Finite Group Databasebeta

← Group #72287412

Character table — Group #72287412

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size11222224444444444444444444888888888888888888888888888161616161616161616161616161616161616161616323232323232323232323232323232323232323232323232323232326464646464646464
order122448822222444444488816161616244444444888888881616161616161616161688888888888161616161616161616168888888888883232323232323232323232323232323244448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111-1-111-1-1-1-11-1-1-1-1-11-111-1-1-1-111111-1-1-1-1-11111-1-1-1-11-1-1iiii−i−i−i−i11-1-11111-1-1iiiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1
χ61111111111111-1-111-1-1-1-11-1-1-1-1-11-111-1-1-1-111111-1-1-1-1-11111-1-1-1-11-1-1iiii−i−i−i−i11-1-11111-1-1iiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111
χ71111111111111-1-111-1-1-1-11-1-1-1-1-11-111-1-1-1-111111-1-1-1-1-11111-1-1-1-11-1-1−i−i−i−iiiii11-1-11111-1-1−i−i−i−i−i−iiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111
χ81111111111111-1-111-1-1-1-11-1-1-1-1-11-111-1-1-1-111111-1-1-1-1-11111-1-1-1-11-1-1−i−i−i−iiiii11-1-11111-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1
χ91111111111-1-1111-1-1111111111-11-1-1-111-1-1111-1-11-1-1111111-1-1-1-1-11-111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−ii−ii−i
χ101111111111-1-1111-1-1111111111-11-1-1-111-1-1111-1-11-1-1111111-1-1-1-1-11-111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−ii−ii
χ111111111111-1-1111-1-1111111111-11-1-1-111-1-1111-1-11-1-1111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−ii−ii−ii
χ121111111111-1-1111-1-1111111111-11-1-1-111-1-1111-1-11-1-1111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii−i−i−i−iiiiii−ii−ii−ii−i
χ131111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-111111-1-1-111-1-111111111-1-11iiii−i−i−i−i-1-1-1-111-1-111ii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−iii−i−iii−i
χ141111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-111111-1-1-111-1-111111111-1-11iiii−i−i−i−i-1-1-1-111-1-111ii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1i−i−iii−i−ii
χ151111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-111111-1-1-111-1-111111111-1-11−i−i−i−iiiii-1-1-1-111-1-111−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111i−i−iii−i−ii
χ161111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-111111-1-1-111-1-111111111-1-11−i−i−i−iiiii-1-1-1-111-1-111−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−iii−i−iii−i
χ1711111111-1-11111111111111111-1-1-1-1-1-1-1111-1-1111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1-1-111
χ1811111111-1-11111111111111111-1-1-1-1-1-1-1111-1-1111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-11111-1-1
χ1911111111-1-11111111111111111-1-1-1-1-1-1-1111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-111-1-111-1-111-1-1-1-11111-1-1
χ2011111111-1-11111111111111111-1-1-1-1-1-1-1111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-111-1-111-1-111-1-11111-1-1-1-111
χ2111111111-1-1111-1-111-1-1-1-11-1-1-1-11-11-1-111-1-11-1-111-1-1-1-1-11111-1-1-1-1-111iiii−i−i−i−i-1-111-1-11111−i−iii−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii1111-1-1-1-1
χ2211111111-1-1111-1-111-1-1-1-11-1-1-1-11-11-1-111-1-11-1-111-1-1-1-1-11111-1-1-1-1-111iiii−i−i−i−i-1-111-1-11111−i−iii−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-1-1-1-11111
χ2311111111-1-1111-1-111-1-1-1-11-1-1-1-11-11-1-111-1-11-1-111-1-1-1-1-11111-1-1-1-1-111−i−i−i−iiiii-1-111-1-11111ii−i−iii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-1-1-1-11111
χ2411111111-1-1111-1-111-1-1-1-11-1-1-1-11-11-1-111-1-11-1-111-1-1-1-1-11111-1-1-1-1-111−i−i−i−iiiii-1-111-1-11111ii−i−iii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i1111-1-1-1-1
χ2511111111-1-1-1-1111-1-11111111111-1111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-11-111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiii−i−ii−iii−i
χ2611111111-1-1-1-1111-1-11111111111-1111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-11-111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−iii−ii−i−ii
χ2711111111-1-1-1-1111-1-11111111111-1111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-11-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii−iii−ii−i−ii
χ2811111111-1-1-1-1111-1-11111111111-1111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-11-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−ii−i−ii−iii−i
χ2911111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111111-1-1-1-1-111-1-11111111111-1iiii−i−i−i−i1111-1-1-1-1-1-1−i−i−i−iiiiiii−i−i11-1-1-1-111-1-11111-1-1−ii−iii−ii−i
χ3011111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111111-1-1-1-1-111-1-11111111111-1iiii−i−i−i−i1111-1-1-1-1-1-1−i−i−i−iiiiiii−i−i-1-11111-1-111-1-1-1-111i−ii−i−ii−ii
χ3111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111111-1-1-1-1-111-1-11111111111-1−i−i−i−iiiii1111-1-1-1-1-1-1iiii−i−i−i−i−i−iii11-1-1-1-111-1-11111-1-1i−ii−i−ii−ii
χ3211111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111111-1-1-1-1-111-1-11111111111-1−i−i−i−iiiii1111-1-1-1-1-1-1iiii−i−i−i−i−i−iii-1-11111-1-111-1-1-1-111−ii−iii−ii−i
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χ342222222222222-2-222-2-2-2-222222-22-222-2-2-2-222222-2-2-222-2-2-2-222222-2-200000000-2-222-2-2-2-222000000000000000000000000000000000000
χ352222222222-2-2222-2-222222-2-2-2-2-22-2-2-222-2-2222-2-22-2-2-2-2-2-2-2-22222-22-20000000022-2-2-2-22222000000000000000000000000000000000000
χ362222222222-2-22-2-2-2-2-2-2-2-222222222-2-2-2-222222-2-2-22222-2-2-2-2-2-2-2-2-2-22000000002222-2-222-2-2000000000000000000000000000000000000
χ3722222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2222-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-222000000000000000000000000000000000000
χ3822222222-2-2222-2-222-2-2-2-2222222-22-2-222-2-22-2-222-2-2-222-2-2-2-22222-2220000000022-2-222-2-2-2-2000000000000000000000000000000000000
χ3922222222-2-2-2-2222-2-222222-2-2-2-22-2222-2-2-2-22-2-2-2-22-2-2-2-2-2-2-2-222222-2200000000-2-2222222-2-2000000000000000000000000000000000000
χ4022222222-2-2-2-22-2-2-2-2-2-2-2-222222-2-2-22222222-2-2-2-2-22222-2-2-2-2-2-2-2-222-200000000-2-2-2-2222222000000000000000000000000000000000000
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χ432222222-2002-2-2222-2-2-2-2-22-2-2-2-200000002-2-2002-222-222-2-222-2-2220002i2i−2i−2i2i2i−2i−2i000000-2200002i−2i00002i−2i00000000000000000000000000
χ442222222-2002-2-2222-2-2-2-2-22-2-2-2-200000002-2-2002-222-222-2-222-2-222000−2i−2i2i2i−2i−2i2i2i000000-220000−2i2i0000−2i2i00000000000000000000000000
χ452222222-2002-2-2-2-22-22222222220000000-22-2002-2-2-22-2-2-2-22222-2-200022-2-2-2-222000000-2200002-20000-2200000000000000000000000000
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χ472222222-2002-2-2-2-22-222222-2-2-2-20000000-22-2002-2-2-222222-2-2-2-222000000000000000002-2002-2002-2-2200-22000000000000000000000000
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χ89444-4-400-400-4-440044000002i22i2−2i2−2i240-400-440000000000−2i22i20000−2i22i22i2−2i2000000000002i2−2i200−2i22i20000000000000000000000000000000000000000
χ90444-4-400-400-4-440044000002i22i2−2i2−2i2-404004-40000000000−2i22i20000−2i22i22i2−2i200000000000−2i22i2002i2−2i20000000000000000000000000000000000000000
χ91444-4-400-400-4-44004400000−2i2−2i22i22i240-400-4400000000002i2−2i200002i2−2i2−2i22i200000000000−2i22i2002i2−2i20000000000000000000000000000000000000000
χ92444-4-400-400-4-44004400000−2i2−2i22i22i2-404004-400000000002i2−2i200002i2−2i2−2i22i2000000000002i2−2i200−2i22i20000000000000000000000000000000000000000
χ9344-44-4-4-400000000004i−4i4i−4i44i−4i4i−4i0000000000000000000004-40000000004ζ−4ζ4ζ3−4ζ3000000000000000000000000000000000000000000000000
χ9444-44-4-4-400000000004i−4i4i−4i44i−4i4i−4i0000000000000000000004-4000000000−4ζ4ζ−4ζ34ζ3000000000000000000000000000000000000000000000000
χ9544-44-4-4-400000000004i−4i4i−4i4−4i4i−4i4i000000000000000000000-4400000004ζ−4ζ00004ζ3−4ζ30000000000000000000000000000000000000000000000
χ9644-44-4-4-400000000004i−4i4i−4i4−4i4i−4i4i000000000000000000000-440000000−4ζ4ζ0000−4ζ34ζ30000000000000000000000000000000000000000000000
χ9744-44-4-4-40000000000−4i4i−4i4i44i−4i4i−4i000000000000000000000-4400000004ζ3−4ζ300004ζ−4ζ0000000000000000000000000000000000000000000000
χ9844-44-4-4-40000000000−4i4i−4i4i44i−4i4i−4i000000000000000000000-440000000−4ζ34ζ30000−4ζ4ζ0000000000000000000000000000000000000000000000
χ9944-44-4-4-40000000000−4i4i−4i4i4−4i4i−4i4i0000000000000000000004-40000000004ζ3−4ζ34ζ−4ζ000000000000000000000000000000000000000000000000
χ10044-44-4-4-40000000000−4i4i−4i4i4−4i4i−4i4i0000000000000000000004-4000000000−4ζ34ζ3−4ζ4ζ000000000000000000000000000000000000000000000000
χ10188-88-88800000000008i−8i−8i8i-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-88-8880000000000−8i8i8i−8i-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-88000000008i−8i000000042−42−424200000000000000000004i2−4i2000000000000000000000000000000000000000000000000000000000000000
χ10488-8-88000000008i−8i0000000−424242−420000000000000000000−4i24i2000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8800000000−8i8i000000042−42−42420000000000000000000−4i24i2000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8800000000−8i8i0000000−424242−4200000000000000000004i2−4i2000000000000000000000000000000000000000000000000000000000000000
χ10716-160008i2−8i208-8000000000000000000000000004i2−4i2000000000000000000000000000000000000000000000000000000000000000000000000
χ10816-160008i2−8i20-8800000000000000000000000000−4i24i2000000000000000000000000000000000000000000000000000000000000000000000000
χ10916-16000−8i28i208-800000000000000000000000000−4i24i2000000000000000000000000000000000000000000000000000000000000000000000000
χ11016-16000−8i28i20-88000000000000000000000000004i2−4i2000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.