Finite Group Databasebeta

← Group #72276565

Character table — Group #72276565

Order 2688.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size1111222222666677777777888888121212121212141414141414141414141414242424242424242424242424282828282828282828282828565656565656565656565656565656565656565656565656565656565656
order122222222271414143366666644444414141414141466666666666628282828282828282828282822226666666622444466661212121212121212121212121212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111111111-1-111-1-1111111111111111111-1-1-1-11111-1-1-1-11111111111111-11-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111111111111111-11-11-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-111-1-1-1-1-1-111111111
χ911111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111111111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111111−1−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
χ1011111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-1-1-11+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ1111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-1-1-1-1111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111-1-1-1-1-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1111+i321−i321+i321−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
χ1211111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-1-1-1-1111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111-1-1-1-1-1-1-1-1-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321111-1-1−1−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
χ1311111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-1-1111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-11111-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321-11-1-1-1−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ1411111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-1-1111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-11111-1-1-1-1-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-11-11111+i321−i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ1511111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-111111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-11-11-1-11+i321−i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ1611111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-11111-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321-11-111−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ1711111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111111111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111111−1+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
χ1811111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-1-1-11−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ1911111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211-1-1-1-1111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111-1-1-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1111−i321+i321−i321+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
χ2011111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211-1-1-1-1111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111-1-1-1-1-1-1-1-1-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321111-1-1−1+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
χ2111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111-1-1111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-11111-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321-11-1-1-1−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ2211111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111-1-1111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-11111-1-1-1-1-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-11-11111−i321+i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ2311111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-111111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-11-11-1-11−i321+i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ2411111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-11111-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321-11-111−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ2522222-2-22-2-22222222222220000002-2-2-22-22-2-22-2-22-2-22-2-200000000000000000000000020-200022000000-2-200000000000000
χ2622222-2-22-2-22222222222220000002-2-2-22-22-2-22-2-22-2-22-2-2000000000000000000000000-202000-2-20000002200000000000000
χ2722222-2-22-2-22222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i30000002-2-2-22-2−1−i31+i31+i3−1+i31−i31−i3−1−i31+i31+i3−1+i31−i31−i300000000000000000000000020-2000−1−i3−1+i30000001+i31−i300000000000000
χ2822222-2-22-2-22222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i30000002-2-2-22-2−1−i31+i31+i3−1+i31−i31−i3−1−i31+i31+i3−1+i31−i31−i3000000000000000000000000-2020001+i31−i3000000−1−i3−1+i300000000000000
χ2922222-2-22-2-22222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i30000002-2-2-22-2−1+i31−i31−i3−1−i31+i31+i3−1+i31−i31−i3−1−i31+i31+i300000000000000000000000020-2000−1+i3−1−i30000001−i31+i300000000000000
χ3022222-2-22-2-22222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i30000002-2-2-22-2−1+i31−i31−i3−1−i31+i31+i3−1+i31−i31−i3−1−i31+i31+i3000000000000000000000000-2020001−i31+i3000000−1+i3−1−i300000000000000
χ312222-22-2-22-2222222222222000000-22-2-2-22-22-2-22-2-22-2-22-2000000000000000000000000020-2000022000000-2-2000000000000
χ322222-22-2-22-2222222222222000000-22-2-2-22-22-2-22-2-22-2-22-20000000000000000000000000-2020000-2-200000022000000000000
χ332222-22-2-22-22222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3000000-22-2-2-221+i3−1−i31+i31−i3−1+i31−i31+i3−1−i31+i31−i3−1+i31−i3000000000000000000000000020-20000−1−i3−1+i30000001+i31−i3000000000000
χ342222-22-2-22-22222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3000000-22-2-2-221+i3−1−i31+i31−i3−1+i31−i31+i3−1−i31+i31−i3−1+i31−i30000000000000000000000000-20200001+i31−i3000000−1−i3−1+i3000000000000
χ352222-22-2-22-22222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3000000-22-2-2-221−i3−1+i31−i31+i3−1−i31+i31−i3−1+i31−i31+i3−1−i31+i3000000000000000000000000020-20000−1+i3−1−i30000001−i31+i3000000000000
χ362222-22-2-22-22222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3000000-22-2-2-221−i3−1+i31−i31+i3−1−i31+i31−i3−1+i31−i31+i3−1−i31+i30000000000000000000000000-20200001−i31+i3000000−1+i3−1−i3000000000000
χ372222-2-22-2-222222222222222-20000-2-222-2-2-2-22-2-22-2-22-2-2222-2-20000000000000000000000000000002-22-20000000000000000
χ382222-2-22-2-22222222222222-220000-2-222-2-2-2-22-2-22-2-22-2-22-2-222000000000000000000000000000000-22-220000000000000000
χ392222-2-22-2-222222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i32-20000-2-222-2-21+i31+i3−1−i31−i31−i3−1+i31+i31+i3−1−i31−i31−i3−1+i322-2-2000000000000000000000000000000−1−i31+i3−1+i31−i30000000000000000
χ402222-2-22-2-222222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-220000-2-222-2-21+i31+i3−1−i31−i31−i3−1+i31+i31+i3−1−i31−i31−i3−1+i3-2-2220000000000000000000000000000001+i3−1−i31−i3−1+i30000000000000000
χ412222-2-22-2-222222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i32-20000-2-222-2-21−i31−i3−1+i31+i31+i3−1−i31−i31−i3−1+i31+i31+i3−1−i322-2-2000000000000000000000000000000−1+i31−i3−1−i31+i30000000000000000
χ422222-2-22-2-222222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-220000-2-222-2-21−i31−i3−1+i31+i31+i3−1−i31−i31−i3−1+i31+i31+i3−1−i3-2-2220000000000000000000000000000001−i3−1+i31+i3−1−i30000000000000000
χ432-2-22222-2-2-222-2-222-2-2-2-222000000222-2-2-2222222-2-2-2-2-2-200000000000000000000000000002i−2i000000000000000000002i−2i2i−2i
χ442-2-22222-2-2-222-2-222-2-2-2-222000000222-2-2-2222222-2-2-2-2-2-20000000000000000000000000000−2i2i00000000000000000000−2i2i−2i2i
χ452-2-22222-2-2-222-2-2−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i3000000222-2-2-2−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31−i31−i31−i300000000000000000000000000002i−2i000000000000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79
χ462-2-22222-2-2-222-2-2−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i3000000222-2-2-2−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31−i31−i31−i30000000000000000000000000000−2i2i00000000000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79
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χ482-2-22222-2-2-222-2-2−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i3000000222-2-2-2−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31−i31−i31+i31+i31+i30000000000000000000000000000−2i2i00000000000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.