Finite Group Databasebeta

← Group #98950

Character table — Group #98950

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222222244444444444444448888888888888888244444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ911111111-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11ii−i−iii−i−i11ii−i−iii−i−i-1-1
χ1011111111-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11−i−iii−i−iii11−i−iii−i−iii-1-1
χ1111111111-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1ii−i−iii−i−i-1-1−i−iii−i−iii11
χ1211111111-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1−i−iii−i−iii-1-1ii−i−iii−i−i11
χ1311111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11ii−i−i−i−iii-1-1ii−i−i−i−iii11
χ1411111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11−i−iiiii−i−i-1-1−i−iiiii−i−i11
χ1511111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1ii−i−i−i−iii11−i−iiiii−i−i-1-1
χ1611111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1−i−iiiii−i−i11ii−i−i−i−iii-1-1
χ172222222222222-2-2-2-2222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ182222222222222-2-2-2-2222-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ19222222222222-22222-2-2-222-2-2-2-2-2-2000000000000000022-2-200000000000000000000
χ20222222222222-22222-2-2-222-2-2-2-2-2-20000000000000000-2-22200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000002i−2i000000002i−2i
χ22222222222222-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000−2i2i00000000−2i2i
χ2322222222-2-2-2-222222222-2-2-2-222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2422222222-2-2-2-222222222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-222-2-22200000000000000000000000000002i−2i00000000−2i2i
χ2622222222-2-2-2-2-22222-2-2-2-2-222-2-2220000000000000000000000000000−2i2i000000002i−2i
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222200000000000000002-22-200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222220000000000000000-22-2200000000000000000000
χ29222-2-2-2-220000-22i2i−2i−2i22-200002i−2i0022-2-2000000002i2i−2i−2i00001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000
χ30222-2-2-2-220000-22i2i−2i−2i22-200002i−2i0022-2-2000000002i2i−2i−2i0000−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000
χ31222-2-2-2-220000-22i2i−2i−2i22-200002i−2i00-2-22200000000−2i−2i2i2i00001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000
χ32222-2-2-2-220000-22i2i−2i−2i22-200002i−2i00-2-22200000000−2i−2i2i2i0000−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000
χ33222-2-2-2-220000-2−2i−2i2i2i22-20000−2i2i0022-2-200000000−2i−2i2i2i00001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000
χ34222-2-2-2-220000-2−2i−2i2i2i22-20000−2i2i0022-2-200000000−2i−2i2i2i0000−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000
χ35222-2-2-2-220000-2−2i−2i2i2i22-20000−2i2i00-2-222000000002i2i−2i−2i00001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000
χ36222-2-2-2-220000-2−2i−2i2i2i22-20000−2i2i00-2-222000000002i2i−2i−2i0000−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000
χ372-2-222-2-2222-2-2-200002-220000002-20000000022-2-22-22-200000000000000i2−i2i2−i2i2−i2i2−i200
χ382-2-222-2-2222-2-2-200002-220000002-20000000022-2-22-22-200000000000000−i2i2−i2i2−i2i2−i2i200
χ392-2-222-2-2222-2-2-200002-220000002-200000000-2-222-22-2200000000000000i2−i2i2−i2−i2i2−i2i200
χ402-2-222-2-2222-2-2-200002-220000002-200000000-2-222-22-2200000000000000−i2i2−i2i2i2−i2i2−i200
χ412-2-222-2-22-2-222-200002-22000000-220000000022-2-2-22-22000000000000002−2−222−2−2200
χ422-2-222-2-22-2-222-200002-22000000-220000000022-2-2-22-2200000000000000−222−2−222−200
χ432-2-222-2-22-2-222-200002-22000000-2200000000-2-2222-22-2000000000000002−2−22−222−200
χ442-2-222-2-22-2-222-200002-22000000-2200000000-2-2222-22-200000000000000−222−22−2−2200
χ45444-4-4-4-44000044i4i−4i−4i-4-440000−4i4i000000000000000000000000000000000000000000
χ46444-4-4-4-4400004−4i−4i4i4i-4-4400004i−4i000000000000000000000000000000000000000000
χ4744-44-44-4-4000000000000004i−4i000022−2222−2200002i2−2i22i2−2i20000000000000000000000000000
χ4844-44-44-4-4000000000000004i−4i0000−2222−22220000−2i22i2−2i22i20000000000000000000000000000
χ4944-44-44-4-400000000000000−4i4i000022−2222−220000−2i22i2−2i22i20000000000000000000000000000
χ5044-44-44-4-400000000000000−4i4i0000−2222−222200002i2−2i22i2−2i20000000000000000000000000000
χ5144-4-44-44-44-44-4000000000000000022−22−22222222−22−2200000000000000000000000000000000
χ5244-4-44-44-44-44-40000000000000000−222222−22−22−22222200000000000000000000000000000000
χ5344-4-44-44-4-44-44000000000000000022−22−2222−22−22222200000000000000000000000000000000
χ5444-4-44-44-4-44-440000000000000000−222222−222222−22−2200000000000000000000000000000000
χ554-444-4-44-4000004i−4i4i−4i00000000000000022−2222−222i2−2i2−2i22i20000000000000000000000000000
χ564-444-4-44-4000004i−4i4i−4i000000000000000−2222−2222−2i22i22i2−2i20000000000000000000000000000
χ574-444-4-44-400000−4i4i−4i4i00000000000000022−2222−22−2i22i22i2−2i20000000000000000000000000000
χ584-444-4-44-400000−4i4i−4i4i000000000000000−2222−22222i2−2i2−2i22i20000000000000000000000000000
χ594-44-444-4-44-4-4404-4-440004-40000000000000000000000000000000000000000000000
χ604-44-444-4-44-4-440-444-4000-440000000000000000000000000000000000000000000000
χ614-44-444-4-4-444-404-4-44000-440000000000000000000000000000000000000000000000
χ624-44-444-4-4-444-40-444-40004-40000000000000000000000000000000000000000000000
χ634-4-444-4-4444-4-440000-44-4000000-440000000000000000000000000000000000000000
χ644-4-444-4-44-4-44440000-44-40000004-40000000000000000000000000000000000000000
χ654-4-4-4-44440000400004-4-4000000000000000000004i−4i−4i4i000000000000000000000000
χ664-4-4-4-44440000400004-4-400000000000000000000−4i4i4i−4i000000000000000000000000
χ674-4-4-4-44440000-40000-4440000000000004-4-4400000000000000000000000000000000
χ684-4-4-4-44440000-40000-444000000000000-444-400000000000000000000000000000000

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