Finite Group Databasebeta

← Group #72270889

Character table — Group #72270889

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444448888888888888888888888881616161616161616161616161616161616161616161616161616161616162424242424242424484848484848484848484848
order122222344446666666222222444444121212122244666666666612121212121212121212224444444466661212121212121212121212121212121288888888444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-11-11-11-11-11-111-1-111-1-111-1-111-1-111-1-1iiii−i−i−i−iii−i−iii−i−iii−i−i
χ101111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-11-11-11-11-11-111-1-111-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−iii−i−iii−i−iii
χ111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-1-11-11-111-1-11-1-111-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−iiiii−i−i−i−iii
χ121111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-1-11-11-111-1-11-1-111-1-11111-1-1-1-111-1-111−i−i−i−iiiiiii−i−i−i−iiiii−i−i
χ131111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-11-11-111-111-1-1-1-111-1-11111-1-1-1-111iiii−i−i−i−iii−i−i−i−iii−i−iii
χ141111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-11-11-111-111-1-1-1-111-1-11111-1-1-1-111−i−i−i−iiiii−i−iiiii−i−iii−i−i
χ151111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-111-11-1-11-11-1-11111-1-1-1-111-1-11111-1-1iiii−i−i−i−i−i−iii−i−iiiii−i−i
χ161111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-111-11-1-11-11-1-11111-1-1-1-111-1-11111-1-1−i−i−i−iiiiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-22-22-22222000022-2-2-2-20000-2-222-2-200000022-2-200000000-2-2-2-200000000222200000000000000000000
χ1822222222222222222222-2-2-2-2-2-22-22-22222000022-2-2-2-20000-2-222-2-2000000-2-22200000000222200000000-2-2-2-200000000000000000000
χ19222222222222222222-2-222-2-2-2-2-22-2222222222-2-222-2-22222-2-2-2-2222222000000-2-20000000000-2-2-2-20000000000000000000000000000
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χ874-4-44-44-244-4-4222-2-22-2-444-4-44-44-4-444-2-22200002-2-222-200002-22-2-22000000000000000000000000000000000000000000000000000000
χ884-4-44-44-244-4-4222-2-22-2-44-444-44-4-444-4-2-22200002-22-2-220000-222-22-2000000000000000000000000000000000000000000000000000000
χ894-4-44-44-2-4-444222-2-22-24-44-4-444-4-444-422-2-20000-22-222-20000-222-22-2000000000000000000000000000000000000000000000000000000
χ904-4-44-44-2-4-444222-2-22-24-4-444-4-44-4-44422-2-20000-222-2-2200002-22-2-22000000000000000000000000000000000000000000000000000000
χ914-4-44-44-2-4-444222-2-22-2-444-44-4-4444-4-422-2-200002-2-22-2200002-2-222-2000000000000000000000000000000000000000000000000000000
χ924-4-44-44-2-4-444222-2-22-2-44-44-444-44-4-4422-2-200002-22-22-20000-22-22-22000000000000000000000000000000000000000000000000000000
χ938888-8-8-48-88-8-44444-4-4000000000000-44-4400000000000000000000000000000000000000000000000000000000000000000000000000
χ948888-8-8-4-88-88-44444-4-40000000000004-44-400000000000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8008000080000-8-80000000000000000004i−4i00000000000000004i−4i4i−4i00000000000000000000000000000000000000000000000000
χ9688-8-8008000080000-8-8000000000000000000−4i4i0000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ9788-8-800-40000-4−4i34i3−4i34i3440000000000000000004i−4i00000000000000004ζ7−4ζ74ζ11−4ζ1100000000000000000000000000000000000000000000000000
χ9888-8-800-40000-4−4i34i3−4i34i344000000000000000000−4i4i0000000000000000−4ζ74ζ7−4ζ114ζ1100000000000000000000000000000000000000000000000000
χ9988-8-800-40000-44i3−4i34i3−4i3440000000000000000004i−4i00000000000000004ζ11−4ζ114ζ7−4ζ700000000000000000000000000000000000000000000000000
χ10088-8-800-40000-44i3−4i34i3−4i344000000000000000000−4i4i0000000000000000−4ζ114ζ11−4ζ74ζ700000000000000000000000000000000000000000000000000
χ1018-88-80080000-800008-800000000000000004-4000000004-44-4000000000000000000000000000000000000000000000000000000000000
χ1028-88-80080000-800008-80000000000000000-4400000000-44-44000000000000000000000000000000000000000000000000000000000000
χ1038-88-800-400004−4i34i34i3−4i3-4400000000000000004-400000000−2−2i32+2i3−2+2i32−2i3000000000000000000000000000000000000000000000000000000000000
χ1048-88-800-400004−4i34i34i3−4i3-440000000000000000-44000000002+2i3−2−2i32−2i3−2+2i3000000000000000000000000000000000000000000000000000000000000
χ1058-88-800-4000044i3−4i3−4i34i3-4400000000000000004-400000000−2+2i32−2i3−2−2i32+2i3000000000000000000000000000000000000000000000000000000000000
χ1068-88-800-4000044i3−4i3−4i34i3-440000000000000000-44000000002−2i3−2+2i32+2i3−2−2i3000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-8-48-8-884-4-4444-4000000000000-444-400000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-8-4-888-84-4-4444-40000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.