Finite Group Databasebeta

← Group #99018

Character table — Group #99018

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888244488888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-22222-2-2-2-222-2-200000000000000002-22-200000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-222-2-20000000000000000-22-2200000000000000000000
χ192222222222-2-2222222-2-222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000
χ202222222222-2-2222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000
χ212222222222-2-2-2-2-2-222-2-2-2-222-2-222000000000000000000002i−2i2i−2i0000000000000000
χ222222222222-2-2-2-2-2-222-2-2-2-222-2-22200000000000000000000−2i2i−2i2i0000000000000000
χ2322222222-2-2222222-2-222-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2422222222-2-2222222-2-222-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2522222222-2-222-2-2-2-2-2-22222-2-2-2-222000000000000000000002i−2i−2i2i0000000000000000
χ2622222222-2-222-2-2-2-2-2-22222-2-2-2-22200000000000000000000−2i2i2i−2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-200000000000000002-2-2200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000-222-200000000000000000000
χ29222-2-22-2-2002i−2i2-22-2002i−2i002i−2i000000002i2i−2i−2i22-2-20000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ30222-2-22-2-2002i−2i2-22-2002i−2i002i−2i000000002i2i−2i−2i22-2-2000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ31222-2-22-2-2002i−2i2-22-2002i−2i002i−2i00000000−2i−2i2i2i-2-2220000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ32222-2-22-2-2002i−2i2-22-2002i−2i002i−2i00000000−2i−2i2i2i-2-222000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ33222-2-22-2-200−2i2i2-22-200−2i2i00−2i2i000000002i2i−2i−2i-2-2220000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ34222-2-22-2-200−2i2i2-22-200−2i2i00−2i2i000000002i2i−2i−2i-2-222000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ35222-2-22-2-200−2i2i2-22-200−2i2i00−2i2i00000000−2i−2i2i2i22-2-20000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ36222-2-22-2-200−2i2i2-22-200−2i2i00−2i2i00000000−2i−2i2i2i22-2-2000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ372-2-2222-2-22i−2i002-2-222i−2i002i−2i00000022-2-200002i−2i2i−2i000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ382-2-2222-2-22i−2i002-2-222i−2i002i−2i00000022-2-200002i−2i2i−2i00000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ392-2-2222-2-22i−2i002-2-222i−2i002i−2i000000-2-2220000−2i2i−2i2i000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ402-2-2222-2-22i−2i002-2-222i−2i002i−2i000000-2-2220000−2i2i−2i2i00000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ412-2-2222-2-2−2i2i002-2-22−2i2i00−2i2i00000022-2-20000−2i2i−2i2i000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ422-2-2222-2-2−2i2i002-2-22−2i2i00−2i2i00000022-2-20000−2i2i−2i2i00000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ432-2-2222-2-2−2i2i002-2-22−2i2i00−2i2i000000-2-22200002i−2i2i−2i000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ442-2-2222-2-2−2i2i002-2-22−2i2i00−2i2i000000-2-22200002i−2i2i−2i00000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ45444-4-44-4-4004i−4i-44-44004i−4i00−4i4i00000000000000000000000000000000000000000000
χ46444-4-44-4-400−4i4i-44-4400−4i4i004i−4i00000000000000000000000000000000000000000000
χ4744-44-4-44-40000000000000000004i−4i22−2222−222i2−2i22i2−2i200000000000000000000000000000000
χ4844-44-4-44-40000000000000000004i−4i−2222−2222−2i22i2−2i22i200000000000000000000000000000000
χ4944-44-4-44-4000000000000000000−4i4i22−2222−22−2i22i2−2i22i200000000000000000000000000000000
χ5044-44-4-44-4000000000000000000−4i4i−2222−22222i2−2i22i2−2i200000000000000000000000000000000
χ5144-4-44-4-4444000000-4-40000000000000022−22−222200002222−22−22000000000000000000000000
χ5244-4-44-4-4444000000-4-400000000000000−222222−220000−22−222222000000000000000000000000
χ5344-4-44-4-44-4-4000000440000000000000022−22−22220000−22−222222000000000000000000000000
χ5444-4-44-4-44-4-40000004400000000000000−222222−2200002222−22−22000000000000000000000000
χ554-444-4-4-440044000000-4-40000000022−22−22220000000022−2222−22000000000000000000000000
χ564-444-4-4-440044000000-4-400000000−222222−2200000000−2222−2222000000000000000000000000
χ574-444-4-4-4400-4-4000000440000000022−22−222200000000−2222−2222000000000000000000000000
χ584-444-4-4-4400-4-40000004400000000−222222−220000000022−2222−22000000000000000000000000
χ594-44-44-44-44i−4i4i−4i0000−4i4i−4i4i00004-4000000000000000000000000000000000000000000
χ604-44-44-44-44i−4i−4i4i0000−4i4i4i−4i0000-44000000000000000000000000000000000000000000
χ614-44-44-44-4−4i4i4i−4i00004i−4i−4i4i0000-44000000000000000000000000000000000000000000
χ624-44-44-44-4−4i4i−4i4i00004i−4i4i−4i00004-4000000000000000000000000000000000000000000
χ634-4-4444-4-44i−4i00-444-44i−4i00−4i4i0000000000000000000000000000000000000000000000
χ644-4-4444-4-4−4i4i00-444-4−4i4i004i−4i0000000000000000000000000000000000000000000000
χ654-4-4-4-4444000044-4-4000000000000000000004i−4i−4i4i0000000000000000000000000000
χ664-4-4-4-4444000044-4-400000000000000000000−4i4i4i−4i0000000000000000000000000000
χ674-4-4-4-44440000-4-4440000000000000000000000004-4-44000000000000000000000000
χ684-4-4-4-44440000-4-444000000000000000000000000-444-4000000000000000000000000

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