Finite Group Databasebeta

← Group #72320828

Character table — Group #72320828

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101
size112222222444444444444888888888888888816161616161616161616161616161616161616161616161616161616323232323232323232323232323232323232323232323232323232326464646464646464
order1222244444444888888882488161616161616161616161616488888161616161616323232323232323232323232323232322224448888888816161616161632323232323232324888881616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-111
χ5111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111
χ6111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1
χ7111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ8111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-11111
χ9111111111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ10111111111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1
χ11111111111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111111111-1-1-1-111111-1-11-1-1-1-1
χ12111111111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-111-11111
χ13111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111
χ14111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-1-1-11111-111-1-1-1-1-1
χ15111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ16111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ17111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1ii−i−i11ii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1i−iii−i−ii−iii−i−i11-1-111-1-1-11-11i−ii−i
χ18111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1ii−i−i11ii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111i−i−i−iiii−i−i−iii11-1-111-1-11-11-1−ii−ii
χ19111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1ii−i−i11ii−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111i−iii−i−ii−i−i−iii-1-111-1-11111-1-1i−i−ii
χ20111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1ii−i−i11ii−i−i−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1i−i−i−iiii−iii−i−i-1-111-1-111-1-111−iii−i
χ21111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1−i−iii11−i−iiiiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111−ii−i−iii−iiii−i−i-1-111-1-11111-1-1−iii−i
χ22111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1−i−iii11−i−iiiiiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−iiii−i−i−ii−i−iii-1-111-1-111-1-111i−i−ii
χ23111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1−i−iii11−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−ii−i−iii−ii−i−iii11-1-111-1-1-11-11−ii−ii
χ24111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1−i−iii11−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111−iiii−i−i−iiii−i−i11-1-111-1-11-11-1i−ii−i
χ25111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-111ii−i−i-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−iiii−i−ii−i−i−iii11-1-1-1-1111-11-1−iii−i
χ26111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-111ii−i−i-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−ii−i−iiii−iii−i−i11-1-1-1-111-11-11i−i−ii
χ27111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-111ii−i−i-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−iiii−i−ii−iii−i−i-1-11111-1-1-1-111−ii−ii
χ28111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-111ii−i−i-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1−ii−i−iiii−i−i−iii-1-11111-1-111-1-1i−ii−i
χ29111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-111−i−iii-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111i−i−i−iii−ii−i−iii-1-11111-1-1-1-111i−ii−i
χ30111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-111−i−iii-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1i−iii−i−i−iiii−i−i-1-11111-1-111-1-1−ii−ii
χ31111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-111−i−iii-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1i−i−i−iii−iiii−i−i11-1-1-1-1111-11-1i−i−ii
χ32111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-111−i−iii-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111i−iii−i−i−ii−i−iii11-1-1-1-111-11-11−iii−i
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χ39222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-222222i2i−2i−2i222i2i−2i−2i000000000000000000000000−2i2i0000−2i2i00000000000000000000
χ40222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-22222−2i−2i2i2i22−2i−2i2i2i0000000000000000000000002i−2i00002i−2i00000000000000000000
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χ43222-2-22-2-222i−2i2i−2i2-22-22i−2i2i−2i00002-22i−2i00002-22i−2i000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000002-2002i−2i00−2ζ2ζ−2ζ32ζ30000000000000000000000
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χ5622-22-222-2-2−2i2i2i−2i-222-2−2i2i2i−2i0000-222i−2i00002-2−2i2i00000000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ-22002i−2i00000000002ζ3−2ζ32ζ−2ζ0000000000000000
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χ7022-2-222-22-2-2-22222-2-222-2-200000000−2i−2i2i2i0000002-2-222i−2i−2i2i2i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000000000000000−222−2−i2i2i2−i200000000
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χ8444-44-444-4-44i−4i−4i4i4-4-44−4i4i4i−4i0000000000000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000000000
χ8544-44-444-4-44i−4i−4i4i-444-44i−4i−4i4i00004-44i−4i0000-44−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ8644-44-444-4-4−4i4i4i−4i4-4-444i−4i−4i4i00000000000000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000000000
χ8744-44-444-4-4−4i4i4i−4i4-4-444i−4i−4i4i0000000000000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000000000
χ8844-44-444-4-4−4i4i4i−4i-444-4−4i4i4i−4i00004-4−4i4i0000-444i−4i0000000000000000000000000000000000000000000000000000000000000000
χ8944-4-444-44-444-4-4-4-44444-4-4000044440000-4-4-4-40000000000000000000000000000000000000000000000000000000000000000
χ9044-4-444-44-444-4-4-4-44444-4-40000-4-4-4-4000044440000000000000000000000000000000000000000000000000000000000000000
χ9144-4-444-44-4-4-444-4-444-4-444000044-4-40000-4-4440000000000000000000000000000000000000000000000000000000000000000
χ9244-4-444-44-4-4-444-4-444-4-4440000-4-444000044-4-40000000000000000000000000000000000000000000000000000000000000000
χ9388888-8-8-8-8000000000000008i−8i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ9488888-8-8-8-800000000000000−8i8i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ95888-8-8-888-8000000000000000000004i2−4i24i2−4i200000000000000000000000000000000000000000000000000000000000000000000
χ96888-8-8-888-800000000000000000000−4i24i2−4i24i200000000000000000000000000000000000000000000000000000000000000000000
χ9788-88-8-8-8880000000000000000000042−42−424200000000000000000000000000000000000000000000000000000000000000000000
χ9888-88-8-8-88800000000000000000000−424242−4200000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-88-88-880000000000008-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-88-88-88000000000000-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10132-32000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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