Finite Group Databasebeta

← Group #10690903

Character table — Group #10690903

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444121212121212121212121212121212121616161616161616161616162424242424242424
order122222222222222222223444466666664444446666666666661212121212121212121212121212121244444444444444444444121212121212121288888888
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
χ5111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-11111−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-11111iiii−i−i−i−i
χ911111111-1-1-1-11111-1-1-1-11-1-1-1-1111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-11-1-1-1-1111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-11111-1-1-1-11-1-1-1-1111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−i−iii−i−iii
χ1211111111-1-1-1-11111-1-1-1-11-1-1-1-1111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-111-1-1-1-111
χ17222222222222222222222-2-2-2-22222222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-100000000
χ1922222222222222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-21111111100000000
χ2022222222222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ2122222222222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ22222222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ23222222222222-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111111111111111-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ24222222222222-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111111111111111-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ25222222222222-2-2-2-2-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-1111100000000
χ26222222222222-2-2-2-2-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-100000000
χ2722222222-2-2-2-22222-2-2-2-2222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ2822222222-2-2-2-22222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ2922222222-2-2-2-22222-2-2-2-2-12222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ3022222222-2-2-2-22222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-2221111-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000002-22-2-1-111-1-11100000000
χ3122222222-2-2-2-22222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122-2-2221111-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000-22-2211-1-111-1-100000000
χ3222222222-2-2-2-2-2-2-2-222222-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
χ3322222222-2-2-2-2-2-2-2-22222-12222-1-1-1-1-1-1-122-2-2-2-211111111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000002-2-22-1-11111-1-100000000
χ3422222222-2-2-2-2-2-2-2-22222-12222-1-1-1-1-1-1-122-2-2-2-211111111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000-222-211-1-1-1-11100000000
χ3522222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1-2-2222211111111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ3622222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1-2-2222211111111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ372222-2-2-2-222-2-222-2-222-2-220000222-2-2-2-200000022-2-222-2-222-2-2000000000000000000000000000000000000000000002−22−22−22−2
χ382222-2-2-2-222-2-222-2-222-2-220000222-2-2-2-200000022-2-222-2-222-2-200000000000000000000000000000000000000000000−22−22−22−22
χ392222-2-2-2-222-2-2-2-222-2-22220000222-2-2-2-200000022-2-2-2-222-2-22200000000000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ402222-2-2-2-222-2-2-2-222-2-22220000222-2-2-2-200000022-2-2-2-222-2-22200000000000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ412222-2-2-2-2-2-22222-2-2-2-22220000222-2-2-2-2000000-2-22222-2-2-2-22200000000000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ422222-2-2-2-2-2-22222-2-2-2-22220000222-2-2-2-2000000-2-22222-2-2-2-22200000000000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ432222-2-2-2-2-2-222-2-22222-2-220000222-2-2-2-2000000-2-222-2-22222-2-2000000000000000000000000000000000000000000002−2−22−222−2
χ442222-2-2-2-2-2-222-2-22222-2-220000222-2-2-2-2000000-2-222-2-22222-2-200000000000000000000000000000000000000000000−222−22−2−22
χ4522-2-222-2-200002-22-2000022i2i−2i−2i2-2-222-2-2002i−2i0000002-22-2000000002i2i−2i−2i00002i2i−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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χ4922-2-222-2-20000-22-22000022i2i−2i−2i2-2-222-2-200−2i2i000000-22-2200000000−2i−2i2i2i00002i2i−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
χ5022-2-222-2-20000-22-22000022i2i−2i−2i2-2-222-2-200−2i2i000000-22-2200000000−2i−2i2i2i00002i2i−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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χ5222-2-222-2-20000-22-2200002−2i−2i2i2i2-2-222-2-2002i−2i000000-22-22000000002i2i−2i−2i0000−2i−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
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χ552-22-22-22-22-22-2000000002−2i2i−2i2i-22-22-22-20000−2i2i2-22-20000000000000000−2i−2i2i2i−2i2i−2i2i1−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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χ904-44-4-44-44-444-40000000040000-44-4-44-44000000-444-4000000000000000000000000000000000000000000000000000000000000
χ914-44-4-44-44-444-400000000-200002-222-22-20000002-2-2200000000−2i32i32i3−2i32i3−2i32i3−2i300000000000000000000000000000000000000000000
χ924-44-4-44-44-444-400000000-200002-222-22-20000002-2-22000000002i3−2i3−2i32i3−2i32i3−2i32i300000000000000000000000000000000000000000000
χ934-4-444-4-44000000004-44-4-24-4-4422-2-222-24-4000000000000-22-22-2-22200000000-222-2000000000000000000000000000000000000
χ944-4-444-4-44000000004-44-4-2-444-422-2-222-2-44000000000000-22-2222-2-2000000002-2-22000000000000000000000000000000000000
χ954-4-444-4-4400000000-44-44-24-4-4422-2-222-2-440000000000002-22-222-2-200000000-222-2000000000000000000000000000000000000
χ964-4-444-4-4400000000-44-44-2-444-422-2-222-24-40000000000002-22-2-2-222000000002-2-22000000000000000000000000000000000000
χ974-4-44-444-4000000004-4-4440000-4-44-444-4000000000000004-4-440000000000000000000000000000000000000000000000000000
χ984-4-44-444-4000000004-4-44-2000022-22-2-2200000000000000-222-2000023−23−232323−23−23230000000000000000000000000000000000000000
χ994-4-44-444-4000000004-4-44-2000022-22-2-2200000000000000-222-20000−232323−23−232323−230000000000000000000000000000000000000000
χ1004-4-44-444-400000000-444-440000-4-44-444-400000000000000-444-40000000000000000000000000000000000000000000000000000
χ1014-4-44-444-400000000-444-4-2000022-22-2-22000000000000002-2-22000023−23−2323−232323−230000000000000000000000000000000000000000
χ1024-4-44-444-400000000-444-4-2000022-22-2-22000000000000002-2-220000−232323−2323−23−23230000000000000000000000000000000000000000

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