Finite Group Databasebeta

← Group #72246942

Character table — Group #72246942

Order 3024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1122223344666667777121212121214141414141414141414141414141414141818181818212121212424282828282828282828282828283636363642424242424242424242424242424242424254548484848484126126126126126
order123366443627121214336662121424223333666666666666414142828121212122142336666666666642428484446612121212121212121212121212122828661212122661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-11111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ3111111111111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i3211111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32
χ4111111111111111−1−i32−1+i32−1−i32−1+i3211111-1−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i3211111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32-1-1-11+i321−i32−1−i32−1+i321+i321+i321−i321−i321111-1-1−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211−1−i32−1+i32-11+i321−i32-11+i321−i32−1−i32−1+i32
χ5111111111111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i3211111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32
χ6111111111111111−1+i32−1−i32−1+i32−1−i3211111-1−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i3211111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32-1-1-11−i321+i32−1+i32−1−i321−i321−i321+i321+i321111-1-1−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211−1+i32−1−i32-11−i321+i32-11−i321+i32−1+i32−1−i32
χ71111111111-111111111-1111111111111111111111-1-1-1111111111111111111111-1-1111-1-1-1111-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ81111111111-111111111-11111-11111-1-1-1-1-1-1-1-11111-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-111-11-1-1-1-1-11-111111-1-1-1-1-1-1-1-1111111-1-1
χ91111111111-11111−1−i32−1+i32−1−i32−1+i32-111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1111-11+i321−i3211−1−i321+i32−1+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i32-11+i321−i32-11+i321−i321+i321−i32
χ101111111111-11111−1−i32−1+i32−1−i32−1+i32-11111-1−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-1-1-111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32-1-1-11+i321−i32−1−i32−1+i321+i321+i321−i321−i32-1-111-111+i321−i32-1-11+i32−1−i321−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-11+i321−i321−1−i32−1+i321−1−i32−1+i321+i321−i32
χ111111111111-11111−1+i32−1−i32−1+i32−1−i32-111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1111-11−i321+i3211−1+i321−i32−1−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i32-11−i321+i32-11−i321+i321−i321+i32
χ121111111111-11111−1+i32−1−i32−1+i32−1−i32-11111-1−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-1-1-111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32-1-1-11−i321+i32−1+i32−1−i321−i321−i321+i321+i32-1-111-111−i321+i32-1-11−i32−1+i321+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-11−i321+i321−1+i32−1−i321−1+i32−1−i321−i321+i32
χ13111111-1-11111-1-1111111111111111111111111111-111-1-1-1-1-1-111111111111111111-1-1-1111-1-1-11-11-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ14111111-1-11111-1-11111111111-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-111-1-11-111111-11-1-1-1-1-11111-1-111-1-1-1111-1-1
χ15111111-1-11111-1-11−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-111-1-11+i321+i321−i321−i3211−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-11−1−i32−1+i32-1-11+i32−1−i321−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-1-1−1−i32−1+i321−1−i32−1+i32-11+i321−i321+i321−i32
χ16111111-1-11111-1-11−1−i32−1+i32−1−i32−1+i3211111-1−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-111-1-11+i321+i321−i321−i3211−1−i32−1+i32-1-1-11+i321−i32−1−i32−1+i321+i321+i321−i321−i3211-1-11-1−1−i32−1+i3211−1−i321+i32−1+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1−1−i32−1+i32-11+i321−i321−1−i32−1+i321+i321−i32
χ17111111-1-11111-1-11−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-111-1-11−i321−i321+i321+i3211−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-11−1+i32−1−i32-1-11−i32−1+i321+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-1-1−1+i32−1−i321−1+i32−1−i32-11−i321+i321−i321+i32
χ18111111-1-11111-1-11−1+i32−1−i32−1+i32−1−i3211111-1−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-111-1-11−i321−i321+i321+i3211−1+i32−1−i32-1-1-11−i321+i32−1+i32−1−i321−i321−i321+i321+i3211-1-11-1−1+i32−1−i3211−1+i321−i32−1−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1−1+i32−1−i32-11−i321+i321−1+i32−1−i321−i321+i32
χ19111111-1-111-11-1-111111-11111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111
χ20111111-1-111-11-1-111111-11111-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111111-1-1111-1-1-111
χ21111111-1-111-11-1-11−1−i32−1+i32−1−i32−1+i32-111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-1-11+i321+i321−i321−i3211−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-11+i321−i32-1-11+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32111+i321−i32-11+i321−i321−1−i32−1+i32−1−i32−1+i32
χ22111111-1-111-11-1-11−1−i32−1+i32−1−i32−1+i32-11111-1−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321-1-1-1-11+i321+i321−i321−i3211−1−i32−1+i32-1-1-11+i321−i32−1−i32−1+i321+i321+i321−i321−i32-1-1-1-1111+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32111+i321−i321−1−i32−1+i32-11+i321−i32−1−i32−1+i32
χ23111111-1-111-11-1-11−1+i32−1−i32−1+i32−1−i32-111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-1-11−i321−i321+i321+i3211−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-11−i321+i32-1-11−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32111−i321+i32-11−i321+i321−1+i32−1−i32−1+i32−1−i32
χ24111111-1-111-11-1-11−1+i32−1−i32−1+i32−1−i32-11111-1−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321-1-1-1-11−i321−i321+i321+i3211−1+i32−1−i32-1-1-11−i321+i32−1+i32−1−i321−i321−i321+i321+i32-1-1-1-1111−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32111−i321+i321−1+i32−1−i32-11−i321+i32−1+i32−1−i32
χ25222-1-1200-1-1220022222-12-1-12222-1-122222222-1-122022000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10002220002020000000000-1-1-1-1-100000
χ26222-1-1200-1-1220022222-12-1-12-222-1-1-2-2-2-2-2-2-2-2-1-122022000000-1-1-1-111111-1-11111-1-1000-222000-20-20000000000-1-111100000
χ27222-1-1200-1-122002−1−i3−1+i3−1−i3−1+i3-12-1-122−1−i3−1+i31+i321−i3222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i3022000000-1-11+i321−i32-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32-1-10002−1−i3−1+i3000−1−i30−1+i300000000001+i321−i32-11+i321−i3200000
χ28222-1-1200-1-122002−1−i3−1+i3−1−i3−1+i3-12-1-12-2−1−i3−1+i31+i321−i32-2-21+i31−i31+i31+i31−i31−i31+i321−i32−1−i3−1+i3022000000-1-11+i321−i32111−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i32-1-1000-2−1−i3−1+i30001+i301−i300000000001+i321−i321−1−i32−1+i3200000
χ29222-1-1200-1-122002−1+i3−1−i3−1+i3−1−i3-12-1-122−1+i3−1−i31−i321+i3222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i3022000000-1-11−i321+i32-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32-1-10002−1+i3−1−i3000−1+i30−1−i300000000001−i321+i32-11−i321+i3200000
χ30222-1-1200-1-122002−1+i3−1−i3−1+i3−1−i3-12-1-12-2−1+i3−1−i31−i321+i32-2-21−i31+i31−i31−i31+i31+i31−i321+i32−1+i3−1−i3022000000-1-11−i321+i32111−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i32-1-1000-2−1+i3−1−i30001−i301+i300000000001−i321+i321−1+i32−1−i3200000
χ31222-1-1200-1-1-22002222212-1-12222-1-122222222-1-1220-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111000-2-2-2000-20-200000000001111100000
χ32222-1-1200-1-1-22002222212-1-12-222-1-1-2-2-2-2-2-2-2-2-1-1220-2-2000000-1-1-1-111111-1-11111110002-2-2000202000000000011-1-1-100000
χ33222-1-1200-1-1-22002−1−i3−1+i3−1−i3−1+i312-1-122−1−i3−1+i31+i321−i3222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i30-2-2000000-1-11+i321−i32-1-1-11+i321−i321+i321−i321+i321+i321−i321−i3211000-21+i31−i30001+i301−i30000000000−1−i32−1+i321−1−i32−1+i3200000
χ34222-1-1200-1-1-22002−1−i3−1+i3−1−i3−1+i312-1-12-2−1−i3−1+i31+i321−i32-2-21+i31−i31+i31+i31−i31−i31+i321−i32−1−i3−1+i30-2-2000000-1-11+i321−i32111−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321100021+i31−i3000−1−i30−1+i30000000000−1−i32−1+i32-11+i321−i3200000
χ35222-1-1200-1-1-22002−1+i3−1−i3−1+i3−1−i312-1-122−1+i3−1−i31−i321+i3222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i30-2-2000000-1-11−i321+i32-1-1-11−i321+i321−i321+i321−i321−i321+i321+i3211000-21−i31+i30001−i301+i30000000000−1+i32−1−i321−1+i32−1−i3200000
χ36222-1-1200-1-1-22002−1+i3−1−i3−1+i3−1−i312-1-12-2−1+i3−1−i31−i321+i32-2-21−i31+i31−i31−i31+i31+i31−i321+i32−1+i3−1−i30-2-2000000-1-11−i321+i32111−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321100021−i31+i3000−1+i30−1−i30000000000−1+i32−1−i32-11−i321+i3200000
χ3722-122-122-1-102-1-1222220-122-12-1-122-1-122-1-1-1-122-1-1000222222-1-1-1-12-1-122-1-1-1-1-1-100-1-12000-1-12020-1-1-1-1-1-1-1-1000000000000
χ3822-122-122-1-102-1-1222220-122-1-2-1-12211-2-2111122-1-1000222222-1-1-1-1-211-2-2-1-1111100-1-1-200011-20-20-1-1-1-11111000000000000
χ3922-122-122-1-102-1-12−1−i3−1+i3−1−i3−1+i30-122-121+i321−i32−1−i3−1+i3-1-1−1−i3−1+i31+i321+i321−i321−i32−1−i3−1+i31+i321−i3200022−1−i3−1−i3−1+i3−1+i3-1-11+i321−i322-1-1−1−i3−1+i31+i321−i321+i321+i321−i321−i3200-1-12000-1-1−1−i30−1+i301+i321+i321−i321−i321+i321+i321−i321−i32000000000000
χ4022-122-122-1-102-1-12−1−i3−1+i3−1−i3−1+i30-122-1-21+i321−i32−1−i3−1+i3111+i31−i3−1−i32−1−i32−1+i32−1+i32−1−i3−1+i31+i321−i3200022−1−i3−1−i3−1+i3−1+i3-1-11+i321−i32-2111+i31−i31+i321−i32−1−i32−1−i32−1+i32−1+i3200-1-1-2000111+i301−i301+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32000000000000
χ4122-122-122-1-102-1-12−1+i3−1−i3−1+i3−1−i30-122-121−i321+i32−1+i3−1−i3-1-1−1+i3−1−i31−i321−i321+i321+i32−1+i3−1−i31−i321+i3200022−1+i3−1+i3−1−i3−1−i3-1-11−i321+i322-1-1−1+i3−1−i31−i321+i321−i321−i321+i321+i3200-1-12000-1-1−1+i30−1−i301−i321−i321+i321+i321−i321−i321+i321+i32000000000000
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χ931212-61212-6-12-12-6-60-266-2000001-2-210000000000000000000022000011000000000000000-1-1000000000000000000000000000000
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χ9512-1212-66-1200-660-200200000-21-120000000000000000002i7−2i70000001-10000000000000−i7i700000000000000000000000000000000
χ9612-12-612-12612i−12i-660-2−6i6i2000001-22-100000000000000000000−2i2i00001-1000000000000000i−i000000000000000000000000000000
χ9712-12-612-126−12i12i-660-26i−6i2000001-22-1000000000000000000002i−2i00001-1000000000000000−ii000000000000000000000000000000
χ982424-12-12-12-1200660-400-400000222200000000000000000000000000-1-100000000000000000000000000000000000000000000000
χ9924-24-12-121212006-60-40040000022-2-200000000000000000000000000-1100000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.