Finite Group Databasebeta

← Group #13047985

Character table — Group #13047985

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11222222222333344444444444446666666666666666666666661212121212121212121212121212121212121212121212121212121212121212121212545454545454108108108
order12333346666336641212121212121212121212123366999999999121218181818181818181812121212121212123636363636363636363636363636363636363636363636363636368824242424266
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ3111111111111111-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1
χ4111111111111111-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111−1−i32−1+i32−1−i32−1+i321111111111111−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32111−1−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+i32111−1−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+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32
χ611111111111−1−i32−1+i32−1−i32−1+i321111111111111−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32111−1−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+i32111−1−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+i32-1-11+i321+i321−i321−i32-11+i321−i32
χ711111111111−1−i32−1+i32−1−i32−1+i32-11111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-11+i321−i32
χ811111111111−1−i32−1+i32−1−i32−1+i32-11111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32-1-11+i321+i321−i321−i321−1−i32−1+i32
χ911111111111−1+i32−1−i32−1+i32−1−i321111111111111−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32111−1+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−i32111−1+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−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32
χ1011111111111−1+i32−1−i32−1+i32−1−i321111111111111−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32111−1+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−i32111−1+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−i32-1-11−i321−i321+i321+i32-11−i321+i32
χ1111111111111−1+i32−1−i32−1+i32−1−i32-11111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-11−i321+i32
χ1211111111111−1+i32−1−i32−1+i32−1−i32-11111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32-1-11−i321−i321+i321+i321−1+i32−1−i32
χ1322222222222222222222222222222222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000
χ14222222222222222-22222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1111111111111111111000000000
χ1522222222222−1−i3−1+i3−1−i3−1+i32222222222222−1−i3−1+i3−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32000000000
χ1622222222222−1−i3−1+i3−1−i3−1+i3-22222-2-2-2-2-2-2-2-2−1−i3−1+i3−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i321+i31−i3−1−i3−1+i31+i31+i31−i31−i3-1-1-11+i321+i321+i321−i321−i321−i32111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32000000000
χ1722222222222−1+i3−1−i3−1+i3−1−i32222222222222−1+i3−1−i3−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32000000000
χ1822222222222−1+i3−1−i3−1+i3−1−i3-22222-2-2-2-2-2-2-2-2−1+i3−1−i3−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i321−i31+i3−1+i3−1−i31−i31−i31+i31+i3-1-1-11−i321−i321−i321+i321+i321+i32111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32000000000
χ19222222-2222222220-2-2-2-2000000002222222222222-2-222222222200-2-20000-2-2-2-2-2-2-2-2-2000000000000000000000000000
χ20222222-2222222220-2-2-2-2000000002222-1-1-1-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-1-100-2-20000111111111−i3−i3−i3i3i3i3−i3−i3−i3i3i3i3−i3−i3−i3i3i3i3000000000
χ21222222-2222222220-2-2-2-2000000002222-1-1-1-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-1-100-2-20000111111111i3i3i3−i3−i3−i3i3i3i3−i3−i3−i3i3i3i3−i3−i3−i3000000000
χ22222222-22222−1−i3−1+i3−1−i3−1+i30-2-2-2-200000000−1−i3−1+i3−1−i3−1+i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31−i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3001+i31−i30000-2-2-21+i31+i31+i31−i31−i31−i3000000000000000000000000000
χ23222222-22222−1−i3−1+i3−1−i3−1+i30-2-2-2-200000000−1−i3−1+i3−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i321+i31−i3-1-1-11+i321+i321+i321−i321−i321−i32001+i31−i30000111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−i3−i3−i3i3i3i3−3+i32−3+i32−3+i323−i323−i323−i323+i323+i323+i32−3−i32−3−i32−3−i32000000000
χ24222222-22222−1−i3−1+i3−1−i3−1+i30-2-2-2-200000000−1−i3−1+i3−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i321+i31−i3-1-1-11+i321+i321+i321−i321−i321−i32001+i31−i30000111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32i3i3i3−i3−i3−i33−i323−i323−i32−3+i32−3+i32−3+i32−3−i32−3−i32−3−i323+i323+i323+i32000000000
χ25222222-22222−1+i3−1−i3−1+i3−1−i30-2-2-2-200000000−1+i3−1−i3−1+i3−1−i3222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31+i3222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3001−i31+i30000-2-2-21−i31−i31−i31+i31+i31+i3000000000000000000000000000
χ26222222-22222−1+i3−1−i3−1+i3−1−i30-2-2-2-200000000−1+i3−1−i3−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i321−i31+i3-1-1-11−i321−i321−i321+i321+i321+i32001−i31+i30000111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−i3−i3−i3i3i3i33+i323+i323+i32−3−i32−3−i32−3−i32−3+i32−3+i32−3+i323−i323−i323−i32000000000
χ27222222-22222−1+i3−1−i3−1+i3−1−i30-2-2-2-200000000−1+i3−1−i3−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i321−i31+i3-1-1-11−i321−i321−i321+i321+i321+i32001−i31+i30000111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32i3i3i3−i3−i3−i3−3−i32−3−i32−3−i323+i323+i323+i323−i323−i323−i32−3+i32−3+i32−3+i32000000000
χ2822-1-1-122-1-1-12222222-1-1-122-1-1-1-1-1-1-1-1-1-12-1-12-1-12-1-1222-1-12-1-12-1-122-1-1-1-1-1-12-1-12-1-12-1-12-1-12-1-12-1-12-1-12-1-12-1-1000000000
χ2922-1-1-122-1-1-12222222-1-1-122-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12-122-12-1-12-1-12-122-1-1-1-1-1-1-12-1-12-1-12-1-12-1-12-1-12-1-12-1-12-1-12-1000000000
χ3022-1-1-122-1-1-12222222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1222-1-12-1-12-1-1222-1-1-1-1-1-1-1-12-1-12-1-12-1-12-1-12-1-12-1-12-1-12-1-12000000000
χ3122-1-1-122-1-1-122222-22-1-1-1-2-2111111-1-1-1-12-1-12-1-12-1-1222-1-12-1-12-1-1-2-2-1-111112-1-12-1-12-1-1-211-211-211-211-211-211000000000
χ3222-1-1-122-1-1-122222-22-1-1-1-2-2111111-1-1-1-1-12-1-12-1-12-122-12-1-12-1-12-1-2-2-1-11111-12-1-12-1-12-11-211-211-211-211-211-21000000000
χ3322-1-1-122-1-1-122222-22-1-1-1-2-2111111-1-1-1-1-1-12-1-12-1-1222-1-12-1-12-1-12-2-2-1-11111-1-12-1-12-1-1211-211-211-211-211-211-2000000000
χ3422-1-1-122-1-1-12−1−i3−1+i3−1−i3−1+i322-1-1-122-1-1-1-1-1-11+i321−i321+i321−i322-1-1−1−i31+i321+i32−1+i31−i321−i32−1−i3−1+i32-1-1−1−i31+i321+i32−1+i31−i321−i32−1−i3−1+i31+i321−i321+i321+i321−i321−i322-1-1−1−i31+i321+i32−1+i31−i321−i322-1-12-1-1−1−i31+i321+i32−1−i31+i321+i32−1+i31−i321−i32−1+i31−i321−i32000000000
χ3522-1-1-122-1-1-12−1−i3−1+i3−1−i3−1+i322-1-1-122-1-1-1-1-1-11+i321−i321+i321−i32-12-11+i32−1−i31+i321−i32−1+i31−i32−1−i3−1+i3-12-11+i32−1−i31+i321−i32−1+i31−i32−1−i3−1+i31+i321−i321+i321+i321−i321−i32-12-11+i32−1−i31+i321−i32−1+i31−i32-12-1-12-11+i32−1−i31+i321+i32−1−i31+i321−i32−1+i31−i321−i32−1+i31−i32000000000
χ3622-1-1-122-1-1-12−1−i3−1+i3−1−i3−1+i322-1-1-122-1-1-1-1-1-11+i321−i321+i321−i32-1-121+i321+i32−1−i31−i321−i32−1+i3−1−i3−1+i3-1-121+i321+i32−1−i31−i321−i32−1+i3−1−i3−1+i31+i321−i321+i321+i321−i321−i32-1-121+i321+i32−1−i31−i321−i32−1+i3-1-12-1-121+i321+i32−1−i31+i321+i32−1−i31−i321−i32−1+i31−i321−i32−1+i3000000000
χ3722-1-1-122-1-1-12−1−i3−1+i3−1−i3−1+i3-22-1-1-1-2-21111111+i321−i321+i321−i322-1-1−1−i31+i321+i32−1+i31−i321−i32−1−i3−1+i32-1-1−1−i31+i321+i32−1+i31−i321−i321+i31−i31+i321−i32−1−i32−1−i32−1+i32−1+i322-1-1−1−i31+i321+i32−1+i31−i321−i32-211-2111+i3−1−i32−1−i321+i3−1−i32−1−i321−i3−1+i32−1+i321−i3−1+i32−1+i32000000000
χ3822-1-1-122-1-1-12−1−i3−1+i3−1−i3−1+i3-22-1-1-1-2-21111111+i321−i321+i321−i32-12-11+i32−1−i31+i321−i32−1+i31−i32−1−i3−1+i3-12-11+i32−1−i31+i321−i32−1+i31−i321+i31−i31+i321−i32−1−i32−1−i32−1+i32−1+i32-12-11+i32−1−i31+i321−i32−1+i31−i321-211-21−1−i321+i3−1−i32−1−i321+i3−1−i32−1+i321−i3−1+i32−1+i321−i3−1+i32000000000
χ3922-1-1-122-1-1-12−1−i3−1+i3−1−i3−1+i3-22-1-1-1-2-21111111+i321−i321+i321−i32-1-121+i321+i32−1−i31−i321−i32−1+i3−1−i3−1+i3-1-121+i321+i32−1−i31−i321−i32−1+i31+i31−i31+i321−i32−1−i32−1−i32−1+i32−1+i32-1-121+i321+i32−1−i31−i321−i32−1+i311-211-2−1−i32−1−i321+i3−1−i32−1−i321+i3−1+i32−1+i321−i3−1+i32−1+i321−i3000000000
χ4022-1-1-122-1-1-12−1+i3−1−i3−1+i3−1−i322-1-1-122-1-1-1-1-1-11−i321+i321−i321+i322-1-1−1+i31−i321−i32−1−i31+i321+i32−1+i3−1−i32-1-1−1+i31−i321−i32−1−i31+i321+i32−1+i3−1−i31−i321+i321−i321−i321+i321+i322-1-1−1+i31−i321−i32−1−i31+i321+i322-1-12-1-1−1+i31−i321−i32−1+i31−i321−i32−1−i31+i321+i32−1−i31+i321+i32000000000
χ4122-1-1-122-1-1-12−1+i3−1−i3−1+i3−1−i322-1-1-122-1-1-1-1-1-11−i321+i321−i321+i32-12-11−i32−1+i31−i321+i32−1−i31+i32−1+i3−1−i3-12-11−i32−1+i31−i321+i32−1−i31+i32−1+i3−1−i31−i321+i321−i321−i321+i321+i32-12-11−i32−1+i31−i321+i32−1−i31+i32-12-1-12-11−i32−1+i31−i321−i32−1+i31−i321+i32−1−i31+i321+i32−1−i31+i32000000000
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χ4722-1-1-12-2-1-1-1222220-211100−i3−i3−i3i3i3i3-1-1-1-1-12-1-12-1-12-1-2-2-12-1-12-1-12-10011−i3i3−i3i31-211-211-21i30−i3−i30i3i30−i3−i30i3i30−i3−i30i3000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.