Finite Group Databasebeta

← Group #10690919

Character table — Group #10690919

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122222222222344446666666444444444466661212121222222222888812121212121212121212242424242424242444444444444424661212888844
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
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
χ2822222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i1111111100000000−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-111000000
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χ30222-2-22-2-2000022i−2i2i−2i222-2-2-2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i00002i−2i2i−2i0000-2-2220000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ31222-2-22-2-2000022i−2i2i−2i222-2-2-2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002i−2i2i−2i000022-2-2000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000002i−2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ32222-2-22-2-2000022i−2i2i−2i222-2-2-2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002i−2i2i−2i0000-2-222000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ33222-2-22-2-200002−2i2i−2i2i222-2-2-2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−2i2i−2i2i000022-2-20000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−2i2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ34222-2-22-2-200002−2i2i−2i2i222-2-2-2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−2i2i−2i2i0000-2-2220000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ35222-2-22-2-200002−2i2i−2i2i222-2-2-2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000−2i2i−2i2i000022-2-2000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−2i2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ36222-2-22-2-200002−2i2i−2i2i222-2-2-2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000−2i2i−2i2i0000-2-222000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3722-22-2-22-2000022i−2i−2i2i2-2-222-2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−2i2i2i−2i22-2-200000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3822-22-2-22-2000022i−2i−2i2i2-2-222-2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−2i2i2i−2i-2-22200000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3922-22-2-22-2000022i−2i−2i2i2-2-222-2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−2i2i2i−2i22-2-20000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ4022-22-2-22-2000022i−2i−2i2i2-2-222-2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−2i2i2i−2i-2-2220000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ4122-22-2-22-200002−2i2i2i−2i2-2-222-2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002i−2i−2i2i22-2-200000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4222-22-2-22-200002−2i2i2i−2i2-2-222-2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002i−2i−2i2i-2-22200000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4322-22-2-22-200002−2i2i2i−2i2-2-222-2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002i−2i−2i2i22-2-20000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4422-22-2-22-200002−2i2i2i−2i2-2-222-2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002i−2i−2i2i-2-2220000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4522-2-22-2-2222-2-2222-2-22-2-2-2-2222-20000000022-2-2-2-2220000000000002-2000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ4622-2-22-2-2222-2-2222-2-22-2-2-2-2222-20000000022-2-2-2-2220000000000002-200000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ4722-2-22-2-2222-2-22-2-2222-2-2-2-222-222i−2i−2i2i−2i2i2i−2i22-2-222-2-2000000000000-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ4822-2-22-2-2222-2-22-2-2222-2-2-2-222-22−2i2i2i−2i2i−2i−2i2i22-2-222-2-2000000000000-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ4922-2-22-2-2222-2-2-1-2-222-11111-1-1-222i−2i−2i2i−2i2i2i−2i-1-111-1-1110000000000001-1−iii−ii−i−ii33−3−333−3−300000000000000−i3i3−i3i3000000
χ5022-2-22-2-2222-2-2-1-2-222-11111-1-1-222i−2i−2i2i−2i2i2i−2i-1-111-1-1110000000000001-1−iii−ii−i−ii−3−333−3−33300000000000000i3−i3i3−i3000000
χ5122-2-22-2-2222-2-2-1-2-222-11111-1-1-22−2i2i2i−2i2i−2i−2i2i-1-111-1-1110000000000001-1i−i−ii−iii−i33−3−333−3−300000000000000i3−i3i3−i3000000
χ5222-2-22-2-2222-2-2-1-2-222-11111-1-1-22−2i2i2i−2i2i−2i−2i2i-1-111-1-1110000000000001-1i−i−ii−iii−i−3−333−3−33300000000000000−i3i3−i3i3000000
χ5322-2-22-2-22-2-222222-2-22-2-2-2-222-222-2-222-2-22-2-222-2-222000000000000-222-2-222-2-2200000000000000000000000000000000
χ5422-2-22-2-22-2-222222-2-22-2-2-2-222-22-222-2-222-2-2-222-2-222000000000000-22-222-2-222-200000000000000000000000000000000
χ5522-2-22-2-22-2-2222-2-2222-2-2-2-2222-200000000-2-22222-2-20000000000002-2000000000000000000002-2-222-2-22000000000000
χ5622-2-22-2-22-2-2222-2-2222-2-2-2-2222-200000000-2-22222-2-20000000000002-200000000000000000000-222-2-222-2000000000000
χ5722-2-22-2-22-2-222-122-2-2-11111-1-1-222-2-222-2-2211-1-111-1-10000000000001-1-111-1-111-1−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i3000000
χ5822-2-22-2-22-2-222-122-2-2-11111-1-1-222-2-222-2-2211-1-111-1-10000000000001-1-111-1-111-1i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i3000000
χ5922-2-22-2-22-2-222-122-2-2-11111-1-1-22-222-2-222-211-1-111-1-10000000000001-11-1-111-1-11−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i3000000
χ6022-2-22-2-22-2-222-122-2-2-11111-1-1-22-222-2-222-211-1-111-1-10000000000001-11-1-111-1-11i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i3000000
χ612-2-2-2222-22-22-220000-22-22-22-200000000002-22-200002-22-22-22-2−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000−i2i2−i2i200
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χ642-2-2-2222-22-22-220000-22-22-22-200000000002-22-20000-22-22-22-22i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000−i2i2−i2i200
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χ662-2-2-2222-2-22-2220000-22-22-22-20000000000-22-2200002-22-2-22-22−222−20000000000−22−222−22−2000000000000000000−222−200
χ672-2-2-2222-2-22-2220000-22-22-22-20000000000-22-220000-22-222-22-22−2−2200000000002−22−2−22−22000000000000000000−222−200
χ682-2-2-2222-2-22-2220000-22-22-22-20000000000-22-220000-22-222-22-2−222−20000000000−22−222−22−20000000000000000002−2−2200
χ69444444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400000000-2-2-2-22222000000000000220000000000000000000000000000000000000000
χ7044444444-4-4-4-4-24444-2-2-2-2-2-2-2-4-4000000002222-2-2-2-2000000000000220000000000000000000000000000000000000000
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χ72444-4-44-4-40000-24i−4i4i−4i-2-2-2222200−2−2i−2−2i2+2i2+2i−2+2i−2+2i2−2i2−2i0000−2i2i−2i2i000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000000000000000
χ73444-4-44-4-40000-2−4i4i−4i4i-2-2-22222002−2i2−2i−2+2i−2+2i2+2i2+2i−2−2i−2−2i00002i−2i2i−2i00000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000000000000000
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χ7544-44-4-44-40000-24i−4i−4i4i-222-2-222002+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
χ7644-44-4-44-40000-24i−4i−4i4i-222-2-22200−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00002i−2i−2i2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000000000
χ7744-44-4-44-40000-2−4i4i4i−4i-222-2-222002−2i−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
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χ824-4444-4-4-44-4-44-2000022-22-2-220000000000-222-200000000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ834-4444-4-4-44-4-44-2000022-22-2-220000000000-222-200000000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ844-4444-4-4-4-444-440000-4-44-444-40000000000-444-40000000000000000000000000000000000000000000000000000000000
χ854-4444-4-4-4-444-4-2000022-22-2-2200000000002-2-22000000000000000000000000006−6−66−666−6000000000000000000000000
χ864-4444-4-4-4-444-4-2000022-22-2-2200000000002-2-2200000000000000000000000000−666−66−6−66000000000000000000000000
χ874-44-4-4-444000040000-4-444-4-440000000000000000004-4-4400000000000000000000000000000000000000000000000000
χ884-44-4-4-444000040000-4-444-4-44000000000000000000-444-400000000000000000000000000000000000000000000000000
χ894-4-44-44-44000040000-44-4-44-4400000000000000000000004-4-440000000000000000000000000000000000000000000000
χ904-4-44-44-44000040000-44-4-44-440000000000000000000000-444-40000000000000000000000000000000000000000000000
χ914-4-4-4444-44-44-4-200002-22-22-220000000000-22-22000000000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ924-4-4-4444-44-44-4-200002-22-22-220000000000-22-220000000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ934-4-4-4444-4-44-44-200002-22-22-2200000000002-22-200000000000022−22−22220000000000−22−222−22−2000000000000000000000000
χ944-4-4-4444-4-44-44-200002-22-22-2200000000002-22-2000000000000−222222−2200000000002−22−2−22−22000000000000000000000000
χ958-88-8-8-8880000-4000044-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-88-880000-400004-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000

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