Finite Group Databasebeta

← Group #72225901

Character table — Group #72225901

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444444444444444448888888888888888888888888888882424242424242424242424242424242432323232323232323232323296969696
order12222234444444466644668888888812121212121212122424242424242424121216161616161616162424242448484848484848484848484848484848888888881616161616161616222466666612124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ8111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-111111-111-1111-1-1-1-111-1-111-1-11111-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1i−ii−i
χ101111-1-111111-111-1111-1-1-1-111-1-111-1-11111-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−ii−ii
χ111111-1-111111-111-1111-1-1-1-111-1-111-1-11111-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−ii−ii
χ121111-1-111111-111-1111-1-1-1-111-1-111-1-11111-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111i−ii−i
χ131111-1-111111-111-1111-1-1-1-111-1-111-1-11111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ141111-1-111111-111-1111-1-1-1-111-1-111-1-11111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ151111-1-111111-111-1111-1-1-1-111-1-111-1-11111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ161111-1-111111-111-1111-1-1-1-111-1-111-1-11111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
χ172222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22200000000-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ182222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22200000000-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ192222222-2-2-2-22222222-2-22222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-20000000022-2-200000000000000000000000022-2-222-2-20000000000000000
χ202222222-2-2-2-22222222-2-22222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-20000000022-2-2000000000000000000000000-2-222-2-2220000000000000000
χ212222222-2-2-2-22222222-2-222-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-222-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ222222222-2-2-2-22222222-2-222-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ23222222-122222222-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ24222222-122222222-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ25222222-122222222-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ26222222-122222222-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ27222222-1-2-2-2-22222-1-1-1-2-2-1-1-2-22222-2-21111-1-1-1-11111-1-1-1-11122-2-222-2-211-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ28222222-1-2-2-2-22222-1-1-1-2-2-1-1-2-22222-2-21111-1-1-1-11111-1-1-1-11122-2-222-2-211-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ29222222-1-2-2-2-22222-1-1-1-2-2-1-1-2-22222-2-21111-1-1-1-11111-1-1-1-111-2-222-2-22211-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ30222222-1-2-2-2-22222-1-1-1-2-2-1-1-2-22222-2-21111-1-1-1-11111-1-1-1-111-2-222-2-22211-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ312222-2-222222-222-2222-2-2-2-2-2-222-2-2222222-2-222-2-2-2-2-2-2-2-2-2-200000000222200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ322222-2-222222-222-2222-2-2-2-2-2-222-2-2222222-2-222-2-2-2-2-2-2-2-2-2-20000000022220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ332222-2-22-2-2-2-2-222-222222-2-22222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22200000000-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
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χ352222-2-22-2-2-2-2-222-222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-2-2-222222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ362222-2-22-2-2-2-2-222-222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-2-2-2222222-2-22222-2-222-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ372222-2-2-12222-222-2-1-1-1-2-21122-2-222-2-2-1-1-1-111-1-1-1-1-1-1-1-1-1-1112222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000000000002-22-2-1-111-1-1110000
χ382222-2-2-12222-222-2-1-1-1-2-21122-2-222-2-2-1-1-1-111-1-1-1-1-1-1-1-1-1-1112222-2-2-2-21111-1-1-1-1-1-1-1-1111111110000000000000000-22-2211-1-111-1-10000
χ392222-2-2-12222-222-2-1-1-1-2-21122-2-222-2-2-1-1-1-111-1-1-1-1-1-1-1-1-1-111-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ402222-2-2-12222-222-2-1-1-1-2-21122-2-222-2-2-1-1-1-111-1-1-1-1-1-1-1-1-1-111-2-2-2-22222111111111111-1-1-1-1-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ412222-2-2-1-2-2-2-2-222-2-1-1-12211-2-2-2-22222111111-1-11111-1-1-1-1-1-122-2-2-2-222-1-111-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ422222-2-2-1-2-2-2-2-222-2-1-1-12211-2-2-2-22222111111-1-11111-1-1-1-1-1-122-2-2-2-222-1-111-1-1-1-111111111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ432222-2-2-1-2-2-2-2-222-2-1-1-12211-2-2-2-22222111111-1-11111-1-1-1-1-1-1-2-22222-2-2-1-1111111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ442222-2-2-1-2-2-2-2-222-2-1-1-12211-2-2-2-22222111111-1-11111-1-1-1-1-1-1-2-22222-2-2-1-1111111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ452-2-222-22000022-2-2-2-22002-2002-22-20000002-22-2000022-2-200002-2002-2002-2000022-2-2000022-2-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
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χ472-2-222-22000022-2-2-2-22002-2002-22-20000002-22-2000022-2-20000-2200-22002-20000-2-2220000-2-222−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ482-2-222-22000022-2-2-2-22002-2002-22-20000002-22-2000022-2-20000-2200-22002-20000-2-2220000-2-222i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ492-2-222-22000022-2-2-2-22002-200-22-220000002-22-20000-2-222002-2002-20000-2222-2-2000022-2-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ502-2-222-22000022-2-2-2-22002-200-22-220000002-22-20000-2-222002-2002-20000-2222-2-2000022-2-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ512-2-222-22000022-2-2-2-22002-200-22-220000002-22-20000-2-22200-2200-220000-22-2-2220000-2-2220000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ522-2-222-22000022-2-2-2-22002-200-22-220000002-22-20000-2-22200-2200-220000-22-2-2220000-2-2220000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ532-2-22-2220000-22-22-2-2200-22002-2-22000000-222-20000-2-222002-200-2200002-222-2-20000-2-22200002−2−22−222−22−2−22−222−20000000000000000
χ542-2-22-2220000-22-22-2-2200-22002-2-22000000-222-20000-2-222002-200-2200002-222-2-20000-2-2220000−222−22−2−22−222−22−2−220000000000000000
χ552-2-22-2220000-22-22-2-2200-22002-2-22000000-222-20000-2-22200-22002-200002-2-2-222000022-2-200002−2−22−222−2−222−22−2−220000000000000000
χ562-2-22-2220000-22-22-2-2200-22002-2-22000000-222-20000-2-22200-22002-200002-2-2-222000022-2-20000−222−22−2−222−2−22−222−20000000000000000
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χ924-4-44-44-200004-44-422-2002-2-4400004-40000-222-222-2-200000000000000-2200−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ934-4-44-44-20000-44-4422-2002-2004-4-440000002-2-22000022-2-2004-400-440000-22-2-222000022-2-2000000000000000000000000000000000000
χ944-4-44-44-20000-44-4422-2002-2004-4-440000002-2-22000022-2-200-44004-40000-2222-2-20000-2-222000000000000000000000000000000000000
χ954-4-44-44-20000-44-4422-2002-200-444-40000002-2-220000-2-22200004-400-44002-20000-2-222000022-2-200000000000000000000000000000000
χ964-4-44-44-20000-44-4422-2002-200-444-40000002-2-220000-2-2220000-44004-4002-2000022-2-20000-2-22200000000000000000000000000000000
χ9788-8-8008008-800008-8-8000000000000008-800000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-800800-8800008-8-800000000000000-8800000000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-800-4008-80000-44400000000000000-4400002i6−2i62i6−2i62i6−2i62i6−2i600000000000000000000000000000000000000000000000000000000000000
χ10088-8-800-4008-80000-44400000000000000-440000−2i62i6−2i62i6−2i62i6−2i62i600000000000000000000000000000000000000000000000000000000000000
χ10188-8-800-400-880000-444000000000000004-400002i6−2i62i6−2i6−2i62i6−2i62i600000000000000000000000000000000000000000000000000000000000000
χ10288-8-800-400-880000-444000000000000004-40000−2i62i6−2i62i62i6−2i62i6−2i600000000000000000000000000000000000000000000000000000000000000
χ1038-88-80088-8000000-88-80000000000008-80000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8008-88000000-88-8000000000000-880000000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-800-48-80000004-44000000000000-440000002i6−2i6−2i62i62i6−2i6−2i62i600000000000000000000000000000000000000000000000000000000000000
χ1068-88-800-48-80000004-44000000000000-44000000−2i62i62i6−2i6−2i62i62i6−2i600000000000000000000000000000000000000000000000000000000000000
χ1078-88-800-4-880000004-440000000000004-40000002i6−2i6−2i62i6−2i62i62i6−2i600000000000000000000000000000000000000000000000000000000000000
χ1088-88-800-4-880000004-440000000000004-4000000−2i62i62i6−2i62i6−2i6−2i62i600000000000000000000000000000000000000000000000000000000000000

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