Finite Group Databasebeta

← Group #9593

Character table — Group #9593

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size1111111111111111222222222222222222222222222222222222222222222222222222228888888888888888
order1222222244444444444444448888888888888888888888888888888888888888888888884444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1711-1-111-1-1ii−i−iii−i−i1-1i−i1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31111-1-1-1-1iiii−i−i−i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-1i−i1-1i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ1811-1-111-1-1ii−i−iii−i−i1-1i−i1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31111-1-1-1-1iiii−i−i−i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-11−ii-11−ii−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ1911-1-111-1-1ii−i−iii−i−i1-1i−i1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-1-1-1-11111−i−i−i−iiiii−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-1i−i-11−iiζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ2011-1-111-1-1ii−i−iii−i−i1-1i−i1-1i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-1-1-1-11111−i−i−i−iiiii−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-11−ii1-1i−i−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ2111-1-111-1-1ii−i−iii−i−i1-1i−i1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31111-1-1-1-1iiii−i−i−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31-1i−i1-1i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ2211-1-111-1-1ii−i−iii−i−i1-1i−i1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31111-1-1-1-1iiii−i−i−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-11−ii-11−iiζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ2311-1-111-1-1ii−i−iii−i−i1-1i−i1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-1-1-1-11111−i−i−i−iiiiiζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31-1i−i-11−ii−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ2411-1-111-1-1ii−i−iii−i−i1-1i−i1-1i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-1-1-1-11111−i−i−i−iiiiiζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-11−ii1-1i−iζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ2511-1-111-1-1−i−iii−i−iii1-1−ii1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1111-1-1-1-1−i−i−i−iiiiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1-1−ii1-1−iiζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ2611-1-111-1-1−i−iii−i−iii1-1−ii1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1111-1-1-1-1−i−i−i−iiiiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-11i−i-11i−i−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ2711-1-111-1-1−i−iii−i−iii1-1−ii1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-1-1-1-11111iiii−i−i−i−i−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1-1−ii-11i−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ2811-1-111-1-1−i−iii−i−iii1-1−ii1-1−iiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-1-1-1-11111iiii−i−i−i−i−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-11i−i1-1−ii−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ2911-1-111-1-1−i−iii−i−iii1-1−ii1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1111-1-1-1-1−i−i−i−iiiii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1-1−ii1-1−ii−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ3011-1-111-1-1−i−iii−i−iii1-1−ii1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1111-1-1-1-1−i−i−i−iiiii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-11i−i-11i−iζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ3111-1-111-1-1−i−iii−i−iii1-1−ii1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-1-1-1-11111iiii−i−i−i−iζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1-1−ii-11i−i−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ3211-1-111-1-1−i−iii−i−iii1-1−ii1-1−ii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-1-1-1-11111iiii−i−i−i−iζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-11i−i1-1−iiζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
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χ3622222222-2-2-2-2-2-2-2-2-2-222-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ372222-2-2-2-22222-2-2-2-222-2-2-2-2220000000000000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ382222-2-2-2-22222-2-2-2-222-2-2-2-22200000000000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ392222-2-2-2-22222-2-2-2-2-2-22222-2-2000000000000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
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χ762-2-222-2-222i−2i−2i2i2i−2i−2i2i0000000000−2ζ32ζ3002ζ3−2ζ3002ζ−2ζ00−2ζ2ζ−i2i2−i2i2i2−i2i2−i22−22−2−22−221+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i0000000000000000
χ772-2-222-2-22−2i2i2i−2i−2i2i2i−2i00000000002ζ−2ζ00−2ζ2ζ00−2ζ32ζ3002ζ3−2ζ3i2−i2i2−i2−i2i2−i2i22−22−2−22−221−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i0000000000000000
χ782-2-222-2-22−2i2i2i−2i−2i2i2i−2i00000000002ζ−2ζ00−2ζ2ζ00−2ζ32ζ3002ζ3−2ζ3−i2i2−i2i2i2−i2i2−i2−22−222−22−2−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i0000000000000000
χ792-2-222-2-22−2i2i2i−2i−2i2i2i−2i0000000000−2ζ2ζ002ζ−2ζ002ζ3−2ζ300−2ζ32ζ3i2−i2i2−i2−i2i2−i2i22−22−2−22−22−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i0000000000000000
χ802-2-222-2-22−2i2i2i−2i−2i2i2i−2i0000000000−2ζ2ζ002ζ−2ζ002ζ3−2ζ300−2ζ32ζ3−i2i2−i2i2i2−i2i2−i2−22−222−22−21−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i0000000000000000
χ812-2-22-222-22i−2i−2i2i−2i2i2i−2i000000002ζ3−2ζ300−2ζ32ζ300−2ζ2ζ002ζ−2ζ00i2−i2−i2i2−i2i2i2−i2−222−22−2−221+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i0000000000000000
χ822-2-22-222-22i−2i−2i2i−2i2i2i−2i000000002ζ3−2ζ300−2ζ32ζ300−2ζ2ζ002ζ−2ζ00−i2i2i2−i2i2−i2−i2i22−2−22−222−2−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i0000000000000000
χ832-2-22-222-22i−2i−2i2i−2i2i2i−2i00000000−2ζ32ζ3002ζ3−2ζ3002ζ−2ζ00−2ζ2ζ00i2−i2−i2i2−i2i2i2−i2−222−22−2−22−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i0000000000000000
χ842-2-22-222-22i−2i−2i2i−2i2i2i−2i00000000−2ζ32ζ3002ζ3−2ζ3002ζ−2ζ00−2ζ2ζ00−i2i2i2−i2i2−i2−i2i22−2−22−222−21+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i0000000000000000
χ852-2-22-222-2−2i2i2i−2i2i−2i−2i2i000000002ζ−2ζ00−2ζ2ζ00−2ζ32ζ3002ζ3−2ζ300i2−i2−i2i2−i2i2i2−i22−2−22−222−21−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i0000000000000000
χ862-2-22-222-2−2i2i2i−2i2i−2i−2i2i000000002ζ−2ζ00−2ζ2ζ00−2ζ32ζ3002ζ3−2ζ300−i2i2i2−i2i2−i2−i2i2−222−22−2−22−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i0000000000000000
χ872-2-22-222-2−2i2i2i−2i2i−2i−2i2i00000000−2ζ2ζ002ζ−2ζ002ζ3−2ζ300−2ζ32ζ300i2−i2−i2i2−i2i2i2−i22−2−22−222−2−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i0000000000000000
χ882-2-22-222-2−2i2i2i−2i2i−2i−2i2i00000000−2ζ2ζ002ζ−2ζ002ζ3−2ζ300−2ζ32ζ300−i2i2i2−i2i2−i2−i2i2−222−22−2−221−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i0000000000000000

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