Finite Group Databasebeta

← Group #494665

Character table — Group #494665

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size112222222224444444444444444444444444441616161616161616112222222224444444444444444444444444441616161616161616
order1222244448822448888888161616161616161616161616161616162444888822222444488224488888881616161616161616161616161616161624448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ911-1-1111-1-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i11-1-1111-1-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ1011-1-1111-1-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii11-1-1111-1-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ1111-1-1111-1-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii11-1-1111-1-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ1211-1-1111-1-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i11-1-1111-1-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ1311-1-1111-1-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii11-1-1111-1-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii
χ1411-1-1111-1-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i11-1-1111-1-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i
χ1511-1-1111-1-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i11-1-1111-1-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i
χ1611-1-1111-1-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii11-1-1111-1-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii
χ17222222222-2-22222-2-2-2-2-2-2-2000000000000000000000000222222222-2-22222-2-2-2-2-2-2-2000000000000000000000000
χ18222222222-2-2-2-2-2-2-2-2-22222000000000000000000000000222222222-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ1922222-2-2-2-2002-2-220000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000022222-2-2-2-2002-2-220000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ2022222-2-2-2-2002-2-220000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000022222-2-2-2-2002-2-220000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ2122222-2-2-2-200-222-20000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000022222-2-2-2-200-222-20000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ2222222-2-2-2-200-222-20000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000022222-2-2-2-200-222-20000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ23222-2-22-22-20000000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−200000000222-2-22-22-20000000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ24222-2-22-22-20000000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000222-2-22-22-20000000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ25222-2-22-22-2000000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000222-2-22-22-2000000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ26222-2-22-22-2000000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000222-2-22-22-2000000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ27222-2-2-22-222200002-2-200002-2-222-2-220000000000000000222-2-2-22-222200002-2-200002-2-222-2-220000000000000000
χ28222-2-2-22-222200002-2-20000-222-2-222-20000000000000000222-2-2-22-222200002-2-20000-222-2-222-20000000000000000
χ29222-2-2-22-22-2-20000-2220000000000002i−2i−2i2i2i−2i−2i2i00000000222-2-2-22-22-2-20000-2220000000000002i−2i−2i2i2i−2i−2i2i00000000
χ30222-2-2-22-22-2-20000-222000000000000−2i2i2i−2i−2i2i2i−2i00000000222-2-2-22-22-2-20000-222000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ3122-22-22-2-220000000002i−2i−2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000022-22-22-2-220000000002i−2i−2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ3222-22-22-2-220000000002i−2i−2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000022-22-22-2-220000000002i−2i−2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ3322-22-22-2-22000000000−2i2i2i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000022-22-22-2-22000000000−2i2i2i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ3422-22-22-2-22000000000−2i2i2i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000022-22-22-2-22000000000−2i2i2i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ3522-22-2-222-2220000-22-20000000000002-2-22-222-20000000022-22-2-222-2220000-22-20000000000002-2-22-222-200000000
χ3622-22-2-222-2220000-22-2000000000000-222-22-2-220000000022-22-2-222-2220000-22-2000000000000-222-22-2-2200000000
χ3722-22-2-222-2-2-200002-2200002i−2i−2i2i−2i2i2i−2i000000000000000022-22-2-222-2-2-200002-2200002i−2i−2i2i−2i2i2i−2i0000000000000000
χ3822-22-2-222-2-2-200002-220000−2i2i2i−2i2i−2i−2i2i000000000000000022-22-2-222-2-2-200002-220000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ3922-2-2222-2-2222-22-2-2-22-2-22200000000000000000000000022-2-2222-2-2222-22-2-2-22-2-222000000000000000000000000
χ4022-2-2222-2-222-22-22-2-2222-2-200000000000000000000000022-2-2222-2-222-22-22-2-2222-2-2000000000000000000000000
χ4122-2-22-2-2220022-2-2000000022−2−2−2−22222−2−2−2−2220000000022-2-22-2-2220022-2-2000000022−2−2−2−22222−2−2−2−22200000000
χ4222-2-22-2-2220022-2-20000000−2−22222−2−2−2−22222−2−20000000022-2-22-2-2220022-2-20000000−2−22222−2−2−2−22222−2−200000000
χ4322-2-22-2-22200-2-222000000022−2−2−2−222−2−22222−2−20000000022-2-22-2-22200-2-222000000022−2−2−2−222−2−22222−2−200000000
χ4422-2-22-2-22200-2-2220000000−2−22222−2−222−2−2−2−2220000000022-2-22-2-22200-2-2220000000−2−22222−2−222−2−2−2−22200000000
χ458-800000004i2−4i2000000000000000000000000000000000008-800000004i2−4i200000000000000000000000000000000000
χ468-80000000−4i24i2000000000000000000000000000000000008-80000000−4i24i200000000000000000000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ491111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111
χ501111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ5111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ5211111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ5311111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ5411111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ5511-1-1111-1-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i-1-111-1-1-11111-11-11-1-11-1-111−i−i−i−iiiii−i−i−i−iiiii-11-11−ii−ii
χ5611-1-1111-1-1-1-11-11-111-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-1-111-1-1-11111-11-11-1-11-1-111−i−i−i−iiiii−i−i−i−iiiii1-11-1i−ii−i
χ5711-1-1111-1-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii-1-111-1-1-11111-11-11-1-11-1-111iiii−i−i−i−iiiii−i−i−i−i-11-11i−ii−i
χ5811-1-1111-1-1-1-11-11-111-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-1-111-1-1-11111-11-11-1-11-1-111iiii−i−i−i−iiiii−i−i−i−i1-11-1−ii−ii
χ5911-1-1111-1-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii-1-111-1-1-111111-11-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1−iii−i
χ6011-1-1111-1-1-1-1-11-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i-1-111-1-1-111111-11-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−ii
χ6111-1-1111-1-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i-1-111-1-1-111111-11-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1i−i−ii
χ6211-1-1111-1-1-1-1-11-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii-1-111-1-1-111111-11-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−i
χ63222222222-2-22222-2-2-2-2-2-2-2000000000000000000000000-2-2-2-2-2-2-2-2-222-2-2-2-22222222000000000000000000000000
χ64222222222-2-2-2-2-2-2-2-2-22222000000000000000000000000-2-2-2-2-2-2-2-2-2222222222-2-2-2-2000000000000000000000000
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χ73222-2-2-22-222200002-2-200002-2-222-2-220000000000000000-2-2-2222-22-2-2-20000-2220000-222-2-222-20000000000000000
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χ76222-2-2-22-22-2-20000-222000000000000−2i2i2i−2i−2i2i2i−2i00000000-2-2-2222-22-22200002-2-20000000000002i−2i−2i2i2i−2i−2i2i00000000
χ7722-22-22-2-220000000002i−2i−2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000-2-22-22-222-2000000000−2i2i2i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ7822-22-22-2-220000000002i−2i−2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000-2-22-22-222-2000000000−2i2i2i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ7922-22-22-2-22000000000−2i2i2i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000-2-22-22-222-20000000002i−2i−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ8022-22-22-2-22000000000−2i2i2i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000-2-22-22-222-20000000002i−2i−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ8122-22-2-222-2220000-22-20000000000002-2-22-222-200000000-2-22-222-2-22-2-200002-22000000000000-222-22-2-2200000000
χ8222-22-2-222-2220000-22-2000000000000-222-22-2-2200000000-2-22-222-2-22-2-200002-220000000000002-2-22-222-200000000
χ8322-22-2-222-2-2-200002-2200002i−2i−2i2i−2i2i2i−2i0000000000000000-2-22-222-2-22220000-22-20000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ8422-22-2-222-2-2-200002-220000−2i2i2i−2i2i−2i−2i2i0000000000000000-2-22-222-2-22220000-22-200002i−2i−2i2i−2i2i2i−2i0000000000000000
χ8522-2-2222-2-2222-22-2-2-22-2-222000000000000000000000000-2-222-2-2-222-2-2-22-2222-222-2-2000000000000000000000000
χ8622-2-2222-2-222-22-22-2-2222-2-2000000000000000000000000-2-222-2-2-222-2-22-22-222-2-2-222000000000000000000000000
χ8722-2-22-2-2220022-2-2000000022−2−2−2−22222−2−2−2−22200000000-2-222-222-2-200-2-2220000000−2−22222−2−2−2−22222−2−200000000
χ8822-2-22-2-2220022-2-20000000−2−22222−2−2−2−22222−2−200000000-2-222-222-2-200-2-222000000022−2−2−2−22222−2−2−2−22200000000
χ8922-2-22-2-22200-2-222000000022−2−2−2−222−2−22222−2−200000000-2-222-222-2-20022-2-20000000−2−22222−2−222−2−2−2−22200000000
χ9022-2-22-2-22200-2-2220000000−2−22222−2−222−2−2−2−22200000000-2-222-222-2-20022-2-2000000022−2−2−2−222−2−22222−2−200000000
χ918-800000004i2−4i200000000000000000000000000000000000-880000000−4i24i200000000000000000000000000000000000
χ928-80000000−4i24i200000000000000000000000000000000000-8800000004i2−4i200000000000000000000000000000000000

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