Finite Group Databasebeta

← Group #72246939

Character table — Group #72246939

Order 3024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112222244444466667777991212121212121212121212121212121214141414141414141414182828282828282828282828284242424242424242424242425454545463636363848484848484848484848484126126
order123346636121212127142828336622212121214242424284848484848484843333666612124336612121212121212122222666666661414282866666666666666661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111-1-111111111111111111111111111-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ4111111111111111111111-1-111111111111111111111111111-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ511111111111111111−1−i32−1+i32−1−i32−1+i32111111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32
χ611111111111111111−1−i32−1+i32−1−i32−1+i32111111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i321111−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32
χ711111111111111111−1−i32−1+i32−1−i32−1+i32-1-11111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321−i32
χ811111111111111111−1−i32−1+i32−1−i32−1+i32-1-11111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32
χ911111111111111111−1+i32−1−i32−1+i32−1−i32111111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32
χ1011111111111111111−1+i32−1−i32−1+i32−1−i32111111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i321111−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32
χ1111111111111111111−1+i32−1−i32−1+i32−1−i32-1-11111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321+i32
χ1211111111111111111−1+i32−1−i32−1+i32−1−i32-1-11111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32
χ131111-11111-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-11-11-11-11-11-11-111-1-111111-11-11-11-11-11-1-1-1
χ141111-11111-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-11-11-11-11-11-1111-1-11111-11-11-11-11-11-11-1-1
χ151111-11111-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-111111-1-1-1-1-1-1-1-11-1-111-11-1-11-11-1-111-1-1-1-11-1-111-11-1-11-1111
χ161111-11111-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-111111-1-1-1-1-1-1-1-1-111-1-11-111-11-1-1-111-1-1-1-1-111-1-11-111-11-111
χ171111-11111-1-1-1-111-1-1−1−i32−1+i32−1−i32−1+i321111111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i321+i321−i32
χ181111-11111-1-1-1-111-1-1−1−i32−1+i32−1−i32−1+i321111111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-11-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i32-11-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i321+i321−i32
χ191111-11111-1-1-1-111-1-1−1−i32−1+i32−1−i32−1+i32-1-111111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321-1-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32-1-1111+i321+i321−i321−i321-1-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i32
χ201111-11111-1-1-1-111-1-1−1−i32−1+i32−1−i32−1+i32-1-111111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-111-11+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32-1-1111+i321+i321−i321−i32-111-11+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i32
χ211111-11111-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321111111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i321−i321+i32
χ221111-11111-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321111111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-11-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i32-11-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i321−i321+i32
χ231111-11111-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i32-1-111111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321-1-11−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32-1-1111−i321−i321+i321+i321-1-11−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i32
χ241111-11111-1-1-1-111-1-1−1+i32−1−i32−1+i32−1−i32-1-111111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-111-11−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32-1-1111−i321−i321+i321+i32-111-11−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i32
χ25222-122-1-1-12-1-1-122222222002-1-1-12-1-1-122-1-1-1-1-1-12-12-12-12-1220-1-1-1-12-12-1-1-1-1-10022000022220000000000-1-10000-1-1-1-100
χ26222-122-1-1-12-1-1-122222222002-1-1-12-1-1-122-1-1-1-1-1-12-12-12-12-1220-1-1-1-12-12-1-1-1-1-100-2-20000-2-2-2-20000000000110000111100
χ27222-122-1-1-12-1-1-12222−1−i3−1+i3−1−i3−1+i3002-1-1-12-1-1-122-1-1-1-1-1-1−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i32−1−i3−1+i301+i321−i321+i321−i32−1−i31+i32−1+i31−i321+i321+i321−i321−i3200220000−1−i3−1−i3−1+i3−1+i30000000000-1-100001+i321+i321−i321−i3200
χ28222-122-1-1-12-1-1-12222−1−i3−1+i3−1−i3−1+i3002-1-1-12-1-1-122-1-1-1-1-1-1−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i32−1−i3−1+i301+i321−i321+i321−i32−1−i31+i32−1+i31−i321+i321+i321−i321−i3200-2-200001+i31+i31−i31−i30000000000110000−1−i32−1−i32−1+i32−1+i3200
χ29222-122-1-1-12-1-1-12222−1+i3−1−i3−1+i3−1−i3002-1-1-12-1-1-122-1-1-1-1-1-1−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i32−1+i3−1−i301−i321+i321−i321+i32−1+i31−i32−1−i31+i321−i321−i321+i321+i3200220000−1+i3−1+i3−1−i3−1−i30000000000-1-100001−i321−i321+i321+i3200
χ30222-122-1-1-12-1-1-12222−1+i3−1−i3−1+i3−1−i3002-1-1-12-1-1-122-1-1-1-1-1-1−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i32−1+i3−1−i301−i321+i321−i321+i32−1+i31−i32−1−i31+i321−i321−i321+i321+i3200-2-200001−i31−i31+i31+i30000000000110000−1+i32−1+i32−1−i32−1−i3200
χ31222-1-22-1-1-1-211122-2-22222002-1-1-12-1-1-1-2-21111112-12-12-12-1-2-20-1-1-1-1-21-211111002-200002-22-20000000000-110000-11-1100
χ32222-1-22-1-1-1-211122-2-22222002-1-1-12-1-1-1-2-21111112-12-12-12-1-2-20-1-1-1-1-21-21111100-220000-22-2200000000001-100001-11-100
χ33222-1-22-1-1-1-211122-2-2−1−i3−1+i3−1−i3−1+i3002-1-1-12-1-1-1-2-2111111−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i321+i31−i301+i321−i321+i321−i321+i3−1−i321−i3−1+i32−1−i32−1−i32−1+i32−1+i32002-20000−1−i31+i3−1+i31−i30000000000-1100001+i32−1−i321−i32−1+i3200
χ34222-1-22-1-1-1-211122-2-2−1−i3−1+i3−1−i3−1+i3002-1-1-12-1-1-1-2-2111111−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i321+i31−i301+i321−i321+i321−i321+i3−1−i321−i3−1+i32−1−i32−1−i32−1+i32−1+i3200-2200001+i3−1−i31−i3−1+i300000000001-10000−1−i321+i32−1+i321−i3200
χ35222-1-22-1-1-1-211122-2-2−1+i3−1−i3−1+i3−1−i3002-1-1-12-1-1-1-2-2111111−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i321−i31+i301−i321+i321−i321+i321−i3−1+i321+i3−1−i32−1+i32−1+i32−1−i32−1−i32002-20000−1+i31−i3−1−i31+i30000000000-1100001−i32−1+i321+i32−1−i3200
χ36222-1-22-1-1-1-211122-2-2−1+i3−1−i3−1+i3−1−i3002-1-1-12-1-1-1-2-2111111−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i321−i31+i301−i321+i321−i321+i321−i3−1+i321+i3−1−i32−1+i32−1+i32−1−i32−1−i3200-2200001−i3−1+i31+i3−1−i300000000001-10000−1+i321−i32−1−i321+i3200
χ3722-122-12-1-1-12-1-12222222200-12-1-1-12-1-1-1-122-1-1-1-1-12-12-12-12220-1-1-1-1-12-12-1-1-1-122002222000000000000-1-100-1-1-1-1000000
χ3822-122-12-1-1-12-1-12222222200-12-1-1-12-1-1-1-122-1-1-1-1-12-12-12-12220-1-1-1-1-12-12-1-1-1-1-2-200-2-2-2-200000000000011001111000000
χ3922-122-12-1-1-12-1-12222−1−i3−1+i3−1−i3−1+i300-12-1-1-12-1-1-1-122-1-1-1-11+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i3−1−i3−1+i301+i321−i321+i321−i321+i32−1−i31−i32−1+i31+i321+i321−i321−i322200−1−i3−1−i3−1+i3−1+i3000000000000-1-1001+i321+i321−i321−i32000000
χ4022-122-12-1-1-12-1-12222−1−i3−1+i3−1−i3−1+i300-12-1-1-12-1-1-1-122-1-1-1-11+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i3−1−i3−1+i301+i321−i321+i321−i321+i32−1−i31−i32−1+i31+i321+i321−i321−i32-2-2001+i31+i31−i31−i30000000000001100−1−i32−1−i32−1+i32−1+i32000000
χ4122-122-12-1-1-12-1-12222−1+i3−1−i3−1+i3−1−i300-12-1-1-12-1-1-1-122-1-1-1-11−i32−1+i31+i32−1−i31−i32−1+i31+i32−1−i3−1+i3−1−i301−i321+i321−i321+i321−i32−1+i31+i32−1−i31−i321−i321+i321+i322200−1+i3−1+i3−1−i3−1−i3000000000000-1-1001−i321−i321+i321+i32000000
χ4222-122-12-1-1-12-1-12222−1+i3−1−i3−1+i3−1−i300-12-1-1-12-1-1-1-122-1-1-1-11−i32−1+i31+i32−1−i31−i32−1+i31+i32−1−i3−1+i3−1−i301−i321+i321−i321+i321−i32−1+i31+i32−1−i31−i321−i321+i321+i32-2-2001−i31−i31+i31+i30000000000001100−1+i32−1+i32−1−i32−1−i32000000
χ4322-12-2-12-1-11-21122-2-2222200-12-1-1-12-1-111-2-21111-12-12-12-12-2-20-1-1-1-11-21-211112-2002-22-2000000000000-1100-11-11000000
χ4422-12-2-12-1-11-21122-2-2222200-12-1-1-12-1-111-2-21111-12-12-12-12-2-20-1-1-1-11-21-21111-2200-22-220000000000001-1001-11-1000000
χ4522-12-2-12-1-11-21122-2-2−1−i3−1+i3−1−i3−1+i300-12-1-1-12-1-111-2-211111+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i31+i31−i301+i321−i321+i321−i32−1−i321+i3−1+i321−i3−1−i32−1−i32−1+i32−1+i322-200−1−i31+i3−1+i31−i3000000000000-11001+i32−1−i321−i32−1+i32000000
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.