Finite Group Databasebeta

← Group #10695701

Character table — Group #10695701

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888888888888888824242424484848484848
order1222222222344666121212124446666661212121212124444888888881212121212121212242424242424242424242424242424244444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ511111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ611111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-11-1-1
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11-111
χ922222222222-2-2222-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2000000002222-2-2-2-200000000000000000000000000
χ1022222222222-2-2222-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000
χ112222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ122222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000
χ132222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000
χ142222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000
χ152222222222-1-2-2-1-1-11111-2-2-2-1-1-1-1-1-111111122-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−30000000000
χ162222222222-1-2-2-1-1-11111-2-2-2-1-1-1-1-1-111111122-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−333330000000000
χ172222222222-1-2-2-1-1-11111-2-2-2-1-1-1-1-1-1111111-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−333330000000000
χ182222222222-1-2-2-1-1-11111-2-2-2-1-1-1-1-1-1111111-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−30000000000
χ19222222-2-2-2-22222222222-2-2222-2-2-2-2-2-2-2-2220000000000000000000000000000000000000000020-200
χ20222222-2-2-2-22222222222-2-2222-2-2-2-2-2-2-2-22200000000000000000000000000000000000000000-20200
χ21222222-2-2-2-22-2-2222-2-2-2-222-222-2-2-2-22222-2-2000000000000000000000000000000000000000000002i−2i
χ22222222-2-2-2-22-2-2222-2-2-2-222-222-2-2-2-22222-2-200000000000000000000000000000000000000000000−2i2i
χ232222-2-22-2-2222222222222-2-2-2-222-2-222-2-2-2-2000022-2-200000000000022-2-222-2-2000000000000000000
χ242222-2-22-2-2222222222222-2-2-2-222-2-222-2-2-2-20000-2-222000000000000-2-222-2-222000000000000000000
χ252222-2-22-2-222-2-2222-2-2-2-2-222-2-222-2-2-2-222220000000022-2-2000000000000000022-2-222-2-20000000000
χ262222-2-22-2-222-2-2222-2-2-2-2-222-2-222-2-2-2-2222200000000-2-2220000000000000000-2-222-2-2220000000000
χ272222-2-22-2-22-122-1-1-1-1-1-1-12-2-211-1-111-1-11111000022-2-2000033−3−333−3−3-1-111-1-11133−3−3−3−3330000000000
χ282222-2-22-2-22-122-1-1-1-1-1-1-12-2-211-1-111-1-11111000022-2-20000−3−333−3−333-1-111-1-111−3−33333−3−30000000000
χ292222-2-22-2-22-122-1-1-1-1-1-1-12-2-211-1-111-1-111110000-2-222000033−3−333−3−311-1-111-1-1−3−33333−3−30000000000
χ302222-2-22-2-22-122-1-1-1-1-1-1-12-2-211-1-111-1-111110000-2-2220000−3−333−3−33311-1-111-1-133−3−3−3−3330000000000
χ312222-2-22-2-22-1-2-2-1-1-11111-22211-1-11111-1-1-1-10000000022-2-233−3−3−3−333−3−33333−3−3-1-111-1-1110000000000
χ322222-2-22-2-22-1-2-2-1-1-11111-22211-1-11111-1-1-1-10000000022-2-2−3−33333−3−333−3−3−3−333-1-111-1-1110000000000
χ332222-2-22-2-22-1-2-2-1-1-11111-22211-1-11111-1-1-1-100000000-2-22233−3−3−3−33333−3−3−3−33311-1-111-1-10000000000
χ342222-2-22-2-22-1-2-2-1-1-11111-22211-1-11111-1-1-1-100000000-2-222−3−33333−3−3−3−33333−3−311-1-111-1-10000000000
χ352222-2-2-222-22222222222-22-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000000020-2000
χ362222-2-2-222-22222222222-22-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000-202000
χ372222-2-2-222-22-2-2222-2-2-2-22-22-2-2-2-22222-2-22200000000000000000000000000000000000022-2-2000000
χ382222-2-2-222-22-2-2222-2-2-2-22-22-2-2-2-22222-2-222000000000000000000000000000000000000-2-222000000
χ3922-2-22-222-2-22002-2-200000002-22-22-2000000002-22−22−22−22−200002-22-22−22−22−22−22−22−22−22−20000000000
χ4022-2-22-222-2-22002-2-200000002-22-22-2000000002-2−22−22−22−2200002-22-2−22−22−22−22−22−22−22−220000000000
χ4122-2-22-222-2-22002-2-200000002-22-22-200000000-222−22−2−22−220000-22-222−22−22−22−2−22−22−22−220000000000
χ4222-2-22-222-2-22002-2-200000002-22-22-200000000-22−22−222−22−20000-22-22−22−22−22−222−22−22−22−20000000000
χ4322-2-22-222-2-2-100-11133−3−3000-11-11-113−33−33−3002-22−22−22−22−23−33−3-11-11ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000
χ4422-2-22-222-2-2-100-11133−3−3000-11-11-113−33−33−3002-2−22−22−22−223−33−3-11-11−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000
χ4522-2-22-222-2-2-100-11133−3−3000-11-11-113−33−33−300-222−22−2−22−22−33−331-11-1ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000
χ4622-2-22-222-2-2-100-11133−3−3000-11-11-113−33−33−300-22−22−222−22−2−33−331-11-1−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000
χ4722-2-22-222-2-2-100-111−3−333000-11-11-11−33−33−33002-22−22−22−22−2−33−33-11-11ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000
χ4822-2-22-222-2-2-100-111−3−333000-11-11-11−33−33−33002-2−22−22−22−22−33−33-11-11−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000
χ4922-2-22-222-2-2-100-111−3−333000-11-11-11−33−33−3300-222−22−2−22−223−33−31-11-1ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000
χ5022-2-22-222-2-2-100-111−3−333000-11-11-11−33−33−3300-22−22−222−22−23−33−31-11-1−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000
χ5122-2-2-222-22-22002-2-20000000-222-2-220000002-2002−2−222−2−22-222-200002−2−222−2−222−2−222−2−220000000000
χ5222-2-2-222-22-22002-2-20000000-222-2-220000002-200−222−2−222−2-222-20000−222−2−222−2−222−2−222−20000000000
χ5322-2-2-222-22-22002-2-20000000-222-2-22000000-22002−2−22−222−22-2-2200002−2−222−2−22−222−2−222−20000000000
χ5422-2-2-222-22-22002-2-20000000-222-2-22000000-2200−222−22−2−222-2-220000−222−2−222−22−2−222−2−220000000000
χ5522-2-2-222-22-2-100-11133−3−30001-1-111-13−3−33−332-2002−2−222−2−221-1-113−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ230000000000
χ5622-2-2-222-22-2-100-11133−3−30001-1-111-13−3−33−332-200−222−2−222−21-1-113−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ230000000000
χ5722-2-2-222-22-2-100-11133−3−30001-1-111-13−3−33−33-22002−2−22−222−2-111-1−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ230000000000
χ5822-2-2-222-22-2-100-11133−3−30001-1-111-13−3−33−33-2200−222−22−2−22-111-1−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ230000000000
χ5922-2-2-222-22-2-100-111−3−3330001-1-111-1−333−33−32-2002−2−222−2−221-1-11−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ70000000000
χ6022-2-2-222-22-2-100-111−3−3330001-1-111-1−333−33−32-200−222−2−222−21-1-11−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ70000000000
χ6122-2-2-222-22-2-100-111−3−3330001-1-111-1−333−33−3-22002−2−22−222−2-111-13−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ70000000000
χ6222-2-2-222-22-2-100-111−3−3330001-1-111-1−333−33−3-2200−222−22−2−22-111-13−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ70000000000
χ63444444-4-4-4-4-244-2-2-2-2-2-2-2-4-44-2-222222222-2-20000000000000000000000000000000000000000000000
χ64444444-4-4-4-4-2-4-4-2-2-2222244-4-2-22222-2-2-2-2220000000000000000000000000000000000000000000000
χ654444-4-4-444-4-244-2-2-2-2-2-2-2-44-42222-2-222-2-2220000000000000000000000000000000000000000000000
χ664444-4-4-444-4-2-4-4-2-2-222224-442222-2-2-2-222-2-20000000000000000000000000000000000000000000000
χ6744-4-44-4-4-4444004-4-400000004-4-44-440000000000000000000000000000000000000000000000000000
χ6844-4-44-4-4-444-200-2222323−23−23000-222-22-2−2323−232323−230000000000000000000000000000000000000000000000
χ6944-4-44-4-4-444-200-222−23−232323000-222-22-223−2323−23−23230000000000000000000000000000000000000000000000
χ7044-4-4-44-44-444004-4-40000000-44-444-40000000000000000000000000000000000000000000000000000
χ7144-4-4-44-44-44-200-2222323−23−230002-22-2-22−232323−23−23230000000000000000000000000000000000000000000000
χ7244-4-4-44-44-44-200-222−23−2323230002-22-2-2223−23−232323−230000000000000000000000000000000000000000000000
χ734-44-400000044-4-4-444-44-40000000000000000000000000000000000000000000000000002i−2i2i−2i000000
χ744-44-400000044-4-4-444-44-4000000000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ754-44-40000004-44-4-44-44-440000000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ764-44-40000004-44-4-44-44-44000000000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ778-88-8000000-48-844-4-44-440000000000000000000000000000000000000000000000000000000000000
χ788-88-8000000-4-8844-44-44-40000000000000000000000000000000000000000000000000000000000000
χ798-8-88000000800-88-800000000000000000000000000000000000000000000000000000000000000000
χ808-8-88000000-4004-4443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-8-88000000-4004-44−434343−430000000000000000000000000000000000000000000000000000000000000

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