Finite Group Databasebeta

← Group #10690749

Character table — Group #10690749

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122222222222344446666666446666888888881212121222224444444412121212121212121212242424242424242422448888888824661212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ911111111-1-1-1-11-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-111iiii−i−i−i−i1-111-1-1ii−i−i1-1
χ1011111111-1-1-1-11-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-1−i−iii11−i−i−i−iiiiiiiii−i−i−i−i-1-111iiii−i−i−i−i-11-1-111−i−iii-11
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χ1211111111-1-1-1-11-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-11111−i−iii11−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−i−i−iiiii-11-1-111ii−i−i1-1
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χ182222222222222-2-2-2-22222222-2-2222200000000-2-2-2-2-2-2-2-222220000-2-20000000000000000-2-22200000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ20222222222222-12222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-100000000-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
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χ904-4-444-4-44-444-4-244-4-422-222-2-2-4422-2-200000000-2-2220000000000002-20000000000000000000000000000000000000000
χ914-4-4-4444-444-4-4-20000222-2-2-2200-22-22−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ924-4-4-4444-444-4-4-20000222-2-2-2200-22-222i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ934-4-4-4444-4-4-444-20000222-2-2-22002-22-222−22−2222−222222−2200000000000000000000000000−222−22−2−22000000000000000000000000
χ944-4-4-4444-4-4-444-20000222-2-2-22002-22-2−222222−2222−22−2222000000000000000000000000002−2−22−222−2000000000000000000000000
χ9588-8-8-8-8880000-40000-4444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-88-880000-400004-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000

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