Finite Group Databasebeta

← Group #10690916

Character table — Group #10690916

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12222222222234444666666644444444446666121212124444444488881212121212121212121224242424242424242222444444444412121212888844
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
χ2522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i11111111000000002i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-111000000
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
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χ3022-2-222-2-22-22-2200002-2-2-222-200000000002-2-2200002i2i−2i−2i2i2i−2i−2i−22−220000000000−2−222−2−222000000000000000000i2−i2i2−i200
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χ3222-2-222-2-22-22-2200002-2-2-222-200000000002-2-220000−2i−2i2i2i−2i−2i2i2i−22−220000000000−2−222−2−222000000000000000000−i2i2−i2i200
χ3322-2-222-2-2-22-22200002-2-2-222-20000000000-222-200002i2i−2i−2i−2i−2i2i2i−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i2000000000000000000−222−200
χ3422-2-222-2-2-22-22200002-2-2-222-20000000000-222-200002i2i−2i−2i−2i−2i2i2ii2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i20000000000000000002−2−2200
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χ3822-2-2-2-22222-2-2222-2-222-2-2-2-222-2−2i−2i2i2i−2i−2i2i2i22-2-2-2-2220000000000002-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ3922-2-2-2-22222-2-22-2-22222-2-2-2-22-220000000022-2-222-2-2000000000000-22000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ4022-2-2-2-22222-2-22-2-22222-2-2-2-22-220000000022-2-222-2-2000000000000-2200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
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χ4222-2-2-2-22222-2-2-122-2-2-1-11111-12-22i2i−2i−2i2i2i−2i−2i-1-11111-1-1000000000000-11−i−iii−i−iiii3−i3i3−i3i3−i3i3−i300000000000000−33−33000000
χ4322-2-2-2-22222-2-2-122-2-2-1-11111-12-2−2i−2i2i2i−2i−2i2i2i-1-11111-1-1000000000000-11ii−i−iii−i−i−i3i3−i3i3−i3i3−i3i300000000000000−33−33000000
χ4422-2-2-2-22222-2-2-122-2-2-1-11111-12-2−2i−2i2i2i−2i−2i2i2i-1-11111-1-1000000000000-11ii−i−iii−i−ii3−i3i3−i3i3−i3i3−i3000000000000003−33−3000000
χ4522-2-2-2-222-2-222222-2-222-2-2-2-22-2200000000-2-222-2-222000000000000-220000000000000000000022-2-2-2-222000000000000
χ4622-2-2-2-222-2-222222-2-222-2-2-2-22-2200000000-2-222-2-222000000000000-2200000000000000000000-2-22222-2-2000000000000
χ4722-2-2-2-222-2-2222-2-22222-2-2-2-222-222-2-2-2-222-2-22222-2-20000000000002-222-2-2-2-22200000000000000000000000000000000
χ4822-2-2-2-222-2-2222-2-22222-2-2-2-222-2-2-22222-2-2-2-22222-2-20000000000002-2-2-22222-2-200000000000000000000000000000000
χ4922-2-2-2-222-2-222-1-2-222-1-11111-12-222-2-2-2-22211-1-1-1-111000000000000-11-1-11111-1-13−33−3−33−3300000000000000−333−3000000
χ5022-2-2-2-222-2-222-1-2-222-1-11111-12-222-2-2-2-22211-1-1-1-111000000000000-11-1-11111-1-1−33−333−33−3000000000000003−3−33000000
χ5122-2-2-2-222-2-222-1-2-222-1-11111-12-2-2-22222-2-211-1-1-1-111000000000000-1111-1-1-1-1113−33−3−33−33000000000000003−3−33000000
χ5222-2-2-2-222-2-222-1-2-222-1-11111-12-2-2-22222-2-211-1-1-1-111000000000000-1111-1-1-1-111−33−333−33−300000000000000−333−3000000
χ532-22-22-22-2000022i−2i2i−2i-222-22-2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002i−2i2i−2i00002i−2i2i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000002-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
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χ552-22-22-22-2000022i−2i2i−2i-222-22-2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002i−2i2i−2i00002i−2i2i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000002-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
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χ844-44-44-44-40000-24i−4i4i−4i2-2-22-22200−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000−2i2i−2i2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000000000
χ854-44-44-44-40000-2−4i4i−4i4i2-2-22-222002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00002i−2i2i−2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000000000
χ864-44-44-44-40000-2−4i4i−4i4i2-2-22-22200−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00002i−2i2i−2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000000000
χ874-44-4-44-44000040000-4-44-4-4440000000000000000004-4-4400000000000000000000000000000000000000000000000000
χ884-44-4-44-44000040000-4-44-4-444000000000000000000-444-400000000000000000000000000000000000000000000000000
χ894-4-444-4-44000040000-4-4-444-4400000000000000000000004-4-440000000000000000000000000000000000000000000000
χ904-4-444-4-44000040000-4-4-444-440000000000000000000000-444-40000000000000000000000000000000000000000000000
χ914-4-44-444-40000-24i−4i−4i4i2-22-22-22002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00002i−2i−2i2i00000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000000000000000000000
χ924-4-44-444-40000-24i−4i−4i4i2-22-22-2200−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00002i−2i−2i2i000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000000000000000000000
χ934-4-44-444-40000-2−4i4i4i−4i2-22-22-22002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000−2i2i2i−2i00000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000000000000000000000
χ944-4-44-444-40000-2−4i4i4i−4i2-22-22-2200−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000−2i2i2i−2i000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000000000000000000000
χ958-88-8-88-880000-4000044-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-888-8-880000-40000444-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000

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