Finite Group Databasebeta

← Group #10690788

Character table — Group #10690788

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444121212121212121212121212121212121616161616161616161616162424242424242424
order122222223444444444444444466666662244446666121212121212121212121212121212121212121212121212888888888888888824446612121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−i
χ61111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-11111−i−i−i−iiiii
χ71111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−i−i−i−iiiii
χ81111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-11111iiii−i−i−i−i
χ9111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-11111-1-111-1-1
χ10111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-11111-1-1-1-111-1-111
χ11111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-111-1-111-1-111
χ12111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-111-1-111-1-1
χ13111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-11-111-1-111-1-1ii−i−i−i−iii
χ14111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-11-11-1-111-1-111−i−iiiii−i−i
χ15111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-11-111-1-111-1-1−i−iiiii−i−i
χ16111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-11-11-1-111-1-111ii−i−i−i−iii
χ172222222222222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-22222-2-2222222222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ19222222222-2-2-2-222-2-2-2-2-2-2-2-22222222222222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-222222222-2-22222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ2122222222-12222222222222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-100000000
χ2222222222-12222222222222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-21111111100000000
χ2322222222-12222222222-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-11111-1-1-1-111111111-1-1-1-100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ2422222222-12222222222-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-11111-1-1-1-111111111-1-1-1-100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ2522222222-12222-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-11111111100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ2622222222-12222-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-11111111100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ2722222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-222221111-1-1-1-1-1-1-1-111111111-1-1-1-11111000000000000000022-2-2-1-1-1-1111100000000
χ2822222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-222221111-1-1-1-1-1-1-1-111111111-1-1-1-111110000000000000000-2-2221111-1-1-1-100000000
χ2922222222-1-2-2-2-222-2-2-2-2222222-1-1-1-1-1-1-1-2-2-2-222111111111111-1-1-1-1-1-1-1-1-1-1-1-1111100000000000000002-2-22-1-11111-1-100000000
χ3022222222-1-2-2-2-222-2-2-2-2222222-1-1-1-1-1-1-1-2-2-2-222111111111111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000-222-211-1-1-1-11100000000
χ3122222222-1-2-2-2-222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-12222-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111111100000000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ3222222222-1-2-2-2-222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-12222-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111111100000000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ3322222222-1-2-2-2-2-2-222222222-2-2-1-1-1-1-1-1-1-2-222-2-211111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ3422222222-1-2-2-2-2-2-222222222-2-2-1-1-1-1-1-1-1-2-222-2-211111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ3522222222-1-2-2-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-1-1-1-11111111111111111-1-1-1-1-1-1-1-100000000000000002-22-2-1-111-1-11100000000
χ3622222222-1-2-2-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000000000000000-22-2211-1-111-1-100000000
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χ3922-222-2-2-220000002i2i−2i−2i−2i−2i2i2i002-222-2-2-200-220000000000-2-2220000−2i−2i2i2i00002i2i−2i−2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i00000000000000000000
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χ452-222-22-2-2222-2-22i−2i2i−2i2i−2i00002i−2i-222-22-2-2000000000022-2-200002i2i−2i−2i000000002i−2i2i−2i00000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ462-222-22-2-2222-2-22i−2i2i−2i2i−2i00002i−2i-222-22-2-2000000000022-2-200002i2i−2i−2i000000002i−2i2i−2i0000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ472-222-22-2-2222-2-2−2i2i−2i2i−2i2i0000−2i2i-222-22-2-2000000000022-2-20000−2i−2i2i2i00000000−2i2i−2i2i00000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
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χ502-222-22-2-22-2-2222i−2i−2i2i−2i2i00002i−2i-222-22-2-20000000000-2-22200002i2i−2i−2i00000000−2i2i−2i2i0000000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
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χ8344-4-4-444-4-20000−4i4i000000004i−4i-2222-2-22000000−2i32i3−2i32i30000−232323−232i−2i−2i2i000000000000000000000000000000000000000000000000
χ8444-4-4-444-4-20000−4i4i000000004i−4i-2222-2-220000002i3−2i32i3−2i3000023−23−23232i−2i−2i2i000000000000000000000000000000000000000000000000
χ854-444-44-4-4-244-4-44i−4i4i−4i4i−4i00004i−4i2-2-22-2220000000000-2-2220000−2i−2i2i2i00000000−2i2i−2i2i000000000000000000000000000000000000
χ864-444-44-4-4-244-4-4−4i4i−4i4i−4i4i0000−4i4i2-2-22-2220000000000-2-22200002i2i−2i−2i000000002i−2i2i−2i000000000000000000000000000000000000
χ874-444-44-4-4-2-4-4444i−4i−4i4i−4i4i00004i−4i2-2-22-222000000000022-2-20000−2i−2i2i2i000000002i−2i2i−2i000000000000000000000000000000000000
χ884-444-44-4-4-2-4-444−4i4i4i−4i4i−4i0000−4i4i2-2-22-222000000000022-2-200002i2i−2i−2i00000000−2i2i−2i2i000000000000000000000000000000000000
χ894-44-44-44-4-24i−4i4i−4i0000004i−4i4i−4i002-22-22-224-40000-2-222−2i2i−2i2i00000000−2i2i−2i2i00000000000000000000000000000000000000000000
χ904-44-44-44-4-24i−4i4i−4i000000−4i4i−4i4i002-22-22-22-44000022-2-2−2i2i−2i2i000000002i−2i2i−2i00000000000000000000000000000000000000000000
χ914-44-44-44-4-2−4i4i−4i4i0000004i−4i4i−4i002-22-22-22-44000022-2-22i−2i2i−2i00000000−2i2i−2i2i00000000000000000000000000000000000000000000
χ924-44-44-44-4-2−4i4i−4i4i000000−4i4i−4i4i002-22-22-224-40000-2-2222i−2i2i−2i000000002i−2i2i−2i00000000000000000000000000000000000000000000
χ934-4-44-4-44440000004-4-44000000-4-44-4-4440000000000000000000000000000004-4-44000000000000000000000000000000000000
χ944-4-44-4-4444000000-444-4000000-4-44-4-444000000000000000000000000000000-444-4000000000000000000000000000000000000
χ954-4-44-4-444-20000004-4-4400000022-222-2-2000000−2i32i32i3−2i300000000000000002i3−2i3−2i32i3-222-2000000000000000000000000000000000000
χ964-4-44-4-444-20000004-4-4400000022-222-2-20000002i3−2i3−2i32i30000000000000000−2i32i32i3−2i3-222-2000000000000000000000000000000000000
χ974-4-44-4-444-2000000-444-400000022-222-2-2000000−2i32i32i3−2i30000000000000000−2i32i32i3−2i32-2-22000000000000000000000000000000000000
χ984-4-44-4-444-2000000-444-400000022-222-2-20000002i3−2i3−2i32i300000000000000002i3−2i3−2i32i32-2-22000000000000000000000000000000000000
χ994-4-4-444-44-200004400004-4-44-4-4222-2-22-200004-4000000000000-22-22-222-2-2-2220000000000000000000000000000000000000000
χ1004-4-4-444-44-20000440000-444-4-4-4222-2-22-20000-44000000000000-22-222-2-2222-2-20000000000000000000000000000000000000000
χ1014-4-4-444-44-20000-4-400004-4-4444222-2-22-20000-440000000000002-22-2-222-222-2-20000000000000000000000000000000000000000
χ1024-4-4-444-44-20000-4-40000-444-444222-2-22-200004-40000000000002-22-22-2-22-2-2220000000000000000000000000000000000000000

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