Finite Group Databasebeta

← Group #72287406

Character table — Group #72287406

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size11222224444444444444444444888888888888888888888888888161616161616161616161616163232323232323232323232323232323232323232323232323232323232323232323232323232323264646464
order122448822244444448888816161616224444444488888881616161616161616161688816161616161616161616222222444444444416161616161616163232323232323232323232323232323216161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ5111111111111111-1-1111111111-1-1-1-1111-1-1-111111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1111-1-1-11-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111-1-1111111111-1-1-1-1111-1-1-111111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1111-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ7111111111111111-1-1111111111-1-1-1-1111-1-1-111111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-11-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111-1-1111111111-1-1-1-1111-1-1-111111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ91111111111111-1-1111-1-1-1-1-1-1-1-11-11-1-1-1-11-1-1111-1-111-1-11111-1-1-1-11-1-111-1-11111-1-111-111-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i
χ101111111111111-1-1111-1-1-1-1-1-1-1-11-11-1-1-1-11-1-1111-1-111-1-11111-1-1-1-11-1-111-1-11111-1-111-111-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii
χ111111111111111-1-1111-1-1-1-1-1-1-1-11-11-1-1-1-11-1-1111-1-111-1-11111-1-1-1-11-1-111-1-11111-1-1-1-11-1-1111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i
χ121111111111111-1-1111-1-1-1-1-1-1-1-11-11-1-1-1-11-1-1111-1-111-1-11111-1-1-1-11-1-111-1-11111-1-1-1-11-1-1111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii
χ131111111111111-1-1-1-11-1-1-1-1-1-1-1-1-11-11-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-11111-1-1-11-1111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii
χ141111111111111-1-1-1-11-1-1-1-1-1-1-1-1-11-11-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-11111-1-1-11-1111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i
χ151111111111111-1-1-1-11-1-1-1-1-1-1-1-1-11-11-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-111-1-1111-11-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii
χ161111111111111-1-1-1-11-1-1-1-1-1-1-1-1-11-11-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-111-1-1111-11-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i
χ1711111111-1-11-1-1111111111-1-1-1-1-11-111-1-11-1-11-1-1-1-111-1-1-1-1-1-11111-11-1-1-1111111-1-11-111-11-1-11-11-11-11-111-1-111-1-111-1-111-1-111-1-111-1-11-11-1
χ1811111111-1-11-1-1111111111-1-1-1-1-11-111-1-11-1-11-1-1-1-111-1-1-1-1-1-11111-11-1-1-1111111-1-11-111-11-1-11-11-11-11-1-1-111-1-111-1-111-1-111-1-111-1-111-11-11
χ1911111111-1-11-1-1111111111-1-1-1-1-11-111-1-11-1-11-1-1-1-111-1-1-1-1-1-11111-11-1-1-1111111-1-1-11-1-11-111-11-11-11-1111-1-111-1-1-1-111-1-111-1-111-1-1111-11-1
χ2011111111-1-11-1-1111111111-1-1-1-1-11-111-1-11-1-11-1-1-1-111-1-1-1-1-1-11111-11-1-1-1111111-1-1-11-1-11-111-11-11-11-11-1-111-1-11111-1-111-1-111-1-111-1-1-11-11
χ2111111111-1-11-1-111-1-111111-1-1-1-11-11-11-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1-111-1-1111-11-11-1-111-11-1-11-1111-1-111-1-111-1-111-1-1-1-111-1-111-11-11
χ2211111111-1-11-1-111-1-111111-1-1-1-11-11-11-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1-111-1-1111-11-11-1-111-11-1-11-11-1-111-1-111-1-111-1-11111-1-111-1-11-11-1
χ2311111111-1-11-1-111-1-111111-1-1-1-11-11-11-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1-111-1-111-11-11-111-1-11-111-11-111-1-111-1-1-1-111-1-11111-1-111-1-1-11-11
χ2411111111-1-11-1-111-1-111111-1-1-1-11-11-11-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1-111-1-111-11-11-111-1-11-111-11-1-1-111-1-11111-1-111-1-1-1-111-1-1111-11-1
χ2511111111-1-11-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-11-1-1111-1-111-1-11ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiii−i−ii
χ2611111111-1-11-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-11-1-1111-1-111-1-11−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−iii−i
χ2711111111-1-11-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-111-111-1-1-111-1-111-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−ii−i−ii
χ2811111111-1-11-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-111-111-1-1-111-1-111-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−iii−i
χ2911111111-1-11-1-1-1-1-1-11-1-1-1-111111111-111-1-1-11-1-111-1-111-1-1-1-1-1-1-1-111-1111111-1-1-1-11-1-1-1111-11-1-11-111-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−iii−i
χ3011111111-1-11-1-1-1-1-1-11-1-1-1-111111111-111-1-1-11-1-111-1-111-1-1-1-1-1-1-1-111-1111111-1-1-1-11-1-1-1111-11-1-11-111-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiii−i−ii
χ3111111111-1-11-1-1-1-1-1-11-1-1-1-111111111-111-1-1-11-1-111-1-111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1111-1-1-11-111-11-1-11ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−iii−i
χ3211111111-1-11-1-1-1-1-1-11-1-1-1-111111111-111-1-1-11-1-111-1-111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1111-1-1-11-111-11-1-11−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−ii−i−ii
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χ34222222222222222-2-222222-2-2-2-2-2-2-2-2222-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2222200000000000000000000000000000000000000000000
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χ362222222222222-2-2-2-22-2-2-2-22222-22-22-2-2-2-222222-2-2-2-222-2-2-2-22222-22222-2-2-2-222-2-200000000000000000000000000000000000000000000
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χ3922222222-2-22-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-222222222-2-222222-2-2-2-2-2-200000000000000000000000000000000000000000000
χ4022222222-2-22-2-2-2-2-2-22-2-2-2-2-2-2-2-22222-222-2-2-22-2-222-2-2-2-22222222222-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
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χ9744-44-4-4-4000000−4i4i004−4i4i004i−4i4i−4i0000000000000000000-44000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ9844-44-4-4-4000000−4i4i004−4i4i004i−4i4i−4i0000000000000000000-4400000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ9944-44-4-4-4000000−4i4i004−4i4i00−4i4i−4i4i00000000000000000004-4000000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ10044-44-4-4-4000000−4i4i004−4i4i00−4i4i−4i4i00000000000000000004-400000000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ10188-88-8880000008i−8i00-8−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-88-888000000−8i8i00-88i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-880000000000000008-84i2−4i2−4i24i20000000000000000000004i2−4i20000000000000000000000000000000000000000000000000000000000000
χ10488-8-880000000000000008-8−4i24i24i2−4i2000000000000000000000−4i24i20000000000000000000000000000000000000000000000000000000000000
χ10588-8-88000000000000000-884i2−4i2−4i24i2000000000000000000000−4i24i20000000000000000000000000000000000000000000000000000000000000
χ10688-8-88000000000000000-88−4i24i24i2−4i20000000000000000000004i2−4i20000000000000000000000000000000000000000000000000000000000000
χ10716-1600082−82000000008-800000000000000000000000042−420000000000000000000000000000000000000000000000000000000000000000000
χ10816-1600082−8200000000-88000000000000000000000000−42420000000000000000000000000000000000000000000000000000000000000000000
χ10916-16000−8282000000008-8000000000000000000000000−42420000000000000000000000000000000000000000000000000000000000000000000
χ11016-16000−828200000000-8800000000000000000000000042−420000000000000000000000000000000000000000000000000000000000000000000

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