1+30000000000000000
χ4944-4-4-44004004-4-400000000-4400000000002-2-2200000000002-2-222-2-220000000000000000
χ5044-4-4-44004004-4-400000000-440000000000-222-20000000000-222-2-222-20000000000000000
χ5144-4-4-4400-200-2222323−23−2300002-200−23230000002-2-220000000000−1−31+31+3−1−3−1+31−31−3−1+30000000000000000
χ5244-4-4-4400-200-2222323−23−2300002-200−2323000000-222-200000000001+3−1−3−1−31+31−3−1+3−1+31−30000000000000000
χ5344-4-4-4400-200-222−23−23232300002-20023−230000002-2-220000000000−1+31−31−3−1+3−1−31+31+3−1−30000000000000000
χ5444-4-4-4400-200-222−23−23232300002-20023−23000000-222-200000000001−3−1+3−1+31−31+3−1−3−1−31+30000000000000000
χ554-44-4000044-4-4-444-44-4000000000000000000000000000000000000000000002i−2i2i−2i000000
χ564-44-4000044-4-4-444-44-400000000000000000000000000000000000000000000−2i2i−2i2i000000
χ574-44-400004-44-4-44-44-44000000000000000000000000000000000000000000002i−2i−2i2i000000
χ584-44-400004-44-4-44-44-4400000000000000000000000000000000000000000000−2i2i2i−2i000000
χ594-4-44004-4400-44-400000000004-400002-22-20000002-22-22-22-2000000000000000000000000
χ604-4-44004-4400-44-400000000004-40000-22-22000000-22-22-22-22000000000000000000000000
χ614-4-44004-4-2002-2223−23−2323000000-220023−232-22-2000000−1+31−3−1−31+3−1+31−3−1−31+3000000000000000000000000
χ624-4-44004-4-2002-2223−23−2323000000-220023−23-22-220000001−3−1+31+3−1−31−3−1+31+3−1−3000000000000000000000000
χ634-4-44004-4-2002-22−232323−23000000-2200−23232-22-2000000−1−31+3−1+31−3−1−31+3−1+31−3000000000000000000000000
χ644-4-44004-4-2002-22−232323−23000000-2200−2323-22-220000001+3−1−31−3−1+31+3−1−31−3−1+3000000000000000000000000
χ654-4-4400-44400-44-40000000000-4400002-2-220000002-22-2-22-22000000000000000000000000
χ664-4-4400-44400-44-40000000000-440000-222-2000000-22-222-22-2000000000000000000000000
χ674-4-4400-44-2002-2223−23−23230000002-200−23232-2-22000000−1−31+3−1+31−31+3−1−31−3−1+3000000000000000000000000
χ684-4-4400-44-2002-2223−23−23230000002-200−2323-222-20000001+3−1−31−3−1+3−1−31+3−1+31−3000000000000000000000000
χ694-4-4400-44-2002-22−232323−230000002-20023−232-2-22000000−1+31−3−1−31+31−3−1+31+3−1−3000000000000000000000000
χ704-4-4400-44-2002-22−232323−230000002-20023−23-222-20000001−3−1+31+3−1−3−1+31−3−1−31+3000000000000000000000000
χ718-88-80000-48-844-4-44-44000000000000000000000000000000000000000000000000000000
χ728-88-80000-4-8844-44-44-4000000000000000000000000000000000000000000000000000000

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