Finite Group Databasebeta

← Group #10690908

Character table — Group #10690908

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444121212121212121212121212121212121616161616161616161616162424242424242424
order12222222222234444444444446666666444444666612121212121212121212121212121212121212121212121244444444444444444444121212121212121288888888
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
χ51111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−i−iii−i−iii
χ1211111111-1-1-1-111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111ii−i−iii−i−i
χ1311111111-1-1-1-11-1-1-1-11111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-11-1-1-1-11111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-11-1-1-1-11111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-11-1-1-1-11111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1ii−i−i−i−iii
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
χ182222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ19222222222222-1222222222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-100000000
χ20222222222222-1222222222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-21111111100000000
χ21222222222222-122222222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ22222222222222-122222222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ23222222222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-1111100000000
χ24222222222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-100000000
χ25222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ26222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ2722222222-2-2-2-222222-2-2-2-222222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-2222222222222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
χ2922222222-2-2-2-2-12222-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ3022222222-2-2-2-2-12222-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ3122222222-2-2-2-2-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000002-22-2-1-111-1-11100000000
χ3222222222-2-2-2-2-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000-22-2211-1-111-1-100000000
χ3322222222-2-2-2-2-1-2-2-2-222222222-1-1-1-1-1-1-1-2-222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ3422222222-2-2-2-2-1-2-2-2-222222222-1-1-1-1-1-1-1-2-222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ3522222222-2-2-2-2-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-122-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000002-2-22-1-11111-1-100000000
χ3622222222-2-2-2-2-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-122-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000-222-211-1-1-1-11100000000
χ372222-2-2-2-222-2-2222-2-222-2-20000222-2-2-2-200000022-2-222-2-222-2-2000000000000000000000000000000000000000000002−22−22−22−2
χ382222-2-2-2-222-2-2222-2-222-2-20000222-2-2-2-200000022-2-222-2-222-2-200000000000000000000000000000000000000000000−22−22−22−22
χ392222-2-2-2-222-2-22-2-222-2-2220000222-2-2-2-200000022-2-2-2-222-2-222000000000000000000000000000000000000000000002−22−2−22−22
χ402222-2-2-2-222-2-22-2-222-2-2220000222-2-2-2-200000022-2-2-2-222-2-22200000000000000000000000000000000000000000000−22−222−22−2
χ412222-2-2-2-2-2-222222-2-2-2-2220000222-2-2-2-2000000-2-22222-2-2-2-22200000000000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ422222-2-2-2-2-2-222222-2-2-2-2220000222-2-2-2-2000000-2-22222-2-2-2-22200000000000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ432222-2-2-2-2-2-2222-2-22222-2-20000222-2-2-2-2000000-2-222-2-22222-2-200000000000000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ442222-2-2-2-2-2-2222-2-22222-2-20000222-2-2-2-2000000-2-222-2-22222-2-200000000000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ4522-2-22-22-20000200002i−2i2i−2i2i2i−2i−2i2-2-22-22-2002-200000000002i−2i2i−2i00002i2i−2i−2i22-2-200001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000
χ4622-2-22-22-20000200002i−2i2i−2i2i2i−2i−2i2-2-22-22-2002-200000000002i−2i2i−2i00002i2i−2i−2i22-2-20000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000
χ4722-2-22-22-20000200002i−2i2i−2i−2i−2i2i2i2-2-22-22-200-2200000000002i−2i2i−2i0000−2i−2i2i2i-2-22200001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000
χ4822-2-22-22-20000200002i−2i2i−2i−2i−2i2i2i2-2-22-22-200-2200000000002i−2i2i−2i0000−2i−2i2i2i-2-2220000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000
χ4922-2-22-22-2000020000−2i2i−2i2i2i2i−2i−2i2-2-22-22-200-220000000000−2i2i−2i2i00002i2i−2i−2i-2-22200001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000
χ5022-2-22-22-2000020000−2i2i−2i2i2i2i−2i−2i2-2-22-22-200-220000000000−2i2i−2i2i00002i2i−2i−2i-2-2220000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000
χ5122-2-22-22-2000020000−2i2i−2i2i−2i−2i2i2i2-2-22-22-2002-20000000000−2i2i−2i2i0000−2i−2i2i2i22-2-200001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000
χ5222-2-22-22-2000020000−2i2i−2i2i−2i−2i2i2i2-2-22-22-2002-20000000000−2i2i−2i2i0000−2i−2i2i2i22-2-20000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000
χ532-22-2-222-2000022i−2i2i−2i00002i−2i2i−2i-22-2-222-200002-200002i−2i2i−2i000000002i−2i2i−2i000022-2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ542-22-2-222-2000022i−2i2i−2i00002i−2i2i−2i-22-2-222-200002-200002i−2i2i−2i000000002i−2i2i−2i000022-2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ552-22-2-222-2000022i−2i2i−2i0000−2i2i−2i2i-22-2-222-20000-2200002i−2i2i−2i00000000−2i2i−2i2i0000-2-2221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
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χ612-2-22-2-2222-22-22000000002-2-22-2-22-2-2222-200002-22-20000000022-2-22-2-2200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
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χ874-44-44-4-440000-2−4i4i4i−4i000000002-22-222-200000000002i−2i−2i2i0000−2i32i32i3−2i30000−2323−23230000000000000000000000000000000000000000
χ884-44-44-4-440000-2−4i4i4i−4i000000002-22-222-200000000002i−2i−2i2i00002i3−2i3−2i32i3000023−2323−230000000000000000000000000000000000000000
χ894-44-4-444-40000-24i−4i4i−4i00004i−4i4i−4i2-222-2-2200004-40000−2i2i−2i2i00000000−2i2i−2i2i0000-2-222000000000000000000000000000000000000
χ904-44-4-444-40000-24i−4i4i−4i0000−4i4i−4i4i2-222-2-220000-440000−2i2i−2i2i000000002i−2i2i−2i000022-2-2000000000000000000000000000000000000
χ914-44-4-444-40000-2−4i4i−4i4i00004i−4i4i−4i2-222-2-220000-4400002i−2i2i−2i00000000−2i2i−2i2i000022-2-2000000000000000000000000000000000000
χ924-44-4-444-40000-2−4i4i−4i4i0000−4i4i−4i4i2-222-2-2200004-400002i−2i2i−2i000000002i−2i2i−2i0000-2-222000000000000000000000000000000000000
χ934-4-4444-4-44-4-444000000000000-4-4444-4-40000004-4-44000000000000000000000000000000000000000000000000000000000000
χ944-4-4444-4-44-4-44-200000000000022-2-2-222000000-222-2000000000000000023−23−232323−23−2323000000000000000000000000000000000000
χ954-4-4444-4-44-4-44-200000000000022-2-2-222000000-222-20000000000000000−232323−23−232323−23000000000000000000000000000000000000
χ964-4-4444-4-4-444-44000000000000-4-4444-4-4000000-444-4000000000000000000000000000000000000000000000000000000000000
χ974-4-4444-4-4-444-4-200000000000022-2-2-2220000002-2-22000000000000000023−23−2323−232323−23000000000000000000000000000000000000
χ984-4-4444-4-4-444-4-200000000000022-2-2-2220000002-2-220000000000000000−232323−2323−23−2323000000000000000000000000000000000000
χ994-4-44-4-4444-44-4-2000000004-4-4422-222-2-24-40000-22-2200000000-2-222-222-200000000000000000000000000000000000000000000
χ1004-4-44-4-4444-44-4-200000000-444-422-222-2-2-440000-22-220000000022-2-22-2-2200000000000000000000000000000000000000000000
χ1014-4-44-4-444-44-44-2000000004-4-4422-222-2-2-4400002-22-20000000022-2-2-222-200000000000000000000000000000000000000000000
χ1024-4-44-4-444-44-44-200000000-444-422-222-2-24-400002-22-200000000-2-2222-2-2200000000000000000000000000000000000000000000

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