Finite Group Databasebeta

← Group #72270016

Character table — Group #72270016

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size11111111222222222222222222222222222244444444444444444444444488888888888888888888888888888888888888888888888888881616161616161616161616162424242424242424484848484848484848484848
order12222222222222222222366666666666666622222222666666666666666622224444444444446666666666661212121212121212121212121212121212121212121212124444121212121212121222224444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911-1-11-1-111111-1-1-1-111-1-11111111-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iiiii−i−i−i−i11-1-111-1-111-1-1ii−i−iii−i−i
χ1011-1-11-1-111111-1-1-1-111-1-11111111-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iiiii−i−i−i−i-1-111-1-111-1-111−i−iii−i−iii
χ1111-1-11-1-111111-1-1-1-111-1-11111111-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−iii
χ1211-1-11-1-111111-1-1-1-111-1-11111111-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−i−i−iiiii-1-111-1-111-1-111ii−i−iii−i−i
χ1311-1-11-1-111111-1-1-1-111-1-11111111-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i11-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−i−i−iiiii11-1-111-1-1-1-111ii−i−i−i−iii
χ1411-1-11-1-111111-1-1-1-111-1-11111111-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i11-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−i−i−iiiii-1-111-1-11111-1-1−i−iiiii−i−i
χ1511-1-11-1-111111-1-1-1-111-1-11111111-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii11-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiii−i−iiiii−i−i−i−i11-1-111-1-1-1-111−i−iiiii−i−i
χ1611-1-11-1-111111-1-1-1-111-1-11111111-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii11-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiii−i−iiiii−i−i−i−i-1-111-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-21111111100000000000000000000
χ1922222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000000000
χ2022222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1111111111111111111111111111111112222-1-1-1-1-1-1-1-100000000000000000000
χ21222222222222-2-222-2-22222222222222222222-2-2-22-2-2-22222-2-2-2-22222-2-2-2-20000000022-2-222-2-2-2-2-2-200000000000000002222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ22222222222222-2-222-2-22222222222222222222-2-2-22-2-2-22222-2-2-2-22222-2-2-2-200000000-2-222-2-222-2-2-2-20000000000000000-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ23222222222222-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-22-2-2-2-1-1-1-11111-1-1-1-111110000000022-2-222-2-21111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-1-1-11111-1-1-1-111110000−i3−i3i3i3−i3−i3i3i300000000000000000000
χ24222222222222-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-22-2-2-2-1-1-1-11111-1-1-1-111110000000022-2-222-2-21111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-1-1-11111-1-1-1-111110000i3i3−i3−i3i3i3−i3−i300000000000000000000
χ25222222222222-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-22-2-2-2-1-1-1-11111-1-1-1-1111100000000-2-222-2-2221111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i31111-1-1-1-11111-1-1-1-10000i3i3−i3−i3i3i3−i3−i300000000000000000000
χ26222222222222-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-22-2-2-2-1-1-1-11111-1-1-1-1111100000000-2-222-2-2221111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i31111-1-1-1-11111-1-1-1-10000−i3−i3i3i3−i3−i3i3i300000000000000000000
χ272222222222-2-2222222-2-22222222222222222-22-2-2-22-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-200000000-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ282222222222-2-2222222-2-22222222222222222-22-2-2-22-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2222200000000-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ292222222222-2-2222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-2-2-22-2-21111-1-1-1-11111-1-1-1-12222-2-2-2-2000000001111-1-1-1-1-1-1-1-111111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000−i3i3−i3i3−i3i3−i3i300000000000000000000
χ302222222222-2-2222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-2-2-22-2-21111-1-1-1-11111-1-1-1-12222-2-2-2-2000000001111-1-1-1-1-1-1-1-111111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000i3−i3i3−i3i3−i3i3−i300000000000000000000
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χ322222222222-2-2222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-2-2-22-2-21111-1-1-1-11111-1-1-1-1-2-2-2-2222200000000111111111111-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000−i3i3−i3i3−i3i3−i3i300000000000000000000
χ332222222222-2-2-2-222-2-2-2-22222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222000000000000000000000000000000002-22-22-2-222-2-2200000000000000000000
χ342222222222-2-2-2-222-2-2-2-22222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222200000000000000000000000000000000-22-22-222-2-222-200000000000000000000
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χ362222222222-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-22211111111111111110000000000000000-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-22-221-1-111-1-1100000000000000000000
χ372222222222-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-22211111111111111110000000000000000-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-22-221-1-111-1-1100000000000000000000
χ382222222222-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-22211111111111111110000000000000000-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32-22-2-111-1-111-100000000000000000000
χ3922222222-2-22222-2-22222222-2-2-2-222-2-2-2-2222-2-22-2-2-22-222-2-222-2-222-2-222-2-200000000000000002-22-2000000000000000000000000000000000000000000002222-2-2-2-2000000000000
χ4022222222-2-22222-2-22222222-2-2-2-222-2-2-2-2222-2-22-2-2-22-222-2-222-2-222-2-222-2-200000000000000002-22-200000000000000000000000000000000000000000000-2-2-2-22222000000000000
χ4122222222-2-222-2-2-2-2-2-222222-2-2-2-222-2-2-2-2222-22-22-22-2222-2-2-2-22222-2-2-2-2220000000000000000-22-22000000000000000000000000000000000000000000000000000000002-22-20000
χ4222222222-2-222-2-2-2-2-2-222222-2-2-2-222-2-2-2-2222-22-22-22-2222-2-2-2-22222-2-2-2-2220000000000000000-22-2200000000000000000000000000000000000000000000000000000000-22-220000
χ4322222222-2-2-2-222-2-222-2-2222-2-2-2-222-2-2-2-22222-2-222-2-22-2-22222-2-2-2-22222-2-20000000000000000-22-2200000000000000000000000000000000000000000000000000002-22-200000000
χ4422222222-2-2-2-222-2-222-2-2222-2-2-2-222-2-2-2-22222-2-222-2-22-2-22222-2-2-2-22222-2-20000000000000000-22-220000000000000000000000000000000000000000000000000000-22-2200000000
χ4522222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2-222-2-2-2-2222222-2222-2-2-222-2-222-2-222-2-22200000000000000002-22-20000000000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ4622222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2-222-2-2-2-2222222-2222-2-2-222-2-222-2-222-2-22200000000000000002-22-2000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ4722-2-22-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-22-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i-2-22200000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
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χ5122-2-22-2-22222222-2-2-2-2-2-2-1-1-1-1-1-1-1111111-1112-2-2-2-2222-1-1-1-111111111-1-1-1-100000000−2i−2i2i2i2i2i−2i−2i11-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3iiii−i−i−i−i−i−i−i−iiiii0000−3−33333−3−300000000000000000000
χ5222-2-22-2-22222222-2-2-2-2-2-2-1-1-1-1-1-1-1111111-1112-2-2-2-2222-1-1-1-111111111-1-1-1-100000000−2i−2i2i2i2i2i−2i−2i11-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3iiii−i−i−i−i−i−i−i−iiiii000033−3−3−3−33300000000000000000000
χ5322-2-22-2-222222-2-2-2-222-2-2-1-1-1-1-1-1-1111111-1112222-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-222-2-22i2i2i2i−2i−2i−2i−2i-1-111-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii2i2i−2i−2i−i−i−i−iiiii00000000000000000000
χ5422-2-22-2-222222-2-2-2-222-2-2-1-1-1-1-1-1-1111111-1112222-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-222-2-2−2i−2i−2i−2i2i2i2i2i-1-111-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−2i−2i2i2iiiii−i−i−i−i00000000000000000000
χ5522-2-22-2-222222-2-2-2-222-2-2-1-1-1-1-1-1-1111111-1112222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-222-2-2222i2i2i2i−2i−2i−2i−2i-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−2i−2i2i2iiiii−i−i−i−i00000000000000000000
χ5622-2-22-2-222222-2-2-2-222-2-2-1-1-1-1-1-1-1111111-1112222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-222-2-222−2i−2i−2i−2i2i2i2i2i-1-1111111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i2i2i−2i−2i−i−i−i−iiiii00000000000000000000
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χ1304-4-444-44-4004-4000000-44-2222i3−2i32i3−2i32-2−2i32i3−2i32i3-22-200000000-222i3−2i300002-2−2i32i30000-222-2-222-20000000000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000000000000000000000000000000
χ1314-4-444-44-400-440000004-44-4-40000-4400004-4400000000-440000004-40000002-2-22-222-20000000000002-22-2-22-22-22-222-22-2000000000000000000000000000000000000000000000000
χ1324-4-444-44-400-440000004-44-4-40000-4400004-4400000000-440000004-4000000-222-22-2-22000000000000-22-222-22-22-22-2-22-22000000000000000000000000000000000000000000000000
χ1334-4-444-44-400-440000004-4-222−2i32i3−2i32i32-22i3−2i32i3−2i3-22-2000000002-22i3−2i30000-22−2i32i300002-2-22-222-2000000000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000000000000000000000
χ1344-4-444-44-400-440000004-4-222−2i32i3−2i32i32-22i3−2i32i3−2i3-22-2000000002-22i3−2i30000-22−2i32i30000-222-22-2-220000000000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3000000000000000000000000000000000000000000000000
χ1354-4-444-44-400-440000004-4-2222i3−2i32i3−2i32-2−2i32i3−2i32i3-22-2000000002-2−2i32i30000-222i3−2i300002-2-22-222-2000000000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000000000000000000000000000000
χ1364-4-444-44-400-440000004-4-2222i3−2i32i3−2i32-2−2i32i3−2i32i3-22-2000000002-2−2i32i30000-222i3−2i30000-222-22-2-220000000000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3000000000000000000000000000000000000000000000000
χ1374-4-44-44-444-40000-4400004-444-4-44-44-444-4-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ1384-4-44-44-444-40000-4400004-444-4-44-44-444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-222-2-222-2000000000000
χ1394-4-44-44-44-4400004-400004-44-444-4-444-4-44-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ1404-4-44-44-44-4400004-400004-44-444-4-444-4-44-44-40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ1418-88-8-8-8888-800008-80000-44-4-444-4-44-444-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1428-88-8-8-888-880000-880000-44-44-4-44-444-4-4444-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1438-8-88-88-888-80000-880000-44-4-444-44-44-4-444-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1448-8-88-88-88-8800008-80000-44-44-4-444-4-444-44-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.