Finite Group Databasebeta

← Group #10690926

Character table — Group #10690926

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12222222222234444666666644444444446666121212124444444488881212121212121212121224242424242424244444444444444412121212888824
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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ911111111-1-1-1-11-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-111-1-1ii−i−i1-1
χ1011111111-1-1-1-11-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii11iiii−i−i−i−i−i−i−i−iiiii11-1-1iiii−i−i−i−i-11-1-111−i−iii-11
χ1111111111-1-1-1-11-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-111−i−i−i−iiiii1-111-1-1−i−iii-11
χ1211111111-1-1-1-11-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-111−i−i−i−iiiii-11-1-111ii−i−i1-1
χ1311111111-1-1-1-11-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−i−i−iiiii-11-1-111ii−i−i-11
χ1411111111-1-1-1-11-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-111-1-1−i−iii1-1
χ1511111111-1-1-1-11-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-111iiii−i−i−i−i-11-1-111−i−iii1-1
χ1611111111-1-1-1-11-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-111iiii−i−i−i−i1-111-1-1ii−i−i-11
χ172222222222222-2-2-2-22222222-2-2000000002222-2-2-2-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ182222222222222-2-2-2-22222222-2-2000000002222-2-2-2-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ20222222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ21222222222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ22222222222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2322222222-2-2-2-2222222222222-2-200000000-2-2-2-222222222-2-2-2-20000-2-20000000000000000-2-22200000000000000000000
χ2422222222-2-2-2-2222222222222-2-200000000-2-2-2-22222-2-2-2-222220000-2-2000000000000000022-2-200000000000000000000
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χ2622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i1111111100000000−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-1000000
χ2722222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i11111111000000002i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-1000000
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χ3022-22-2-22-2000022i−2i2i−2i22-2-22-2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i00002i−2i2i−2i0000−2i−2i2i2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ3122-22-2-22-2000022i−2i2i−2i22-2-22-2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002i−2i2i−2i00002i2i−2i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000002-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ3222-22-2-22-2000022i−2i2i−2i22-2-22-2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002i−2i2i−2i0000−2i−2i2i2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3322-22-2-22-200002−2i2i−2i2i22-2-22-2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−2i2i−2i2i00002i2i−2i−2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3422-22-2-22-200002−2i2i−2i2i22-2-22-2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−2i2i−2i2i0000−2i−2i2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000002-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
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χ3622-22-2-22-200002−2i2i−2i2i22-2-22-2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000−2i2i−2i2i0000−2i−2i2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000002-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
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χ382-22-22-22-2000022i−2i−2i2i2-22-2-22-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−2i2i2i−2i−2i−2i2i2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ392-22-22-22-2000022i−2i−2i2i2-22-2-22-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−2i2i2i−2i2i2i−2i−2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ402-22-22-22-2000022i−2i−2i2i2-22-2-22-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−2i2i2i−2i−2i−2i2i2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000-221+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
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χ422-22-22-22-200002−2i2i2i−2i2-22-2-22-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002i−2i−2i2i−2i−2i2i2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
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χ452-2-222-2-2222-2-220000-2-2-2222-2000000000022-2-200002-22-22-22-2−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000−i2i2−i2i200
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χ472-2-222-2-2222-2-220000-2-2-2222-2000000000022-2-20000-22-22-22-22−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000i2−i2i2−i200
χ482-2-222-2-2222-2-220000-2-2-2222-2000000000022-2-20000-22-22-22-22i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i2000000000000000000−i2i2−i2i200
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χ672-2-2-2-2222-22-22-1-2-222-111-111-12-2-222-2-222-21-11-1-1-111000000000000-111-1-111-1-113−33−3−33−33000000000000003−3−33000000
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χ854-44-44-44-40000-24i−4i−4i4i-22-222-22002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00002i−2i−2i2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000000000
χ864-44-44-44-40000-24i−4i−4i4i-22-222-2200−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00002i−2i−2i2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000000000
χ874-44-44-44-40000-2−4i4i4i−4i-22-222-22002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000−2i2i2i−2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000000000
χ884-44-44-44-40000-2−4i4i4i−4i-22-222-2200−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000−2i2i2i−2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000000000
χ894-4-444-4-4444-4-4-20000222-2-2-220000000000-2-222000000000000−2i22i2−2i22i20000000000i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ904-4-444-4-4444-4-4-20000222-2-2-220000000000-2-2220000000000002i2−2i22i2−2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ914-4-444-4-44-4-444-20000222-2-2-22000000000022-2-200000000000022−22−22220000000000−2−22222−2−2000000000000000000000000
χ924-4-444-4-44-4-444-20000222-2-2-22000000000022-2-2000000000000−222222−22000000000022−2−2−2−222000000000000000000000000
χ934-4-4-4-44444-44-4-2-4-444-222-222-2-4400000000-22-22-2-2220000000000002-20000000000000000000000000000000000000000
χ944-4-4-4-4444-44-44-244-4-4-222-222-2-44000000002-22-222-2-20000000000002-20000000000000000000000000000000000000000
χ9588-8-888-8-80000-400004-4444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-88-8-80000-4000044-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).