Finite Group Databasebeta

← Group #72246915

Character table — Group #72246915

Order 3024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222244666677771212121212121414141414141414141414182424282828282828282828282828282828283636363636364242424242424242424263636363636384848484848484848484108126126
order12336636447143366121221214242333346666121242142336612121212121212121212121228288484848444121212121212121222666612121212121212121212281212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-11111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111
χ3111111111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32
χ4111111111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i32-1−1−i32−1−i32−1+i32−1+i321+i321−i32111−1−i32−1+i32−1−i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32111111-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321−1−i32−1+i32
χ5111111111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32
χ6111111111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i32-1−1+i32−1+i32−1−i32−1−i321−i321+i32111−1+i32−1−i32−1+i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32111111-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−1+i32−1−i32
χ7111111111-11111111-1111111111111111-11111111111111111111-111-1-11-11-11-11-11-1-1-1-1-1-1-11-11-11-11-11-1-1-1-1
χ8111111111-11111111-111111111-11111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-111-11-1-11-11111111-111-11-1-11-11-1-1-1
χ9111111111-111−1−i32−1+i32−1−i32−1+i321-11111−1−i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-111−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321-111-1-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32-1-11+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32-11+i321−i32
χ10111111111-111−1−i32−1+i32−1−i32−1+i321-11111−1−i32−1−i32−1+i32−1+i32-1−1−i32−1−i32−1+i32−1+i321+i321−i32-111−1−i32−1+i32−1−i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i321-111-1-1-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32-11+i321−i32
χ11111111111-111−1+i32−1−i32−1+i32−1−i321-11111−1+i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-111−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321-111-1-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32-1-11−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32-11−i321+i32
χ12111111111-111−1+i32−1−i32−1+i32−1−i321-11111−1+i32−1+i32−1−i32−1−i32-1−1+i32−1+i32−1−i32−1−i321−i321+i32-111−1+i32−1−i32−1+i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i321-111-1-1-11−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-11−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32-11−i321+i32
χ1311111111-11111111-11111111111111111-1111111111111111111-11-1-111-11-11-11-11-11-1-1-1-1-1-1-11-11-11-11-11-1-1-1
χ1411111111-11111111-1111111111-11111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11-111-11-11111111-1-11-111-11-1-1-1-1
χ1511111111-1111−1−i32−1+i32−1−i32−1+i32-111111−1−i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-111−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-1-111-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32-1-11+i321+i321−i321−i32-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32-11+i321−i32
χ1611111111-1111−1−i32−1+i32−1−i32−1+i32-111111−1−i32−1−i32−1+i32−1+i32-1−1−i32−1−i32−1+i32−1+i321+i321−i32-111−1−i32−1+i32−1−i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32-11-1-1111-11+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i3211−1−i32−1−i32−1+i32−1+i321-11+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32-11+i321−i32
χ1711111111-1111−1+i32−1−i32−1+i32−1−i32-111111−1+i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-111−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-1-111-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32-1-11−i321−i321+i321+i32-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32-11−i321+i32
χ1811111111-1111−1+i32−1−i32−1+i32−1−i32-111111−1+i32−1+i32−1−i32−1−i32-1−1+i32−1+i32−1−i32−1−i321−i321+i32-111−1+i32−1−i32−1+i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32-11-1-1111-11−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i3211−1+i32−1+i32−1−i32−1−i321-11−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32-11−i321+i32
χ1911111111-1-1111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111
χ2011111111-1-1111111-1-111111111-11111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111111
χ2111111111-1-111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321+i321+i321−i321−i321−1−i32−1+i32
χ2211111111-1-111−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1−i32−1+i32−1+i32-1−1−i32−1−i32−1+i32−1+i321+i321−i32111−1−i32−1+i32−1−i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32-1-1-1-1-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32
χ2311111111-1-111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321−i321−i321+i321+i321−1+i32−1−i32
χ2411111111-1-111−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1+i32−1−i32−1−i32-1−1+i32−1+i32−1−i32−1−i321−i321+i32111−1+i32−1−i32−1+i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32-1-1-1-1-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32
χ25222-12-1-1-1022222220-12-12-12-12-122-12-1220-1-1-1-1-1-12-1-1-12-12-1-1-1-1-10200-1-102020202020000000-10-10-10-10-1000
χ26222-12-1-1-1022222220-12-12-12-12-1-22-12-1-2-20-1-1-1-1-1-1-2111-21-2111110200-1-10-202020-20-2000000010-10-10101000
χ27222-12-1-1-10222−1−i3−1+i3−1−i3−1+i30-12-12-1−1−i31+i32−1+i31−i322−1−i31+i32−1+i31−i32−1−i3−1+i30-1-11+i321−i321+i321−i322-1-1-1−1−i31+i32−1+i31−i321+i321+i321−i321−i320200-1-1020−1−i30−1+i30−1−i30−1+i30000000-101+i3201−i3201+i3201−i32000
χ28222-12-1-1-10222−1−i3−1+i3−1−i3−1+i30-12-12-1−1−i31+i32−1+i31−i32-2−1−i31+i32−1+i31−i321+i31−i30-1-11+i321−i321+i321−i32-21111+i3−1−i321−i3−1+i32−1−i32−1−i32−1+i32−1+i320200-1-10-20−1−i30−1+i301+i301−i30000000101+i3201−i320−1−i320−1+i32000
χ29222-12-1-1-10222−1+i3−1−i3−1+i3−1−i30-12-12-1−1+i31−i32−1−i31+i322−1+i31−i32−1−i31+i32−1+i3−1−i30-1-11−i321+i321−i321+i322-1-1-1−1+i31−i32−1−i31+i321−i321−i321+i321+i320200-1-1020−1+i30−1−i30−1+i30−1−i30000000-101−i3201+i3201−i3201+i32000
χ30222-12-1-1-10222−1+i3−1−i3−1+i3−1−i30-12-12-1−1+i31−i32−1−i31+i32-2−1+i31−i32−1−i31+i321−i31+i30-1-11−i321+i321−i321+i32-21111−i3−1+i321+i3−1−i32−1+i32−1+i32−1−i32−1−i320200-1-10-20−1+i30−1−i301−i301+i30000000101−i3201+i320−1+i320−1−i32000
χ31222-12-1-1-10-2222222012-12-12-12-122-12-1220-1-1-1-1-1-12-1-1-12-12-1-1-1-1-10-200110-20-20-20-20-20000000101010101000
χ32222-12-1-1-10-2222222012-12-12-12-1-22-12-1-2-20-1-1-1-1-1-1-2111-21-2111110-20011020-20-202020000000-101010-10-1000
χ33222-12-1-1-10-222−1−i3−1+i3−1−i3−1+i3012-12-1−1−i31+i32−1+i31−i322−1−i31+i32−1+i31−i32−1−i3−1+i30-1-11+i321−i321+i321−i322-1-1-1−1−i31+i32−1+i31−i321+i321+i321−i321−i320-200110-201+i301−i301+i301−i3000000010−1−i320−1+i320−1−i320−1+i32000
χ34222-12-1-1-10-222−1−i3−1+i3−1−i3−1+i3012-12-1−1−i31+i32−1+i31−i32-2−1−i31+i32−1+i31−i321+i31−i30-1-11+i321−i321+i321−i32-21111+i3−1−i321−i3−1+i32−1−i32−1−i32−1+i32−1+i320-200110201+i301−i30−1−i30−1+i30000000-10−1−i320−1+i3201+i3201−i32000
χ35222-12-1-1-10-222−1+i3−1−i3−1+i3−1−i3012-12-1−1+i31−i32−1−i31+i322−1+i31−i32−1−i31+i32−1+i3−1−i30-1-11−i321+i321−i321+i322-1-1-1−1+i31−i32−1−i31+i321−i321−i321+i321+i320-200110-201−i301+i301−i301+i3000000010−1+i320−1−i320−1+i320−1−i32000
χ36222-12-1-1-10-222−1+i3−1−i3−1+i3−1−i3012-12-1−1+i31−i32−1−i31+i32-2−1+i31−i32−1−i31+i321−i31+i30-1-11−i321+i321−i321+i32-21111−i3−1+i321+i3−1−i32−1+i32−1+i32−1−i32−1−i320-200110201−i301+i30−1+i30−1−i30000000-10−1+i320−1−i3201−i3201+i32000
χ3722-12-12-1-120222222-10-12-12-12-122-12-12220-1-1-1-1-1-1-12-1-1-12-12-1-1-1-120-1-1002020202020000000-10-10-10-10-10000
χ3822-12-12-1-120222222-10-12-12-12-12-2-12-12-2-20-1-1-1-1-1-11-2111-21-2111120-1-100-202020-20-2000000010-10-101010000
χ3922-12-12-1-12022−1−i3−1+i3−1−i3−1+i3-10-12-121+i32−1−i31−i32−1+i321+i32−1−i31−i32−1+i3−1−i3−1+i30-1-11+i321−i321+i321−i32-12-1-11+i32−1−i31−i32−1+i31+i321+i321−i321−i3220-1-10020−1−i30−1+i30−1−i30−1+i30000000-101+i3201−i3201+i3201−i320000
χ4022-12-12-1-12022−1−i3−1+i3−1−i3−1+i3-10-12-121+i32−1−i31−i32−1+i3-21+i32−1−i31−i32−1+i31+i31−i30-1-11+i321−i321+i321−i321-211−1−i321+i3−1+i321−i3−1−i32−1−i32−1+i32−1+i3220-1-100-20−1−i30−1+i301+i301−i30000000101+i3201−i320−1−i320−1+i320000
χ4122-12-12-1-12022−1+i3−1−i3−1+i3−1−i3-10-12-121−i32−1+i31+i32−1−i321−i32−1+i31+i32−1−i3−1+i3−1−i30-1-11−i321+i321−i321+i32-12-1-11−i32−1+i31+i32−1−i31−i321−i321+i321+i3220-1-10020−1+i30−1−i30−1+i30−1−i30000000-101−i3201+i3201−i3201+i320000
χ4222-12-12-1-12022−1+i3−1−i3−1+i3−1−i3-10-12-121−i32−1+i31+i32−1−i3-21−i32−1+i31+i32−1−i31−i31+i30-1-11−i321+i321−i321+i321-211−1+i321−i3−1−i321+i3−1+i32−1+i32−1−i32−1−i3220-1-100-20−1+i30−1−i301−i301+i30000000101−i3201+i320−1+i320−1−i320000
χ4322-12-12-1-1-2022222210-12-12-12-122-12-12220-1-1-1-1-1-1-12-1-1-12-12-1-1-1-1-201100-20-20-20-20-200000001010101010000
χ4422-12-12-1-1-2022222210-12-12-12-12-2-12-12-2-20-1-1-1-1-1-11-2111-21-21111-20110020-20-202020000000-101010-10-10000
χ4522-12-12-1-1-2022−1−i3−1+i3−1−i3−1+i310-12-121+i32−1−i31−i32−1+i321+i32−1−i31−i32−1+i3−1−i3−1+i30-1-11+i321−i321+i321−i32-12-1-11+i32−1−i31−i32−1+i31+i321+i321−i321−i32-201100-201+i301−i301+i301−i3000000010−1−i320−1+i320−1−i320−1+i320000
χ4622-12-12-1-1-2022−1−i3−1+i3−1−i3−1+i310-12-121+i32−1−i31−i32−1+i3-21+i32−1−i31−i32−1+i31+i31−i30-1-11+i321−i321+i321−i321-211−1−i321+i3−1+i321−i3−1−i32−1−i32−1+i32−1+i32-201100201+i301−i30−1−i30−1+i30000000-10−1−i320−1+i3201+i3201−i320000
χ4722-12-12-1-1-2022−1+i3−1−i3−1+i3−1−i310-12-121−i32−1+i31+i32−1−i321−i32−1+i31+i32−1−i3−1+i3−1−i30-1-11−i321+i321−i321+i32-12-1-11−i32−1+i31+i32−1−i31−i321−i321+i321+i32-201100-201−i301+i301−i301+i3000000010−1+i320−1−i320−1+i320−1−i320000
χ4822-12-12-1-1-2022−1+i3−1−i3−1+i3−1−i310-12-121−i32−1+i31+i32−1−i3-21−i32−1+i31+i32−1−i31−i31+i30-1-11−i321+i321−i321+i321-211−1+i321−i3−1−i321+i3−1+i32−1+i32−1−i32−1−i32-201100201−i301+i30−1+i30−1−i30000000-10−1+i320−1−i3201−i3201+i320000
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.