Finite Group Databasebeta

← Group #13157615

Character table — Group #13157615

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171
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χ3111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
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χ6922222-1222-12-12-1-1-1-1-12-12-1222-1-1-1-1-1-1-1-100-2-200-2-20000111100001100−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32001−i31−i3001−i31−i30000−1+i32−1+i32−1+i32−1+i320000−1+i32−1+i3200−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32001+i31+i3001+i31+i30000−1−i32−1−i32−1−i32−1−i320000−1−i32−1−i3200
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χ1191111111111111111111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+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+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−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32
χ1201111111111111111111111-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-11−1−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−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+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+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32
χ1211111111111111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-11−1−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−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+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+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ1221111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-11-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+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−i321+i321+i321+i321+i32−1−i321+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+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−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+i321−i321−i321−i321−i32−1+i321−i32
χ123222222-2-22222222222-2-2-2-200000-2-200000000000000000000220000-20−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3000001+i31+i300000000000000000000−1−i3−1−i300001+i30−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3000001−i31−i300000000000000000000−1+i3−1+i300001−i30
χ124222222-2-22222222222-2-2-2-200000-2-200000000000000000000-2-2000020−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3000001+i31+i3000000000000000000001+i31+i30000−1−i30−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3000001−i31−i3000000000000000000001−i31−i30000−1+i30
χ12522222-1222-12-12-1-1-1-1-12-12-1222-1-1-1-1-1-1-1-1002200220000-1-1-1-10000-1-100−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i3200−1−i3−1−i300−1−i3−1−i300001+i321+i321+i321+i3200001+i321+i3200−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i3200−1+i3−1+i300−1+i3−1+i300001−i321−i321−i321−i3200001−i321−i3200
χ12622222-1222-12-12-1-1-1-1-12-12-1222-1-1-1-1-1-1-1-100-2-200-2-20000111100001100−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32001+i31+i3001+i31+i30000−1−i32−1−i32−1−i32−1−i320000−1−i32−1−i3200−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32001−i31−i3001−i31−i30000−1+i32−1+i32−1+i32−1+i320000−1+i32−1+i3200
χ12722222-1222-12-12-1-1-1-1-12-12-1-2-2-211-1-11111002200-2-2000011110000-1-100−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i321+i31+i31+i3−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i3200−1−i3−1−i3001+i31+i30000−1−i32−1−i32−1−i32−1−i3200001+i321+i3200−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i321−i31−i31−i3−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i3200−1+i3−1+i3001−i31−i30000−1+i32−1+i32−1+i32−1+i3200001−i321−i3200
χ12822222-1222-12-12-1-1-1-1-12-12-1-2-2-211-1-1111100-2-200220000-1-1-1-100001100−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i321+i31+i31+i3−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32001+i31+i300−1−i3−1−i300001+i321+i321+i321+i320000−1−i32−1−i3200−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i321−i31−i31−i3−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32001−i31−i300−1+i3−1+i300001−i321−i321−i321−i320000−1+i32−1+i3200
χ1292222-1222-12-12-12-1-1-1-1-12-122-1-122-1-1-1-1-1-122002200-1-1-1-1000000-1-10000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i32−1−i3−1−i300−1−i3−1−i3001+i321+i321+i321+i320000001+i321+i320000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i32−1+i3−1+i300−1+i3−1+i3001−i321−i321−i321−i320000001−i321−i320000
χ1302222-1222-12-12-12-1-1-1-1-12-122-1-122-1-1-1-1-1-1-2-200-2-2001111000000110000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i31+i3001+i31+i300−1−i32−1−i32−1−i32−1−i32000000−1−i32−1−i320000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i31−i3001−i31−i300−1+i32−1+i32−1+i32−1+i32000000−1+i32−1+i320000
χ1312222-1222-12-12-12-1-1-1-1-12-12-211-2-2-1-111112200-2-2001111000000-1-10000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i3−1−i32−1−i321+i31+i31+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i3−1−i3001+i31+i300−1−i32−1−i32−1−i32−1−i320000001+i321+i320000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i3−1+i32−1+i321−i31−i31−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i3−1+i3001−i31−i300−1+i32−1+i32−1+i32−1+i320000001−i321−i320000
χ1322222-1222-12-12-12-1-1-1-1-12-12-211-2-2-1-11111-2-2002200-1-1-1-1000000110000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i3−1−i32−1−i321+i31+i31+i321+i32−1−i32−1−i32−1−i32−1−i321+i31+i300−1−i3−1−i3001+i321+i321+i321+i32000000−1−i32−1−i320000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i3−1+i32−1+i321−i31−i31−i321−i32−1+i32−1+i32−1+i32−1+i321−i31−i300−1+i3−1+i3001−i321−i321−i321−i32000000−1+i32−1+i320000
χ13322-2-2220022-2-2-2-222-2-20000000000000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i22-2000000−1−i3−1−i31+i31+i3−1−i3−1−i300−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i31+i30000000000000000000ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ7−ζ13−1−i31+i3000000−1+i3−1+i31−i31−i3−1+i3−1+i300−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i31−i30000000000000000000ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23−ζ5−ζ23−1+i31−i3000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.