Finite Group Databasebeta

← Group #10694310

Character table — Group #10694310

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
χ51111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-1-1-1
χ61111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111
χ71111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-1-1-1-11111
χ81111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-11-1-111-1-1111111-1-1-1-1
χ911111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-1ii−i−iii−i−i
χ1011111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-11111−i−iii−i−iii
χ1111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-1−i−iii−i−iii
χ1211111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-11111ii−i−iii−i−i
χ1311111111-1-1-1-11-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-11-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-11-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-11-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1ii−i−i−i−iii
χ17222222222222222222222-2-2-2-22222222-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222222-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
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
χ21222222222222-122222222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-11111-1-1-1-111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ22222222222222-122222222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-11111-1-1-1-111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ23222222222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111111111111111-1-1-1-1-1-1-1-100000000000000002-22-2-1-111-1-11100000000
χ24222222222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000000000000000-22-2211-1-111-1-100000000
χ25222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-11111111100000000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ26222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-11111111100000000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ2722222222-2-2-2-222222-2-2-2-222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ2922222222-2-2-2-2-12222-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ3022222222-2-2-2-2-12222-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ3122222222-2-2-2-2-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-11111000000000000000022-2-2-1-1-1-1111100000000
χ3222222222-2-2-2-2-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-111110000000000000000-2-2221111-1-1-1-100000000
χ3322222222-2-2-2-2-1-2-2-2-222222222-1-1-1-1-1-1-122-2-2-2-211111111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3i3−i3−i3i300000000
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χ3522222222-2-2-2-2-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-1111100000000000000002-2-22-1-11111-1-100000000
χ3622222222-2-2-2-2-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000-222-211-1-1-1-11100000000
χ37222-22-2-2-222-2-2222-2-222-2-2000022-22-2-2-200000022-2-222-2-2000022-2-200000000000000000000000000000000000000002−22−22−22−2
χ38222-22-2-2-222-2-2222-2-222-2-2000022-22-2-2-200000022-2-222-2-2000022-2-20000000000000000000000000000000000000000−22−22−22−22
χ39222-22-2-2-222-2-22-2-222-2-222000022-22-2-2-200000022-2-2-2-2220000-2-22200000000000000000000000000000000000000002−22−2−22−22
χ40222-22-2-2-222-2-22-2-222-2-222000022-22-2-2-200000022-2-2-2-2220000-2-2220000000000000000000000000000000000000000−22−222−22−2
χ41222-22-2-2-2-2-222222-2-2-2-222000022-22-2-2-2000000-2-22222-2-20000-2-2220000000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
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χ44222-22-2-2-2-2-2222-2-22222-2-2000022-22-2-2-2000000-2-222-2-222000022-2-20000000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
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χ904-44-4-4-4444-44-4-200000000-4-4442-2222-2-20000-44-22-22000000000000000022-2-22-22-2000000000000000000000000000000000000
χ914-44-4-4-444-44-44-20000000044-4-42-2222-2-20000-442-22-2000000000000000022-2-2-22-22000000000000000000000000000000000000
χ924-44-4-4-444-44-44-200000000-4-4442-2222-2-200004-42-22-20000000000000000-2-2222-22-2000000000000000000000000000000000000
χ934-4-444-44-40000-24-44-400004i−4i−4i4i22-2-22-22004i−4i000000-22-2200000000−2i−2i2i2i0000−2i2i2i−2i000000000000000000000000000000000000
χ944-4-444-44-40000-24-44-40000−4i4i4i−4i22-2-22-2200−4i4i000000-22-22000000002i2i−2i−2i00002i−2i−2i2i000000000000000000000000000000000000
χ954-4-444-44-40000-2-44-4400004i−4i−4i4i22-2-22-2200−4i4i0000002-22-2000000002i2i−2i−2i0000−2i2i2i−2i000000000000000000000000000000000000
χ964-4-444-44-40000-2-44-440000−4i4i4i−4i22-2-22-22004i−4i0000002-22-200000000−2i−2i2i2i00002i−2i−2i2i000000000000000000000000000000000000
χ974-4-4-444-44000044-4-4400000000-4-4-444-4400000000004-4-4400000000000000000000000000000000000000000000000000000000
χ984-4-4-444-4400004-444-400000000-4-4-444-440000000000-444-400000000000000000000000000000000000000000000000000000000
χ994-4-4-444-440000-24-4-4400000000222-2-22-20000000000-222-2−2i32i32i3−2i3000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ1004-4-4-444-440000-24-4-4400000000222-2-22-20000000000-222-22i3−2i3−2i32i300000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ1014-4-4-444-440000-2-444-400000000222-2-22-200000000002-2-22−2i32i32i3−2i300000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ1024-4-4-444-440000-2-444-400000000222-2-22-200000000002-2-222i3−2i3−2i32i3000000002i3−2i3−2i32i30000000000000000000000000000000000000000

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