Finite Group Databasebeta

← Group #72311881

Character table — Group #72311881

Order 8192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113
size11222444444888888888888161616161616161616161616161616161616161632323232323232323232646464646464646464646464128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128128256256256256
order12222222222222222222222222222222222224444442244444444244444444444444444444444444444444444444444444444444488884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ511111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ811111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ91111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-111111-1-111-1-1-1-111-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−i11-1-1iiii−i−i−i−iii−i−iii−i−i11-1-1
χ101111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-111111-1-111-1-1-1-111-1-1ii−i−i-1-111ii−i−i−i−iiiii−i−i-1-111−i−i−i−iiiii−i−iiiii−i−i-1-111
χ111111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-111111-1-111-1-1-1-111-1-1−i−iii11-1-1−i−iii−i−iii−i−iii11-1-1−i−i−i−iiiii−i−iii−i−iii11-1-1
χ121111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-111111-1-111-1-1-1-111-1-1−i−iii-1-111−i−iiiii−i−i−i−iii-1-111iiii−i−i−i−iii−i−i−i−iii-1-111
χ131111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-11-1-111-1-1-1-11111-1-111ii−i−i11-1-1−i−iii−i−iiiii−i−i11-1-1iiii−i−i−i−i−i−iii−i−iii-1-111
χ141111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-11-1-111-1-1-1-11111-1-111ii−i−i-1-111−i−iiiii−i−iii−i−i-1-111−i−i−i−iiiiiii−i−i−i−iii11-1-1
χ151111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-11-1-111-1-1-1-11111-1-111−i−iii11-1-1ii−i−iii−i−i−i−iii11-1-1−i−i−i−iiiiiii−i−iii−i−i-1-111
χ161111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-11-1-111-1-1-1-11111-1-111−i−iii-1-111ii−i−i−i−iii−i−iii-1-111iiii−i−i−i−i−i−iiiii−i−i11-1-1
χ17222222222222222222222-2-22222222-2-22222-222-2-2-2-2-22-222-2-2-2-2200-2-22-20000000000000022-2-2000000000000-2-22200000000000000000000
χ18222222222222222222222-2-22222222-2-22222-222-2-2-2-2-22-222-2-2-2-2200-2-22-200000000000000-2-22200000000000022-2-200000000000000000000
χ192222222222222222222-2-222222-2-2-2-2222-2-2-22222222-22-2-2-2-2-222200-2-2-22000000000000002222000000000000-2-2-2-200000000000000000000
χ202222222222222222222-2-222222-2-2-2-2222-2-2-22222222-22-2-2-2-2-222200-2-2-2200000000000000-2-2-2-2000000000000222200000000000000000000
χ2122222222222222222-2-222222222222-2-2-22222-2-22-2-222-22-2-22222-222-2-2-2-2222222-2-2-2-200000000000000000000000000000000000000000000
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χ2322222222222222222-2-222-2-2222222222-2222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-20022-22000000000000000000000000000000000000000000000000002i−2i2i−2i
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χ2522222222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-22-2-22-2-22-2-2-222-2-222-200222-2000000000000000000000000000000000000000000000000002i−2i−2i2i
χ2622222222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-22-2-22-2-22-2-2-222-2-222-200222-200000000000000000000000000000000000000000000000000−2i2i2i−2i
χ2722222222222222222-2-2-2-2-2-2222-2-2-2-222-2-2-2-2-2-2-2-222-22-222222-2-2-222-2-22222-2-2-2-2-2-22200000000000000000000000000000000000000000000
χ2822222222222222222-2-2-2-2-2-2222-2-2-2-222-2-2-2-2-2-2-2-222-22-222222-2-2-2-2-2-2-222-2-2222222-2-200000000000000000000000000000000000000000000
χ2922222222222222-2-22222222-2-2-222-2-22222-2-222222222-2222-2-2-2-2-200-22-2-20000000000000000002222000000000000000000000000-2-2-2-20000
χ3022222222222222-2-22222222-2-2-222-2-22222-2-222222222-2222-2-2-2-2-200-22-2-2000000000000000000-2-2-2-200000000000000000000000022220000
χ3122222222222222-2-222222-2-2-2-2-222-2-2-2-222-2-2-222-2-2-2-2-2-2-2222222-2002-2-2200000000000000000000002i2i−2i−2i0000000000000000−2i−2i2i2i00000000
χ3222222222222222-2-222222-2-2-2-2-222-2-2-2-222-2-2-222-2-2-2-2-2-2-2222222-2002-2-220000000000000000000000−2i−2i2i2i00000000000000002i2i−2i−2i00000000
χ3322222222222222-2-2222-2-222-2-2-2-2-222222-2222222222-2-2-2-2-222-2-2-2002-22-2000000000000000000000022220000000000000000-2-2-2-200000000
χ3422222222222222-2-2222-2-222-2-2-2-2-222222-2222222222-2-2-2-2-222-2-2-2002-22-20000000000000000000000-2-2-2-20000000000000000222200000000
χ3522222222222222-2-2222-2-2-2-2-2-2-2-2-222-2-22-222-222-2-2-2-22-22-2-2-2-222-200-22220000000000000000002i2i−2i−2i000000000000000000000000−2i−2i2i2i0000
χ3622222222222222-2-2222-2-2-2-2-2-2-2-2-222-2-22-222-222-2-2-2-22-22-2-2-2-222-200-2222000000000000000000−2i−2i2i2i0000000000000000000000002i2i−2i−2i0000
χ3722222222222222-2-22-2-22222-2-2-222-2-2-2-2-22-2-22-2-22-2-22222-2-2-2-2-2-22002-22200000000002222000000000000-2-2-2-2000000000000000000000000
χ3822222222222222-2-22-2-22222-2-2-222-2-2-2-2-22-2-22-2-22-2-22222-2-2-2-2-2-22002-2220000000000-2-2-2-20000000000002222000000000000000000000000
χ3922222222222222-2-22-2-222-2-2-2-2-222-2-222-22-2-2-2-2-2-222-2-22-2-2-22222200-222-200000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ4022222222222222-2-22-2-222-2-2-2-2-222-2-222-22-2-2-2-2-2-222-2-22-2-2-22222200-222-20000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ4122222222222222-2-22-2-2-2-222-2-2-2-2-222-2-2-2-2222-2-22-2-22-22-22222-2-2200-22-22000000000000000000000000000000000022-2-2-2-222000000000000
χ4222222222222222-2-22-2-2-2-222-2-2-2-2-222-2-2-2-2222-2-22-2-22-22-22222-2-2200-22-220000000000000000000000000000000000-2-22222-2-2000000000000
χ4322222222222222-2-22-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-2-2-222-222222-2-2222002-2-2-200000000002i2i−2i−2i000000000000−2i−2i2i2i000000000000000000000000
χ4422222222222222-2-22-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-2-2-222-222222-2-2222002-2-2-20000000000−2i−2i2i2i0000000000002i2i−2i−2i000000000000000000000000
χ4544444444-4-444-4-400-40044440004-400000-400400-400-440-4000000000000000000000000000000000002-22-200000000000000002-22-200000000
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χ5144444444-4-444-4-400-400-4-4-4-4000-4400000400-400400440-4000000000000000000000000000000000002i−2i−2i2i00000000000000002i−2i−2i2i00000000
χ5244444444-4-444-4-400-400-4-4-4-4000-4400000400-400400440-400000000000000000000000000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i00000000
χ534444444-444-4-44-444-44400004-4-400000040000-4-40000040000000-4000000000000000000004-400000000000000000000000000000000000000
χ544444444-444-4-44-444-44400004-4-400000040000-4-40000040000000-400000000000000000000-4400000000000000000000000000000000000000
χ554444444-444-4-44-444-4-4-400004-4-4000000-400004400000-4000000040000000000000000000000000000000000004i−4i0000000000000000000000
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χ6144444-4-44444-4-4-400444004400000004-4-4000-44-444-4-40000000000220000-2-222-2-22-22-200000000000000000000000000000000000000000000
χ6244444-4-44444-4-4-400444004400000004-4-4000-44-444-4-40000000000-2-2000022-2-222-22-2200000000000000000000000000000000000000000000
χ6344444-4-44444-4-4-40044400-4-40000000-44-400044-4-4-4440000000000220000-2-2-2-2222-2-2200000000000000000000000000000000000000000000
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χ6744444-4-44444-4-4-4004-4-400-4-400000004-440004-44-44-440000000000220000-2-2-2-222-222-200000000000000000000000000000000000000000000
χ6844444-4-44444-4-4-4004-4-400-4-400000004-440004-44-44-440000000000-2-200002222-2-22-2-2200000000000000000000000000000000000000000000
χ6944444-4-44-4-44-44400-4000044000004-400004-4-400-4004000004-40000000000000000000000000002-22-20000000000000000000000002-22-20000
χ7044444-4-44-4-44-44400-4000044000004-400004-4-400-4004000004-4000000000000000000000000000-22-22000000000000000000000000-22-220000
χ7144444-4-44-4-44-44400-400004400000-440000-44-400-400400000-440000000000000000000000000002-22-2000000000000000000000000-22-220000
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χ7344444-4-44-4-44-44400-40000-4-4000004-400004-4400400-400000-440000000000000000000000000002i−2i−2i2i000000000000000000000000−2i2i2i−2i0000
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χ7544444-4-44-4-44-44400-40000-4-400000-440000-44400400-4000004-40000000000000000000000000002i−2i−2i2i0000000000000000000000002i−2i−2i2i0000
χ7644444-4-44-4-44-44400-40000-4-400000-440000-44400400-4000004-4000000000000000000000000000−2i2i2i−2i000000000000000000000000−2i2i2i−2i0000
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χ788888888-8-8-8-8-8-880080000000000000-8-8000000008800000000000000000000000000000000000000000000000000000000000000000000000
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χ8388-88-80008-800000008-84400000-4-40000040000000000004-40000000000000000000002-22-20000000000002-22-2000000000000000000000000
χ8488-88-80008-800000008-84400000-4-40000040000000000004-4000000000000000000000-22-22000000000000-22-22000000000000000000000000
χ8588-88-80008-800000008-8-4-4000004400000-4000000000000-440000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000000000000000000000
χ8688-88-80008-800000008-8-4-4000004400000-4000000000000-44000000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000000000000000000000
χ8788-88-80008-80000000-884400000-4-4000004000000000000-440000000000000000000002-22-2000000000000-22-22000000000000000000000000
χ8888-88-80008-80000000-884400000-4-4000004000000000000-44000000000000000000000-22-220000000000002-22-2000000000000000000000000
χ8988-88-80008-80000000-88-4-4000004400000-40000000000004-40000000000000000000002i−2i−2i2i000000000000−2i2i2i−2i000000000000000000000000
χ9088-88-80008-80000000-88-4-4000004400000-40000000000004-4000000000000000000000−2i2i2i−2i0000000000002i−2i−2i2i000000000000000000000000
χ9188-8-8800-800800044000008-8-44-40000000000000000000000004-404-40000004-400000000000000000000000000000000000000000000000000
χ9288-8-8800-800800044000008-8-44-40000000000000000000000004-40-44000000-4400000000000000000000000000000000000000000000000000
χ9388-8-8800-80080004400000-88-44-4000000000000000000000000-4404-4000000-4400000000000000000000000000000000000000000000000000
χ9488-8-8800-80080004400000-88-44-4000000000000000000000000-440-440000004-400000000000000000000000000000000000000000000000000
χ9588-8-8800-8008000-4-4000008-84-44000000000000000000000000-4400000004-4004-4000000000000000000000000000000000000000000000000
χ9688-8-8800-8008000-4-4000008-84-44000000000000000000000000-440000000-4400-44000000000000000000000000000000000000000000000000
χ9788-8-8800-8008000-4-400000-884-440000000000000000000000004-400000004-400-44000000000000000000000000000000000000000000000000
χ9888-8-8800-8008000-4-400000-884-440000000000000000000000004-40000000-44004-4000000000000000000000000000000000000000000000000
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χ1001616-1616-16000-1616000000000-8-8000008-80000080000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1011616-16-1616001600-16000880000000-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021616-16-1616001600-16000-8-8000000088-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10316-160008-800000008-80008-80000000440000-4-40000000000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ10416-160008-800000008-80008-80000000440000-4-4000000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ10516-160008-800000008-8000-880000000-4-40000440000000000000000000000000000000000000000000000000000000002-22-2-22-22000000000000
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χ10716-160008-80000000-880008-80000000-4-40000440000000000000000000000000000000000000000000000000000000002-2-222-2-22000000000000
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χ11016-160008-80000000-88000-880000000440000-4-4000000000000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ111323232-32-32000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11232-32000-16160000000000000000000008-80000-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ11332-32000-1616000000000000000000000-8800008-800000000000000000000000000000000000000000000000000000000000000000000000000000

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