Finite Group Databasebeta

← Group #98974

Character table — Group #98974

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444224444448888888888888888244488888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111
χ9111111111-1-1-1-111-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-1111ii−i−iii−i−iii−i−iii−i−i-1-1
χ10111111111-1-1-1-111-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-1111−i−iii−i−iii−i−iii−i−iii-1-1
χ11111111111-1-1-1-111-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1ii−i−iii−i−i−i−iii−i−iii11
χ12111111111-1-1-1-111-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1−i−iii−i−iiiii−i−iii−i−i11
χ13111111111-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-11-1-1ii−i−i−i−iiiii−i−i−i−iii11
χ14111111111-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-11-1-1−i−iiiii−i−i−i−iiiii−i−i11
χ15111111111-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-111ii−i−i−i−iii−i−iiiii−i−i-1-1
χ16111111111-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-111−i−iiiii−i−iii−i−i−i−iii-1-1
χ17222222222222222-2-2-2-22-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ19222222222-2-2-2-2222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ20222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ2122222222-22222-2-22222-2-2-222-2-2-2-2000000000000000022-2-200000000000000000000
χ2222222222-22222-2-22222-2-2-222-2-2-2-20000000000000000-2-22200000000000000000000
χ2322222222-22222-2-2-2-2-2-2-222-2-222-2-2000000000000000000002i−2i00000000000000002i−2i
χ2422222222-22222-2-2-2-2-2-2-222-2-222-2-200000000000000000000−2i2i0000000000000000−2i2i
χ2522222222-2-2-2-2-2-2-22222-2-2-2-2-22222000000000000000000002i−2i0000000000000000−2i2i
χ2622222222-2-2-2-2-2-2-22222-2-2-2-2-2222200000000000000000000−2i2i00000000000000002i−2i
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000002-22-200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000-22-2200000000000000000000
χ29222-2-2-2-2222i2i−2i−2i-2-2000020000002i−2i2i2i−2i−2i0000000022-2-2000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00
χ30222-2-2-2-2222i2i−2i−2i-2-2000020000002i−2i2i2i−2i−2i0000000022-2-200000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00
χ31222-2-2-2-2222i2i−2i−2i-2-2000020000002i−2i−2i−2i2i2i00000000-2-222000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00
χ32222-2-2-2-2222i2i−2i−2i-2-2000020000002i−2i−2i−2i2i2i00000000-2-22200000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00
χ33222-2-2-2-222−2i−2i2i2i-2-200002000000−2i2i2i2i−2i−2i00000000-2-222000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00
χ34222-2-2-2-222−2i−2i2i2i-2-200002000000−2i2i2i2i−2i−2i00000000-2-22200000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00
χ35222-2-2-2-222−2i−2i2i2i-2-200002000000−2i2i−2i−2i2i2i0000000022-2-2000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00
χ36222-2-2-2-222−2i−2i2i2i-2-200002000000−2i2i−2i−2i2i2i0000000022-2-200000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00
χ372-2-222-2-22200002-222-2-2-22-2000000000000002i2i−2i−2i2i−2i2i−2i000000i2−i2i2−i22−22−20000000000
χ382-2-222-2-22200002-222-2-2-22-2000000000000002i2i−2i−2i2i−2i2i−2i000000−i2i2−i2i2−22−220000000000
χ392-2-222-2-22200002-222-2-2-22-200000000000000−2i−2i2i2i−2i2i−2i2i000000i2−i2i2−i2−22−220000000000
χ402-2-222-2-22200002-222-2-2-22-200000000000000−2i−2i2i2i−2i2i−2i2i000000−i2i2−i2i22−22−20000000000
χ412-2-222-2-22200002-2-2-222-2-22000000000000002i2i−2i−2i−2i2i−2i2i0000002−2−22−i2i2i2−i20000000000
χ422-2-222-2-22200002-2-2-222-2-22000000000000002i2i−2i−2i−2i2i−2i2i000000−222−2i2−i2−i2i20000000000
χ432-2-222-2-22200002-2-2-222-2-2200000000000000−2i−2i2i2i2i−2i2i−2i0000002−2−22i2−i2−i2i20000000000
χ442-2-222-2-22200002-2-2-222-2-2200000000000000−2i−2i2i2i2i−2i2i−2i000000−222−2−i2i2i2−i20000000000
χ45444-4-4-4-44-44i4i−4i−4i440000-4000000−4i4i0000000000000000000000000000000000000000
χ46444-4-4-4-44-4−4i−4i4i4i440000-40000004i−4i0000000000000000000000000000000000000000
χ4744-44-44-4-400000004i−4i4i−4i00000000022−2222−222i22i2−2i2−2i200000000000000000000000000000000
χ4844-44-44-4-400000004i−4i4i−4i000000000−2222−2222−2i2−2i22i22i200000000000000000000000000000000
χ4944-44-44-4-40000000−4i4i−4i4i00000000022−2222−22−2i2−2i22i22i200000000000000000000000000000000
χ5044-44-44-4-40000000−4i4i−4i4i000000000−2222−22222i22i2−2i2−2i200000000000000000000000000000000
χ5144-4-44-44-400000000000000004i−4i002i2−2i2−2i22i2000022−2222−220000000000000000000000000000
χ5244-4-44-44-400000000000000004i−4i00−2i22i22i2−2i20000−2222−22220000000000000000000000000000
χ5344-4-44-44-40000000000000000−4i4i002i2−2i2−2i22i20000−2222−22220000000000000000000000000000
χ5444-4-44-44-40000000000000000−4i4i00−2i22i22i2−2i2000022−2222−220000000000000000000000000000
χ554-444-4-44-404i−4i4i−4i004i−4i−4i4i0004-400000000000000000000000000000000000000000000
χ564-444-4-44-404i−4i4i−4i00−4i4i4i−4i000-4400000000000000000000000000000000000000000000
χ574-444-4-44-40−4i4i−4i4i004i−4i−4i4i000-4400000000000000000000000000000000000000000000
χ584-444-4-44-40−4i4i−4i4i00−4i4i4i−4i0004-400000000000000000000000000000000000000000000
χ594-44-444-4-404-4-4400000000000000000002i2−2i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ604-44-444-4-404-4-440000000000000000000−2i22i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ614-44-444-4-40-444-400000000000000000002i2−2i22i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ624-44-444-4-40-444-40000000000000000000−2i22i2−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ634-4-444-4-44-40000-4444-4-44-440000000000000000000000000000000000000000000000
χ644-4-444-4-44-40000-44-4-44444-40000000000000000000000000000000000000000000000
χ654-4-4-4-444440000-440000-4000000000000000000004i−4i−4i4i000000000000000000000000
χ664-4-4-4-444440000-440000-400000000000000000000−4i4i4i−4i000000000000000000000000
χ674-4-4-4-4444-400004-4000040000000000004-4-4400000000000000000000000000000000
χ684-4-4-4-4444-400004-400004000000000000-444-400000000000000000000000000000000

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