Finite Group Databasebeta

← Group #72271630

Character table — Group #72271630

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1122222222222444444444444444444444444448888888888888888888888888888888816161616161616161616161616161616161616161616161648484848484848484848484848484848
order1222234444666444466888888881212121212121212121212122444668888121212121212242424242424242424242424242424242224444466666612121212121212121212244488881616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ7111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ8111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-1
χ91111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ101111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111-1-111
χ121111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-111-1-1
χ131111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ141111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ151111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
χ161111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111
χ172222222222222222222-2-2-2-2-2-2-2-2222222222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ182222222222222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ192222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ202222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-222-2-222-2-222-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2122222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ2322222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-2111111-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
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χ2522222-12222-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1111111111111111100000000−i3−i3i3i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
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χ2722222-12222-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211222211111111111111-1-1-1-1-1-1-1-100000000−i3−i3i3i3i3−i3i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ2822222-12222-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211222211111111111111-1-1-1-1-1-1-1-100000000i3i3−i3−i3−i3i3−i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
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χ3022222-12222-1-1-1-2-2-2-2-1-12222-2-2-2-2-1-111111111-1-122-2-2-1-1-2-222-1-111111111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3−i3i3−i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
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χ3422222-12222-1-1-1-2-2-2-2-1-1-2-2-2-22222-1-111111111-1-122-2-2-1-122-2-2-1-11111-1-1-1-11111-1-1-1-11111-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ3522222-12222-1-1-1-2-2-2-2-1-1-2-2-2-22222-1-111111111-1-1-2-22211-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ3622222-12222-1-1-1-2-2-2-2-1-1-2-2-2-22222-1-111111111-1-1-2-22211-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ37222-2-22-222-22-2-22i2i−2i−2i2-22i2i−2i−2i22-2-22-22i2i2i2i−2i−2i−2i−2i2-2000000000000000022-2-22i2i−2i−2i00000000000000000000000000000000002i−2i2-20000000000
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χ4822-22-2222-2-22-2-22i−2i2i−2i-22−2i2i−2i2i-22-22-222i2i−2i−2i2i2i−2i−2i2-20000000000000000-22-22−2i2i−2i2i0000000000000000000000000000000000000000-22−2i2i0000
χ4922-22-2222-2-22-2-2−2i2i−2i2i-222i−2i2i−2i-22-22-22−2i−2i2i2i−2i−2i2i2i2-20000000000000000-22-222i−2i2i−2i00000000000000000000000000000000000000002-2−2i2i0000
χ5022-22-2222-2-22-2-2−2i2i−2i2i-222i−2i2i−2i-22-22-22−2i−2i2i2i−2i−2i2i2i2-20000000000000000-22-222i−2i2i−2i0000000000000000000000000000000000000000-222i−2i0000
χ5122-22-2222-2-22-2-2−2i2i−2i2i-22−2i2i−2i2i2-22-2-22−2i−2i2i2i−2i−2i2i2i2-200000000000000002-22-2−2i2i−2i2i000000000000000000000000000000000000000000002i−2i-22
χ5222-22-2222-2-22-2-2−2i2i−2i2i-22−2i2i−2i2i2-22-2-22−2i−2i2i2i−2i−2i2i2i2-200000000000000002-22-2−2i2i−2i2i00000000000000000000000000000000000000000000−2i2i2-2
χ5322-2-222-22-222222-2-22-2-22-2-222-2-22-2-222-2-2-2-2222200000000000000002-2-222-2-22000000002-2002-2002-22-200002-22-200000000000000000000
χ5422-2-222-22-222222-2-22-2-22-2-222-2-22-2-222-2-2-2-2222200000000000000002-2-222-2-2200000000-2200-2200-22-220000-22-2200000000000000000000
χ5522-2-222-22-222222-2-22-2-2-222-2-222-2-2-222-2-2-2-222220000000000000000-222-2-222-200000000002-2002-2000022-2-200002-22-20000000000000000
χ5622-2-222-22-222222-2-22-2-2-222-2-222-2-2-222-2-2-2-222220000000000000000-222-2-222-20000000000-2200-220000-2-2220000-22-220000000000000000
χ5722-2-222-22-22222-222-2-2-22-2-22-222-2-2-2-2-22222-2-2220000000000000000-222-22-2-2200000000002-200-22000022-2-20000-22-220000000000000000
χ5822-2-222-22-22222-222-2-2-22-2-22-222-2-2-2-2-22222-2-2220000000000000000-222-22-2-220000000000-22002-20000-2-22200002-22-20000000000000000
χ5922-2-222-22-22222-222-2-2-2-222-22-2-22-2-2-2-22222-2-22200000000000000002-2-22-222-2000000002-200-22002-22-20000-22-2200000000000000000000
χ6022-2-222-22-22222-222-2-2-2-222-22-2-22-2-2-2-22222-2-22200000000000000002-2-22-222-200000000-22002-200-22-2200002-22-200000000000000000000
χ6122-2-22-1-22-22-1-1-12-2-22112-2-222-2-2211-1-11111-1-1-1-10000−i3i30000−i3i3−i3−i3i3i3-111-1-111-1−i3−i3i3i3−i3−i3i3i32-2002-200-11-11−i3i3i3−i3-11-11−i3i3i3−i30000000000000000
χ6222-2-22-1-22-22-1-1-12-2-22112-2-222-2-2211-1-11111-1-1-1-10000−i3i30000−i3i3−i3−i3i3i3-111-1-111-1−i3−i3i3i3−i3−i3i3i3-2200-22001-11-1i3−i3−i3i31-11-1i3−i3−i3i30000000000000000
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χ6722-2-22-1-22-22-1-1-12-2-2211-222-2-222-211-1-11111-1-1-1-10000i3−i30000i3−i3i3i3−i3−i31-1-111-1-11−i3−i3i3i3−i3−i3i3i3002-2002-2i3−i3−i3i3-1-111i3−i3−i3i3-11-110000000000000000
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χ7022-2-22-1-22-22-1-1-1-222-2112-2-22-222-21111-1-1-1-111-1-10000−i3i30000−i3i3i3i3−i3−i31-1-11-111-1i3i3−i3−i3−i3−i3i3i300-22002-2−i3i3i3−i311-1-1i3−i3−i3i3-11-110000000000000000
χ7122-2-22-1-22-22-1-1-1-222-2112-2-22-222-21111-1-1-1-111-1-10000i3−i30000i3−i3−i3−i3i3i31-1-11-111-1−i3−i3i3i3i3i3−i3−i3002-200-22−i3i3i3−i3-1-111i3−i3−i3i31-11-10000000000000000
χ7222-2-22-1-22-22-1-1-1-222-2112-2-22-222-21111-1-1-1-111-1-10000i3−i30000i3−i3−i3−i3i3i31-1-11-111-1−i3−i3i3i3i3i3−i3−i300-22002-2i3−i3−i3i311-1-1−i3i3i3−i3-11-110000000000000000
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χ7622-2-22-1-22-22-1-1-1-222-211-222-22-2-221111-1-1-1-111-1-10000i3−i30000i3−i3−i3−i3i3i3-111-11-1-11i3i3−i3−i3−i3−i3i3i3-22002-2001-11-1i3−i3−i3i3-11-11−i3i3i3−i30000000000000000
χ77444444-4-4-4-444400004400000000-4-400000000-4-4004-4000000004-44-400000000000000000000000000000000000000000000000000000000
χ78444444-4-4-4-444400004400000000-4-400000000-4-400-4400000000-44-4400000000000000000000000000000000000000000000000000000000
χ7944444-2-4-4-4-4-2-2-20000-2-20000000022−2i32i3−2i32i3−2i32i3−2i32i322004-4−2i32i300002i3−2i3-22-2200000000000000000000000000000000000000000000000000000000
χ8044444-2-4-4-4-4-2-2-20000-2-20000000022−2i32i3−2i32i3−2i32i3−2i32i32200-442i3−2i30000−2i32i32-22-200000000000000000000000000000000000000000000000000000000
χ8144444-2-4-4-4-4-2-2-20000-2-200000000222i3−2i32i3−2i32i3−2i32i3−2i322004-42i3−2i30000−2i32i3-22-2200000000000000000000000000000000000000000000000000000000
χ8244444-2-4-4-4-4-2-2-20000-2-200000000222i3−2i32i3−2i32i3−2i32i3−2i32200-44−2i32i300002i3−2i32-22-200000000000000000000000000000000000000000000000000000000
χ83444-4-444-4-444-4-400004-400000000-4400000000-440000004i−4i00000000000000004i−4i4i−4i00000000000000000000000000000000000000000000
χ84444-4-444-4-444-4-400004-400000000-4400000000-44000000−4i4i0000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000
χ85444-4-4-24-4-44-2220000-22000000002-223−2323−23−2323−23232-20000004i−4i0000000000000000−2i2i−2i2i−2i32i3−2i32i30000000000000000000000000000000000000000
χ86444-4-4-24-4-44-2220000-22000000002-223−2323−23−2323−23232-2000000−4i4i00000000000000002i−2i2i−2i2i3−2i32i3−2i30000000000000000000000000000000000000000
χ87444-4-4-24-4-44-2220000-22000000002-2−2323−232323−2323−232-20000004i−4i0000000000000000−2i2i−2i2i2i3−2i32i3−2i30000000000000000000000000000000000000000
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χ89444-4-4-2-444-4-2224i4i−4i−4i-224i4i−4i−4i44-4-4-22−2i−2i−2i−2i2i2i2i2i-220000000000000000-2-222−2i−2i2i2i000000000000000000000000000000000000000000000000
χ90444-4-4-2-444-4-2224i4i−4i−4i-22−4i−4i4i4i-4-444-22−2i−2i−2i−2i2i2i2i2i-22000000000000000022-2-22i2i−2i−2i000000000000000000000000000000000000000000000000
χ91444-4-4-2-444-4-222−4i−4i4i4i-224i4i−4i−4i-4-444-222i2i2i2i−2i−2i−2i−2i-22000000000000000022-2-2−2i−2i2i2i000000000000000000000000000000000000000000000000
χ92444-4-4-2-444-4-222−4i−4i4i4i-22−4i−4i4i4i44-4-4-222i2i2i2i−2i−2i−2i−2i-220000000000000000-2-2222i2i−2i−2i000000000000000000000000000000000000000000000000
χ9344-44-44-4-4444-4-40000-44000000004-400000000-44000000004-40000000000000000004-4-440000000000000000000000000000000000000000
χ9444-44-44-4-4444-4-40000-44000000004-400000000-4400000000-44000000000000000000-444-40000000000000000000000000000000000000000
χ9544-44-4-244-4-4-2224i−4i4i−4i2-24i−4i4i−4i4-44-42-2−2i−2i2i2i−2i−2i2i2i-220000000000000000-22-22−2i2i−2i2i000000000000000000000000000000000000000000000000
χ9644-44-4-244-4-4-2224i−4i4i−4i2-2−4i4i−4i4i-44-442-2−2i−2i2i2i−2i−2i2i2i-2200000000000000002-22-22i−2i2i−2i000000000000000000000000000000000000000000000000
χ9744-44-4-244-4-4-222−4i4i−4i4i2-24i−4i4i−4i-44-442-22i2i−2i−2i2i2i−2i−2i-2200000000000000002-22-2−2i2i−2i2i000000000000000000000000000000000000000000000000
χ9844-44-4-244-4-4-222−4i4i−4i4i2-2−4i4i−4i4i4-44-42-22i2i−2i−2i2i2i−2i−2i-220000000000000000-22-222i−2i2i−2i000000000000000000000000000000000000000000000000
χ9944-44-4-2-4-444-22200002-200000000-2223−23−232323−23−23232-2000000004-40000000000000023−23−2323-222-20000000000000000000000000000000000000000
χ10044-44-4-2-4-444-22200002-200000000-2223−23−232323−23−23232-200000000-4400000000000000−232323−232-2-220000000000000000000000000000000000000000
χ10144-44-4-2-4-444-22200002-200000000-22−232323−23−232323−232-2000000004-400000000000000−232323−23-222-20000000000000000000000000000000000000000
χ10244-44-4-2-4-444-22200002-200000000-22−232323−23−232323−232-200000000-440000000000000023−23−23232-2-220000000000000000000000000000000000000000
χ10344-4-4444-44-44440000-4-4000000004400000000-4-44-400440000-4-4000000000000000000000000000000000000000000000000000000000000
χ10444-4-4444-44-44440000-4-4000000004400000000-4-4-4400-4-4000044000000000000000000000000000000000000000000000000000000000000
χ10544-4-44-24-44-4-2-2-200002200000000-2-2−2i32i32i3−2i32i3−2i3−2i32i3224-400-2-2000022−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ10644-4-44-24-44-4-2-2-200002200000000-2-2−2i32i32i3−2i32i3−2i3−2i32i322-4400220000-2-22i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ10744-4-44-24-44-4-2-2-200002200000000-2-22i3−2i3−2i32i3−2i32i32i3−2i3224-400-2-20000222i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ10844-4-44-24-44-4-2-2-200002200000000-2-22i3−2i3−2i32i3−2i32i32i3−2i322-4400220000-2-2−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ10916-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11016-16000-800008−8i38i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11116-16000-8000088i3−8i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).