Finite Group Databasebeta

← Group #124685

Character table — Group #124685

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222222222222444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222222222-2-2-2-222-2-2-2-222-2-200000000000000000000000000000000
χ1822222222222222222222-2-22222-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-2222-2-2-2-222-2-222-2-22200000000000000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ21222-22-2-2-222-22222-2-2-2-2-2220000-2-200002-20000000000000000002−22−22−22−200000000
χ22222-22-2-2-222-22222-2-2-2-2-2220000-2-200002-2000000000000000000−22−22−22−2200000000
χ23222-22-2-2-222-22222-2-2-2-2-2-2-20000220000-22000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ24222-22-2-2-222-22222-2-2-2-2-2-2-20000220000-22000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ25222-22-2-2-222-2-2-2-2-22222-2220000-2-20000-220000000000000000002−2−222−2−2200000000
χ26222-22-2-2-222-2-2-2-2-22222-2220000-2-20000-22000000000000000000−222−2−222−200000000
χ27222-22-2-2-222-2-2-2-2-22222-2-2-200002200002-2000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ28222-22-2-2-222-2-2-2-2-22222-2-2-200002200002-2000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ29222-22-2-2-2-2-2222-2-222-2-22002i2i−2i−2i000000002i−2i0000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ30222-22-2-2-2-2-2222-2-222-2-22002i2i−2i−2i000000002i−2i000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ31222-22-2-2-2-2-2222-2-222-2-2200−2i−2i2i2i00000000−2i2i0000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ32222-22-2-2-2-2-2222-2-222-2-2200−2i−2i2i2i00000000−2i2i000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ33222-22-2-2-2-2-22-2-222-2-2222002i2i−2i−2i00000000−2i2i0000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ34222-22-2-2-2-2-22-2-222-2-2222002i2i−2i−2i00000000−2i2i000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ35222-22-2-2-2-2-22-2-222-2-222200−2i−2i2i2i000000002i−2i0000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ36222-22-2-2-2-2-22-2-222-2-222200−2i−2i2i2i000000002i−2i000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ3722-2-2-22-222-2200000000-22i−2i2i−2i2i−2i2i−2i2-2000000000022-2-200002i2i−2i−2i0000000000000000
χ3822-2-2-22-222-2200000000-22i−2i2i−2i2i−2i2i−2i2-20000000000-2-2220000−2i−2i2i2i0000000000000000
χ3922-2-2-22-222-2200000000-22i−2i−2i2i−2i2i2i−2i-2200000022-2-200002i2i−2i−2i00000000000000000000
χ4022-2-2-22-222-2200000000-22i−2i−2i2i−2i2i2i−2i-22000000-2-2220000−2i−2i2i2i00000000000000000000
χ4122-2-2-22-222-2200000000-2−2i2i2i−2i2i−2i−2i2i-2200000022-2-20000−2i−2i2i2i00000000000000000000
χ4222-2-2-22-222-2200000000-2−2i2i2i−2i2i−2i−2i2i-22000000-2-22200002i2i−2i−2i00000000000000000000
χ4322-2-2-22-222-2200000000-2−2i2i−2i2i−2i2i−2i2i2-2000000000022-2-20000−2i−2i2i2i0000000000000000
χ4422-2-2-22-222-2200000000-2−2i2i−2i2i−2i2i−2i2i2-20000000000-2-22200002i2i−2i−2i0000000000000000
χ4544444444-4-4-444-4-4-4-444-4000000000000000000000000000000000000000000000000
χ4644444444-4-4-4-4-44444-4-4-4000000000000000000000000000000000000000000000000
χ4744-44-4-44-44-4-40000000044i−4i0000−4i4i0000000000000000000000000000000000000000
χ4844-44-4-44-44-4-4000000004−4i4i00004i−4i0000000000000000000000000000000000000000
χ4944-44-4-44-4-44400000000-4004-4-44000000000000000000000000000000000000000000
χ5044-44-4-44-4-44400000000-400-444-4000000000000000000000000000000000000000000
χ5144-4-4-44-44-44-400000000400000000004-4000000000000000000000000000000000000
χ5244-4-4-44-44-44-40000000040000000000-44000000000000000000000000000000000000
χ534-444-4-4-44000004-44-40000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ544-444-4-4-44000004-44-4000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ554-444-4-4-4400000-44-440000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ564-444-4-4-4400000-44-44000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ574-44-4-444-4000004-4-4400000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ584-44-4-444-4000004-4-440000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ594-44-4-444-400000-444-400000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ604-44-4-444-400000-444-40000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ614-4-4444-4-40004-400004-4000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ624-4-4444-4-40004-400004-400000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ634-4-4444-4-4000-440000-44000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ644-4-4444-4-4000-440000-4400000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ654-4-4-44-4440004-40000-4400000000000000000000000002-2-222-2-220000000000000000
χ664-4-4-44-4440004-40000-440000000000000000000000000-222-2-222-20000000000000000
χ674-4-4-44-444000-4400004-400000000000000000000000002-2-22-222-20000000000000000
χ684-4-4-44-444000-4400004-40000000000000000000000000-222-22-2-220000000000000000

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