Finite Group Databasebeta

← Group #10691275

Character table — Group #10691275

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122244442234444446661212121222444444446612121212121288888888444466121212121212121212121212121212128888888888888824242424888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-111-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ91111-1-1-1-1-1-11111-1-11111-1-1-1-1111-111-1-1-1-1-1-11111-1-1iiii−i−i−i−iii−i−i111-111-1-1-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−ii−iii−i−i11-1-11-1
χ101111-1-1-1-1-1-11111-1-11111-1-1-1-1111-111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−iii111-111-1-1-1-1−i−i−i−iiiiiii−i−iiiii−i−i−i−i−ii−i−iii-1-111-11
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-1111-111-1-1-1-1-1-11111-1-1−i−i−i−iiiiiii−i−i111-111-1-1-1-1iiii−i−i−i−i−i−iii−i−i−i−iiiiii−iii−i−i-1-111-11
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-1111-111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−iii111-111-1-1-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−ii−i−iii11-1-11-1
χ131111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11-1-1-11111-1-11111-1-1iiii−i−i−i−iii−i−i-1-11-1-1-11111iiii−i−i−i−iii−i−i−i−i−i−iiiii−ii−i−iii11-1-1-11
χ141111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11-1-1-11111-1-11111-1-1iiii−i−i−i−i−i−iii-1-11-1-1-11111−i−i−i−iiiiiii−i−i−i−i−i−iiiiii−iii−i−i-1-1111-1
χ151111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11-1-1-11111-1-11111-1-1−i−i−i−iiiiiii−i−i-1-11-1-1-11111iiii−i−i−i−i−i−iiiiiii−i−i−i−i−ii−i−iii-1-1111-1
χ161111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11-1-1-11111-1-11111-1-1−i−i−i−iiiii−i−iii-1-11-1-1-11111−i−i−i−iiiii−i−iiiiiii−i−i−i−ii−iii−i−i11-1-1-11
χ1722222222222-2-22-2-22222222222-2-2-2-2-2-2222222-2-2-2-200000000000022-2-2-2-222-2-200000000000000000000000000000000
χ1822222222222-2-22-2-222222222-2-2-2-22222-2-22222-2-2-2-2000000000000-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ202222222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
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χ332222-2-2-2-2222-2-2-222-2222-2-2-2-2002-200000022-2-2-2-222000000000000002-200000000000000000022-2-2-2-222000000000000
χ342222-2-2-2-2222-2-2-222-2222-2-2-2-2002-200000022-2-2-2-222000000000000002-2000000000000000000-2-22222-2-2000000000000
χ352222-2-2-2-2-2-22-2-22222222-2-2-2-222-22-2-222-2-2-2-222-2-22200000000000022-22-2-2-2-22200000000000000000000000000000000
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χ442222-2-2-2-2-2-2-1-2-22222-1-1-11111-2-2-2222-2-22211-1-111-1-1000000000000111-1-1-1-1-111−3−33333−3−3000000000000003−3−33000000
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χ4622-2-22i−2i2i−2i0022-202i−2i02-2-22i−2i2i−2i000000000000002-22i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−1−i1+i−1+i1−i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000−22i2−i200
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χ844-44-44i−4i−4i4i004000000-4-444i−4i−4i4i000000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000000000
χ854-44-4−4i4i4i−4i004000000-4-44−4i4i4i−4i0000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000000000
χ864-44-4−4i4i4i−4i004000000-4-44−4i4i4i−4i000000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000000000
χ874-4-4444-4-44-4-200-40042-22-2-2224-40000004-4-22-220000000000000000-220000-220000000000000000000000000000000000
χ884-4-4444-4-44-4-200-40042-22-2-222-44000000-44-22-2200000000000000002-200002-20000000000000000000000000000000000
χ894-4-4444-4-4-44-200400-42-22-2-22200004i−4i4i−4i002-22-200000000000000000000−2i2i00−2i2i00000000000000000000000000000000
χ904-4-4444-4-4-44-200400-42-22-2-2220000−4i4i−4i4i002-22-2000000000000000000002i−2i002i−2i00000000000000000000000000000000
χ914-4-44-4-4444-4-200400-42-2222-2-200004i−4i−4i4i00-222-200000000000000000000−2i2i002i−2i00000000000000000000000000000000
χ924-4-44-4-4444-4-200400-42-2222-2-20000−4i4i4i−4i00-222-2000000000000000000002i−2i00−2i2i00000000000000000000000000000000
χ934-4-44-4-444-44-200-40042-2222-2-24-4000000-442-2-220000000000000000-2200002-20000000000000000000000000000000000
χ944-4-44-4-444-44-200-40042-2222-2-2-440000004-42-2-2200000000000000002-20000-220000000000000000000000000000000000
χ958-88-88i−8i−8i8i00-400000044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i00-400000044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.