Finite Group Databasebeta

← Group #10690579

Character table — Group #10690579

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222222223444444446666666666666662222444466666666121212121212121212121212121212122244444466661212121212121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ18222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ21222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ22222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
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χ2622222222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2722222222-2-2-2-22-2-22222-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-22222-2-2222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2922222222-2-2-2-2-122-2-2-2-222-1-1-111111111-1-1-1-122-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-2-2-2-2-122-2-2-2-222-1-1-111111111-1-1-1-122-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
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χ43222-22-2-2-2-2-2222−2i2i2i2i−2i−2i−2i2i22-2-2-2-2-222222-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
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χ7522-2-2-2-222-222-22-2-22-2-22222-2-2-2-22222-2-2-2-2220000000000000000-222-22-2-22000000000000000000000000000000000000000000002-2-22
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χ78444-44-4-4-444-4-4-2−4i4i−4i−4i4i4i−4i4i-2-22-2-2-2-22222-222200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ79444-44-4-4-4-4-444-24i−4i−4i−4i4i4i4i−4i-2-222222-2-2-2-2-22220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ80444-44-4-4-4-4-444-2−4i4i4i4i−4i−4i−4i4i-2-222222-2-2-2-2-222200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ8144-4-4-4-4444-4-44-2444-4-44-4-4-222-2-22222-2-222-2-20000000000000000-222-2-222-2000000000000000000000000000000000000000000000000
χ8244-4-4-4-4444-4-44-2-4-4-444-444-222-2-22222-2-222-2-200000000000000002-2-222-2-22000000000000000000000000000000000000000000000000
χ8344-4-4-4-444-444-4-244-444-4-4-4-22222-2-2-2-22222-2-20000000000000000-222-22-2-22000000000000000000000000000000000000000000000000
χ8444-4-4-4-444-444-4-2-4-44-4-4444-22222-2-2-2-22222-2-200000000000000002-2-22-222-2000000000000000000000000000000000000000000000000
χ854-444-4-44-40000400000000-44400000000-4-44-40000004i−4i000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ864-444-4-44-40000400000000-44400000000-4-44-4000000−4i4i00000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ874-444-4-44-40000-2000000002-2-2−2i32i3−2i32i3−2i32i3−2i32i322-220000004i−4i000000000000000023−2323−23−2i2i−2i2i0000000000000000000000000000000000000000
χ884-444-4-44-40000-2000000002-2-2−2i32i3−2i32i3−2i32i3−2i32i322-22000000−4i4i0000000000000000−2323−23232i−2i2i−2i0000000000000000000000000000000000000000
χ894-444-4-44-40000-2000000002-2-22i3−2i32i3−2i32i3−2i32i3−2i322-220000004i−4i0000000000000000−2323−2323−2i2i−2i2i0000000000000000000000000000000000000000
χ904-444-4-44-40000-2000000002-2-22i3−2i32i3−2i32i3−2i32i3−2i322-22000000−4i4i000000000000000023−2323−232i−2i2i−2i0000000000000000000000000000000000000000
χ914-44-4-44-440000400000000-44-400000000-44-444-40000004-44-4000000000000000000000000000000000000000000000000000000000000
χ924-44-4-44-440000400000000-44-400000000-44-44-44000000-44-44000000000000000000000000000000000000000000000000000000000000
χ934-44-4-44-440000-2000000002-22−2i32i3−2i32i32i3−2i32i3−2i32-22-24-4000000-22-22−2i32i3−2i32i300000000000000000000000000000000000000000000000000000000
χ944-44-4-44-440000-2000000002-22−2i32i3−2i32i32i3−2i32i3−2i32-22-2-440000002-22-22i3−2i32i3−2i300000000000000000000000000000000000000000000000000000000
χ954-44-4-44-440000-2000000002-222i3−2i32i3−2i3−2i32i3−2i32i32-22-24-4000000-22-222i3−2i32i3−2i300000000000000000000000000000000000000000000000000000000
χ964-44-4-44-440000-2000000002-222i3−2i32i3−2i3−2i32i3−2i32i32-22-2-440000002-22-2−2i32i3−2i32i300000000000000000000000000000000000000000000000000000000
χ974-4-444-4-440000400000000-4-44000000004-4-4400004-40000000000000000004-4-4400000000000000000000000000000000000000000000
χ984-4-444-4-440000400000000-4-44000000004-4-440000-44000000000000000000-444-400000000000000000000000000000000000000000000
χ994-4-444-4-440000-20000000022-2−2i32i32i3−2i3−2i32i32i3−2i3-222-200004-4000000000000000000-222-2−2i32i32i3−2i30000000000000000000000000000000000000000
χ1004-4-444-4-440000-20000000022-2−2i32i32i3−2i3−2i32i32i3−2i3-222-20000-440000000000000000002-2-222i3−2i3−2i32i30000000000000000000000000000000000000000
χ1014-4-444-4-440000-20000000022-22i3−2i3−2i32i32i3−2i3−2i32i3-222-200004-4000000000000000000-222-22i3−2i3−2i32i30000000000000000000000000000000000000000
χ1024-4-444-4-440000-20000000022-22i3−2i3−2i32i32i3−2i3−2i32i3-222-20000-440000000000000000002-2-22−2i32i32i3−2i30000000000000000000000000000000000000000
χ1034-4-4-4444-40000400000000-4-4-400000000444-4004-4000000004-4-4400000000000000000000000000000000000000000000000000000000
χ1044-4-4-4444-40000400000000-4-4-400000000444-400-4400000000-444-400000000000000000000000000000000000000000000000000000000
χ1054-4-4-4444-40000-200000000222−2i32i32i3−2i32i3−2i3−2i32i3-2-2-22004-40000−2i32i32i3−2i3-222-200000000000000000000000000000000000000000000000000000000
χ1064-4-4-4444-40000-200000000222−2i32i32i3−2i32i3−2i3−2i32i3-2-2-2200-4400002i3−2i3−2i32i32-2-2200000000000000000000000000000000000000000000000000000000
χ1074-4-4-4444-40000-2000000002222i3−2i3−2i32i3−2i32i32i3−2i3-2-2-22004-400002i3−2i3−2i32i3-222-200000000000000000000000000000000000000000000000000000000
χ1084-4-4-4444-40000-2000000002222i3−2i3−2i32i3−2i32i32i3−2i3-2-2-2200-440000−2i32i32i3−2i32-2-2200000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.