Finite Group Databasebeta

← Group #10690798

Character table — Group #10690798

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444121212121212121212121212121212121616161616161616161616162424242424242424
order12222222344444444444444446666666224444666612121212121212121212121212121212121212121212121288888888888888884444121212121212121288888888
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
χ51111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-111-1-1iiii−i−i−i−i
χ61111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111-1-111−i−i−i−iiiii
χ71111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-111-1-1−i−i−i−iiiii
χ81111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111-1-111iiii−i−i−i−i
χ9111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-1111-1-1-1-111ii−i−iii−i−i
χ10111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-111-1-1-11111-1-1−i−iii−i−iii
χ11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-1111-1-1-1-111−i−iii−i−iii
χ12111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-111-1-1-11111-1-1ii−i−iii−i−i
χ13111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111
χ14111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1
χ15111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1
χ16111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ172222222222222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-22222-2-22222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ19222222222-2-2-2-22222-2-22222-2-2222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-222-2-2-2-222222222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
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
χ2322222222-12222222222-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ2422222222-12222222222-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ2522222222-12222-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ2622222222-12222-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ2722222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000002-22-2-1-111-1-11100000000
χ2822222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-22-2211-1-111-1-100000000
χ2922222222-1-2-2-2-22222-2-22222-2-2-1-1-1-1-1-1-122-2-2-2-2-1-1-1-111111111-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ3022222222-1-2-2-2-22222-2-22222-2-2-1-1-1-1-1-1-122-2-2-2-2-1-1-1-111111111-1-1-1-111111111-1-1-1-100000000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ3122222222-1-2-2-2-22222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-222221111-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000000000002-2-22-1-11111-1-100000000
χ3222222222-1-2-2-2-22222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-222221111-1-1-1-11111-1-1-1-1-1-1-1-1111111110000000000000000-222-211-1-1-1-11100000000
χ3322222222-1-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-1111111111111-1-1-1-1-1-1-1-1000000000000000022-2-2-1-1-1-1111100000000
χ3422222222-1-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-1111111111111-1-1-1-1-1-1-1-10000000000000000-2-2221111-1-1-1-100000000
χ3522222222-1-2-2-2-2-2-2-2-222-2-2-2-222-1-1-1-1-1-1-122-2-222-1-1-1-1111111111111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ3622222222-1-2-2-2-2-2-2-2-222-2-2-2-222-1-1-1-1-1-1-122-2-222-1-1-1-1111111111111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ3722-22-2-22-2200002i2i−2i−2i002i2i−2i−2i002-22-2-22-22-2000022-2-2000000002i2i−2i−2i000000002i2i−2i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00000000000000000000
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χ3922-22-2-22-2200002i2i−2i−2i00−2i−2i2i2i002-22-2-22-2-220000-2-222000000002i2i−2i−2i00000000−2i−2i2i2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i00000000000000000000
χ4022-22-2-22-2200002i2i−2i−2i00−2i−2i2i2i002-22-2-22-2-220000-2-222000000002i2i−2i−2i00000000−2i−2i2i2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i00000000000000000000
χ4122-22-2-22-220000−2i−2i2i2i002i2i−2i−2i002-22-2-22-2-220000-2-22200000000−2i−2i2i2i000000002i2i−2i−2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i00000000000000000000
χ4222-22-2-22-220000−2i−2i2i2i002i2i−2i−2i002-22-2-22-2-220000-2-22200000000−2i−2i2i2i000000002i2i−2i−2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i00000000000000000000
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χ452-222-2-2-2222i2i−2i−2i2-22-22i−2i00002i−2i-222-2-2-22000000000000002i2i−2i−2i2-22-200002i2i−2i−2i000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ462-222-2-2-2222i2i−2i−2i2-22-22i−2i00002i−2i-222-2-2-22000000000000002i2i−2i−2i2-22-200002i2i−2i−2i00000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ472-222-2-2-2222i2i−2i−2i-22-22−2i2i0000−2i2i-222-2-2-22000000000000002i2i−2i−2i-22-220000−2i−2i2i2i000000000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i
χ482-222-2-2-2222i2i−2i−2i-22-22−2i2i0000−2i2i-222-2-2-22000000000000002i2i−2i−2i-22-220000−2i−2i2i2i00000000000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i
χ492-222-2-2-222−2i−2i2i2i2-22-2−2i2i0000−2i2i-222-2-2-2200000000000000−2i−2i2i2i2-22-20000−2i−2i2i2i000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ502-222-2-2-222−2i−2i2i2i2-22-2−2i2i0000−2i2i-222-2-2-2200000000000000−2i−2i2i2i2-22-20000−2i−2i2i2i00000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ512-222-2-2-222−2i−2i2i2i-22-222i−2i00002i−2i-222-2-2-2200000000000000−2i−2i2i2i-22-2200002i2i−2i−2i000000000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ522-222-2-2-222−2i−2i2i2i-22-222i−2i00002i−2i-222-2-2-2200000000000000−2i−2i2i2i-22-2200002i2i−2i−2i00000000000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ532-22-22-22-222i−2i2i−2i0000002i−2i2i−2i00-22-22-22-200002-2000000002i−2i2i−2i000022-2-200002i−2i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
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χ8344-4-44-4-44-200000000−4i4i00004i−4i-222-222-2000000−2i32i32i3−2i3000000000000−2323−23232i−2i−2i2i0000000000000000000000000000000000000000
χ8444-4-44-4-44-200000000−4i4i00004i−4i-222-222-20000002i3−2i3−2i32i300000000000023−2323−232i−2i−2i2i0000000000000000000000000000000000000000
χ854-444-4-4-44-24i4i−4i−4i4-44-44i−4i00004i−4i2-2-2222-200000000000000−2i−2i2i2i-22-220000−2i−2i2i2i0000000000000000000000000000000000000000
χ864-444-4-4-44-24i4i−4i−4i-44-44−4i4i0000−4i4i2-2-2222-200000000000000−2i−2i2i2i2-22-200002i2i−2i−2i0000000000000000000000000000000000000000
χ874-444-4-4-44-2−4i−4i4i4i4-44-4−4i4i0000−4i4i2-2-2222-2000000000000002i2i−2i−2i-22-2200002i2i−2i−2i0000000000000000000000000000000000000000
χ884-444-4-4-44-2−4i−4i4i4i-44-444i−4i00004i−4i2-2-2222-2000000000000002i2i−2i−2i2-22-20000−2i−2i2i2i0000000000000000000000000000000000000000
χ894-44-44-44-4-24i−4i4i−4i0000004i−4i4i−4i002-22-22-2200004-400000000−2i2i−2i2i0000-2-2220000−2i2i−2i2i000000000000000000000000000000000000
χ904-44-44-44-4-24i−4i4i−4i000000−4i4i−4i4i002-22-22-220000-4400000000−2i2i−2i2i000022-2-200002i−2i2i−2i000000000000000000000000000000000000
χ914-44-44-44-4-2−4i4i−4i4i0000004i−4i4i−4i002-22-22-220000-44000000002i−2i2i−2i000022-2-20000−2i2i−2i2i000000000000000000000000000000000000
χ924-44-44-44-4-2−4i4i−4i4i000000−4i4i−4i4i002-22-22-2200004-4000000002i−2i2i−2i0000-2-22200002i−2i2i−2i000000000000000000000000000000000000
χ934-4-4444-4-4400004i−4i−4i4i00000000-4-4444-4-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ944-4-4444-4-440000−4i4i4i−4i00000000-4-4444-4-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ954-4-4444-4-4-200004i−4i−4i4i0000000022-2-2-2220000000000−2i32i32i3−2i30000−2i2i2i−2i−232323−2300000000000000000000000000000000000000000000
χ964-4-4444-4-4-200004i−4i−4i4i0000000022-2-2-22200000000002i3−2i3−2i32i30000−2i2i2i−2i23−23−232300000000000000000000000000000000000000000000
χ974-4-4444-4-4-20000−4i4i4i−4i0000000022-2-2-2220000000000−2i32i32i3−2i300002i−2i−2i2i23−23−232300000000000000000000000000000000000000000000
χ984-4-4444-4-4-20000−4i4i4i−4i0000000022-2-2-22200000000002i3−2i3−2i32i300002i−2i−2i2i−232323−2300000000000000000000000000000000000000000000
χ994-4-4-4-4444-200000000444-4-44-4-42222-2-2-2004-4000000-2-222000000000000-22-22-222-2000000000000000000000000000000000000
χ1004-4-4-4-4444-20000000044-444-4-4-42222-2-2-200-4400000022-2-2000000000000-22-222-2-22000000000000000000000000000000000000
χ1014-4-4-4-4444-200000000-4-44-4-44442222-2-2-200-4400000022-2-20000000000002-22-2-222-2000000000000000000000000000000000000
χ1024-4-4-4-4444-200000000-4-4-444-4442222-2-2-2004-4000000-2-2220000000000002-22-22-2-22000000000000000000000000000000000000

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