Finite Group Databasebeta

← Group #10697309

Character table — Group #10697309

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888888888888888824242424484848484848
order12222234444446661212121244466121212121212121212128888888888882424242424242424242424242424242424242424242424244444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ511111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1
χ611111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-1-1-11
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1111-1
χ9222222222-222-2222-2-2-2-2-2-2-22222-2-2-2-222-2-222-2-200000000000000002222-2-2-2-2000000000000000000
χ10222222222-222-2222-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-2220000000000000000-2-2-2-22222000000000000000000
χ112222222-2-22-2-2222222222-2-222-2-222-2-2-2-2-2-2000022-2-200002222-2-2-2-200000000000000000000000000
χ122222222-2-22-2-2222222222-2-222-2-222-2-2-2-2-2-20000-2-2220000-2-2-2-2222200000000000000000000000000
χ132222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-222-2-2220000000022-2-200000000000000002222-2-2-2-20000000000
χ142222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-222-2-22200000000-2-2220000000000000000-2-2-2-222220000000000
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000
χ19222222-122-222-2-1-1-11111-2-2-2-1-1-1-11111-1-11122-2-20000000033−3−333−3−3-1-1-1-1111133−3−333−3−30000000000
χ20222222-122-222-2-1-1-11111-2-2-2-1-1-1-11111-1-11122-2-200000000−3−333−3−333-1-1-1-11111−3−333−3−3330000000000
χ21222222-122-222-2-1-1-11111-2-2-2-1-1-1-11111-1-111-2-2220000000033−3−333−3−31111-1-1-1-1−3−333−3−3330000000000
χ22222222-122-222-2-1-1-11111-2-2-2-1-1-1-11111-1-111-2-22200000000−3−333−3−3331111-1-1-1-133−3−333−3−30000000000
χ23222222-1-2-22-2-22-1-1-1-1-1-1-12-2-2-1-111-1-1111111000022-2-20000-1-1-1-1111133−3−333−3−333−3−3−3−3330000000000
χ24222222-1-2-22-2-22-1-1-1-1-1-1-12-2-2-1-111-1-1111111000022-2-20000-1-1-1-11111−3−333−3−333−3−33333−3−30000000000
χ25222222-1-2-22-2-22-1-1-1-1-1-1-12-2-2-1-111-1-11111110000-2-22200001111-1-1-1-133−3−333−3−3−3−33333−3−30000000000
χ26222222-1-2-22-2-22-1-1-1-1-1-1-12-2-2-1-111-1-11111110000-2-22200001111-1-1-1-1−3−333−3−33333−3−3−3−3330000000000
χ27222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-111-1-10000000022-2-233−3−3−3−333−3−33333−3−3-1-1-1-111110000000000
χ28222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-111-1-10000000022-2-2−3−33333−3−333−3−3−3−333-1-1-1-111110000000000
χ29222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-111-1-100000000-2-22233−3−3−3−33333−3−3−3−3331111-1-1-1-10000000000
χ30222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-111-1-100000000-2-222−3−33333−3−3−3−33333−3−31111-1-1-1-10000000000
χ312222-2-22222-2-222222222-2-22-2-222-2-2-2-2-2-222000000000000000000000000000000000000000020-2000
χ322222-2-22222-2-222222222-2-22-2-222-2-2-2-2-2-2220000000000000000000000000000000000000000-202000
χ332222-2-2222-2-2-2-2222-2-2-2-222-2-2-2222222-2-2-2-20000000000000000000000000000000000002i2i−2i−2i000000
χ342222-2-2222-2-2-2-2222-2-2-2-222-2-2-2222222-2-2-2-2000000000000000000000000000000000000−2i−2i2i2i000000
χ352222-2-22-2-222222222222-22-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000002000-2
χ362222-2-22-2-222222222222-22-2-2-2-2-2-2-22222-2-200000000000000000000000000000000000000000-20002
χ372222-2-22-2-2-222-2222-2-2-2-22-22-2-2-2-222-2-2222200000000000000000000000000000000000000000002-20
χ382222-2-22-2-2-222-2222-2-2-2-22-22-2-2-2-222-2-222220000000000000000000000000000000000000000000-220
χ3922-2-22-222-202-202-2-200000002-22-200002-200002-22−22−22−22−22−22−22−22−200002-22-22−22−22−22−20000000000
χ4022-2-22-222-202-202-2-200000002-22-200002-200002-2−22−22−22−22−22−22−22−2200002-22-2−22−22−22−220000000000
χ4122-2-22-222-202-202-2-200000002-22-200002-20000-222−22−2−22−222−22−22−22−20000-22-22−22−22−22−220000000000
χ4222-2-22-222-202-202-2-200000002-22-200002-20000-22−22−222−22−2−22−22−22−220000-22-222−22−22−22−20000000000
χ4322-2-22-22-220-2202-2-200000002-2-220000-22002-2002−2−222−2−222−22−2−22−222-22-200002−22−2−22−220000000000
χ4422-2-22-22-220-2202-2-200000002-2-220000-22002-200−222−2−222−2−22−222−22−22-22-20000−22−222−22−20000000000
χ4522-2-22-22-220-2202-2-200000002-2-220000-2200-22002−2−22−222−22−22−2−22−22-22-220000−22−222−22−20000000000
χ4622-2-22-22-220-2202-2-200000002-2-220000-2200-2200−222−22−2−22−22−222−22−2-22-2200002−22−2−22−220000000000
χ4722-2-22-2-12-202-20-1113−33−3000-11-113−33−3-113−3002-22−22−22−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−333−3-11-11ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ4822-2-22-2-12-202-20-1113−33−3000-11-113−33−3-113−3002-2−22−22−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−333−3-11-11−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ4922-2-22-2-12-202-20-1113−33−3000-11-113−33−3-113−300-222−22−2−22−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ233−3−331-11-1−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ5022-2-22-2-12-202-20-1113−33−3000-11-113−33−3-113−300-22−22−222−22−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ233−3−331-11-1ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ5122-2-22-2-12-202-20-111−33−33000-11-11−33−33-11−33002-22−22−22−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ73−3−33-11-11ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ5222-2-22-2-12-202-20-111−33−33000-11-11−33−33-11−33002-2−22−22−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ73−3−33-11-11−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ5322-2-22-2-12-202-20-111−33−33000-11-11−33−33-11−3300-222−22−2−22−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−333−31-11-1−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ5422-2-22-2-12-202-20-111−33−33000-11-11−33−33-11−3300-22−22−222−22−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−333−31-11-1ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ5522-2-22-2-1-220-220-1113−33−3000-111-13−3−331-1−332-2002−2−222−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23-11-113−3−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ5622-2-22-2-1-220-220-1113−33−3000-111-13−3−331-1−332-200−222−2−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23-11-113−3−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ5722-2-22-2-1-220-220-1113−33−3000-111-13−3−331-1−33-22002−2−22−222−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ231-11-1−333−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ5822-2-22-2-1-220-220-1113−33−3000-111-13−3−331-1−33-2200−222−22−2−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ231-11-1−333−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ5922-2-22-2-1-220-220-111−33−33000-111-1−333−31-13−32-2002−2−222−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7-11-11−333−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ6022-2-22-2-1-220-220-111−33−33000-111-1−333−31-13−32-200−222−2−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7-11-11−333−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ6122-2-22-2-1-220-220-111−33−33000-111-1−333−31-13−3-22002−2−22−222−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ71-11-13−3−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ6222-2-22-2-1-220-220-111−33−33000-111-1−333−31-13−3-2200−222−22−2−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ71-11-13−3−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ634444-4-4-2444-4-44-2-2-2-2-2-2-2-4-4422-2-2222222-2-20000000000000000000000000000000000000000000000
χ644444-4-4-244-4-4-4-4-2-2-2222244-422-2-2-2-2-2-222220000000000000000000000000000000000000000000000
χ654444-4-4-2-4-44444-2-2-2-2-2-2-2-44-4222222-2-2-2-2220000000000000000000000000000000000000000000000
χ664444-4-4-2-4-4-444-4-2-2-222224-442222-2-222-2-2-2-20000000000000000000000000000000000000000000000
χ6744-4-4-4444-40-4404-4-40000000-444-40000-44000000000000000000000000000000000000000000000000
χ6844-4-4-444-4404-404-4-40000000-44-4400004-4000000000000000000000000000000000000000000000000
χ6944-4-4-44-24-40-440-22223−2323−230002-2-22−2323−23232-223−230000000000000000000000000000000000000000000000
χ7044-4-4-44-24-40-440-222−2323−23230002-2-2223−2323−232-2−23230000000000000000000000000000000000000000000000
χ7144-4-4-44-2-4404-40-22223−2323−230002-22-2−232323−23-22−23230000000000000000000000000000000000000000000000
χ7244-4-4-44-2-4404-40-222−2323−23230002-22-223−23−2323-2223−230000000000000000000000000000000000000000000000
χ734-44-400400400-4-44-444-4-40000000000000000000000000000000000000000000000000002-22-2000000
χ744-44-400400400-4-44-444-4-4000000000000000000000000000000000000000000000000000-22-22000000
χ754-44-400400-4004-44-4-4-4440000000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ764-44-400400-4004-44-4-4-444000000000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ778-88-800-400800-84-44-4-4440000000000000000000000000000000000000000000000000000000000000
χ788-88-800-400-80084-4444-4-40000000000000000000000000000000000000000000000000000000000000
χ798-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

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