Finite Group Databasebeta

← Group #72245538

Character table — Group #72245538

Order 2016.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size112222222444444446666666666667777121212121212121212121212121212121212141414141414141414141414141428282828282828282828282828282828848484848484848484848484
order122344666226666121271414142121424242424242336614141414282842424242424242428484848433666666661212121266666666666612121212246688121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111−1+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−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ411111111111111111111111111111−1+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−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i32-1-11−i321+i321−i321−i321+i321+i32
χ511111111111111111111111111111−1−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+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ611111111111111111111111111111−1−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+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i32-1-11+i321−i321+i321+i321−i321−i32
χ7111111111-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1
χ8111111111-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111
χ9111111111-1-1-1-1-1-111111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-1-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i32
χ10111111111-1-1-1-1-1-111111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-1-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i32111−i321+i32−1+i32−1+i32−1−i32−1−i32
χ11111111111-1-1-1-1-1-111111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-1-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i32
χ12111111111-1-1-1-1-1-111111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-1-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i32111+i321−i32−1−i32−1−i32−1+i32−1+i32
χ1311-11-11-1-111-111-1-11-11-1-1111-1-1-1-111111111-1-11-11111-1-1-1-111-1-111-1-1-1-1-1-111-1-1111-11-111-1-111-1-11-11-11-1111-1-1-11-11-1
χ1411-11-11-1-111-111-1-11-11-1-1111-1-1-1-111111111-1-11-11111-1-1-1-111-1-111-1-1-1-1-1-111-1-1111-11-111-1-111-1-11-11-1-11-1-1-1111-11-11
χ1511-11-11-1-111-111-1-11-11-1-1111-1-1-1-111−1+i32−1−i32−1+i32−1−i3211-1-11-11111-1-1-1-111-1-1−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1−i321+i321-1−1+i32−1−i321-11−i321+i32−1+i321−i32−1−i321+i32
χ1611-11-11-1-111-111-1-11-11-1-1111-1-1-1-111−1+i32−1−i32−1+i32−1−i3211-1-11-11111-1-1-1-111-1-1−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1−i321+i32-111−i321+i32-11−1+i32−1−i321−i32−1+i321+i32−1−i32
χ1711-11-11-1-111-111-1-11-11-1-1111-1-1-1-111−1−i32−1+i32−1−i32−1+i3211-1-11-11111-1-1-1-111-1-1−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1+i321−i321-1−1−i32−1+i321-11+i321−i32−1−i321+i32−1+i321−i32
χ1811-11-11-1-111-111-1-11-11-1-1111-1-1-1-111−1−i32−1+i32−1−i32−1+i3211-1-11-11111-1-1-1-111-1-1−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1+i321−i32-111+i321−i32-11−1−i32−1+i321+i32−1−i321−i32−1+i32
χ1911-11-11-1-11-11-1-1111-11-1-1111-1-1-1-1111111-1-1111-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-111-11-11-1-111-1-1111-11-11-111-11-1-1-11-11
χ2011-11-11-1-11-11-1-1111-11-1-1111-1-1-1-1111111-1-1111-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-111-11-11-1-111-1-1111-11-1-11-1-11-1111-11-1
χ2111-11-11-1-11-11-1-1111-11-1-1111-1-1-1-111−1+i32−1−i32−1+i32−1−i32-1-1111-1-1-1-1-1111111-1-1−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i321-1−1+i32−1−i32-111−i321+i321−i32−1+i321+i32−1−i32
χ2211-11-11-1-11-11-1-1111-11-1-1111-1-1-1-111−1+i32−1−i32−1+i32−1−i32-1-1111-1-1-1-1-1111111-1-1−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i32-111−i321+i321-1−1+i32−1−i32−1+i321−i32−1−i321+i32
χ2311-11-11-1-11-11-1-1111-11-1-1111-1-1-1-111−1−i32−1+i32−1−i32−1+i32-1-1111-1-1-1-1-1111111-1-1−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i321-1−1−i32−1+i32-111+i321−i321+i32−1−i321−i32−1+i32
χ2411-11-11-1-11-11-1-1111-11-1-1111-1-1-1-111−1−i32−1+i32−1−i32−1+i32-1-1111-1-1-1-1-1111111-1-1−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i32-111+i321−i321-1−1−i32−1+i32−1−i321+i32−1+i321−i32
χ252222-2-2222000000-2-222222222222222220000-2-200000000-2-2-2-22222222222-2-2-2-2000000000000-2-2-2-2000000000000
χ262222-2-2222000000-2-2222222222222−1+i3−1−i3−1+i3−1−i30000-2-200000000-2-2-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i31−i31+i31−i31+i30000000000001−i31−i31+i31+i3000000000000
χ272222-2-2222000000-2-2222222222222−1−i3−1+i3−1−i3−1+i30000-2-200000000-2-2-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000000000001+i31+i31−i31−i3000000000000
χ28222-122-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ29222-122-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3222222-1-1-1-1-1-1-1-1-1-1-1-11−i321+i32−1+i3−1−i31−i321−i321+i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32000000000000
χ30222-122-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3222222-1-1-1-1-1-1-1-1-1-1-1-11+i321−i32−1−i3−1+i31+i321+i321−i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32000000000000
χ31222-122-1-1-1-2-21111-1-12222-1-1-1-1-1-1-1-12222-2-2-2-22211111111-1-1-1-1-1-122-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1000000000000
χ32222-122-1-1-1-2-21111-1-12222-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3-2-2-2-22211111111-1-1-1-11−i321+i32−1+i3−1−i31−i321−i321+i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32000000000000
χ33222-122-1-1-1-2-21111-1-12222-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3-2-2-2-22211111111-1-1-1-11+i321−i32−1−i3−1+i31+i321+i321−i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32000000000000
χ34222-1-2-2-1-1-100i3−i3i3−i3112222-1-1-1-1-1-1-1-122220000-2-2i3i3−i3−i3i3i3−i3−i31111-1-122-1-1-1-1-1-1-2-2-2-20000i3−i3i3−i3i3−i3i3−i31111000000000000
χ35222-1-2-2-1-1-100i3−i3i3−i3112222-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i30000-2-2i3i3−i3−i3i3i3−i3−i311111−i321+i32−1+i3−1−i31−i321−i321+i321+i321−i321+i321−i31+i31−i31+i30000−3−i323+i32−3−i323+i323−i32−3+i323−i32−3+i32−1+i32−1+i32−1−i32−1−i32000000000000
χ36222-1-2-2-1-1-100i3−i3i3−i3112222-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i30000-2-2i3i3−i3−i3i3i3−i3−i311111+i321−i32−1−i3−1+i31+i321+i321−i321−i321+i321−i321+i31−i31+i31−i300003−i32−3+i323−i32−3+i32−3−i323+i32−3−i323+i32−1−i32−1−i32−1+i32−1+i32000000000000
χ37222-1-2-2-1-1-100−i3i3−i3i3112222-1-1-1-1-1-1-1-122220000-2-2−i3−i3i3i3−i3−i3i3i31111-1-122-1-1-1-1-1-1-2-2-2-20000−i3i3−i3i3−i3i3−i3i31111000000000000
χ38222-1-2-2-1-1-100−i3i3−i3i3112222-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i30000-2-2−i3−i3i3i3−i3−i3i3i311111−i321+i32−1+i3−1−i31−i321−i321+i321+i321−i321+i321−i31+i31−i31+i300003+i32−3−i323+i32−3−i32−3+i323−i32−3+i323−i32−1+i32−1+i32−1−i32−1−i32000000000000
χ39222-1-2-2-1-1-100−i3i3−i3i3112222-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i30000-2-2−i3−i3i3i3−i3−i3i3i311111+i321−i32−1−i3−1+i31+i321+i321−i321−i321+i321−i321+i31−i31+i31−i30000−3+i323−i32−3+i323−i323+i32−3−i323+i32−3−i32−1−i32−1−i32−1+i32−1+i32000000000000
χ4022-222-2-2-22000000-222-2-2222-2-2-2-22222220000-2200000000-2-22222-2-2-2-2-2-22222-2-2000000000000-22-22000000000000
χ4122-222-2-2-22000000-222-2-2222-2-2-2-222−1+i3−1−i3−1+i3−1−i30000-2200000000-2-222−1+i3−1−i31−i31+i31−i31−i31+i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i30000000000001−i3−1+i31+i3−1−i3000000000000
χ4222-222-2-2-22000000-222-2-2222-2-2-2-222−1−i3−1+i3−1−i3−1+i30000-2200000000-2-222−1−i3−1+i31+i31−i31+i31+i31−i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i30000000000001+i3−1−i31−i3−1+i3000000000000
χ4322-2-12-211-100i3−i3−i3i31-12-2-22-1-11111-1-122220000-22i3i3−i3−i3−i3−i3i3i311-1-1-1-1-2-21111-1-122-2-20000i3−i3−i3i3i3−i3−i3i31-11-1000000000000
χ4422-2-12-211-100i3−i3−i3i31-12-2-22-1-11111-1-1−1+i3−1−i3−1+i3−1−i30000-22i3i3−i3−i3−i3−i3i3i311-1-11−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i3−1−i31−i31+i30000−3−i323+i323+i32−3−i323−i32−3+i32−3+i323−i32−1+i321−i32−1−i321+i32000000000000
χ4522-2-12-211-100i3−i3−i3i31-12-2-22-1-11111-1-1−1−i3−1+i3−1−i3−1+i30000-22i3i3−i3−i3−i3−i3i3i311-1-11+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i3−1+i31+i31−i300003−i32−3+i32−3+i323−i32−3−i323+i323+i32−3−i32−1−i321+i32−1+i321−i32000000000000
χ4622-2-12-211-100−i3i3i3−i31-12-2-22-1-11111-1-122220000-22−i3−i3i3i3i3i3−i3−i311-1-1-1-1-2-21111-1-122-2-20000−i3i3i3−i3−i3i3i3−i31-11-1000000000000
χ4722-2-12-211-100−i3i3i3−i31-12-2-22-1-11111-1-1−1+i3−1−i3−1+i3−1−i30000-22−i3−i3i3i3i3i3−i3−i311-1-11−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i3−1−i31−i31+i300003+i32−3−i32−3−i323+i32−3+i323−i323−i32−3+i32−1+i321−i32−1−i321+i32000000000000
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Here ζ is a primitive root of unity of order 21 (ζ21 = 1); i = ζ5.