Finite Group Databasebeta

← Group #280425

Character table — Group #280425

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1111111-1-111-1
χ71111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-111-1
χ81111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-1111111-1-1111111-1-1-1-11111-1-11-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111-111-1-11111-1-1-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-111111-1-111-1-1-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111
χ17222222222-22-2-222-2-20000-22222002222-2-200-2-200000000000000-2000000000000
χ18222222222-22-2-222-2-20000-2222200-2-2-2-22200-2-2000000000000002000000000000
χ19222222222-22-2-222-2-20000-2-2-2-2-20022-2-222002200000000000000-2000000000000
χ20222222222-22-2-222-2-20000-2-2-2-2-200-2-222-2-20022000000000000002000000000000
χ2122222222-22-222-2-22-22222-20000-2-2000000220022-2-200000000000-200000000000
χ2222222222-22-222-2-22-22222-20000-2-2000000-2-200-2-22200000000000200000000000
χ2322222222-22-222-2-22-2-2-2-2-2-20000220000002200-2-22200000000000-200000000000
χ2422222222-22-222-2-22-2-2-2-2-2-2000022000000-2-20022-2-200000000000200000000000
χ25222-2-2-2-220-202-200202i2i−2i−2i022−2−2000000002-22−22i−2i00i2i2−i2−i2i2i2−i2−i2000000002−200000
χ26222-2-2-2-220-202-200202i2i−2i−2i022−2−200000000-222−2−2i2i00i2i2−i2−i2−i2−i2i2i200000000−2200000
χ27222-2-2-2-220-202-200202i2i−2i−2i0−2−222000000002-2−222i−2i00−i2−i2i2i2−i2−i2i2i200000000−2200000
χ28222-2-2-2-220-202-200202i2i−2i−2i0−2−22200000000-22−22−2i2i00−i2−i2i2i2i2i2−i2−i2000000002−200000
χ29222-2-2-2-220-202-20020−2i−2i2i2i022−2−2000000002-22−2−2i2i00−i2−i2i2i2−i2−i2i2i2000000002−200000
χ30222-2-2-2-220-202-20020−2i−2i2i2i022−2−200000000-222−22i−2i00−i2−i2i2i2i2i2−i2−i200000000−2200000
χ31222-2-2-2-220-202-20020−2i−2i2i2i0−2−222000000002-2−22−2i2i00i2i2−i2−i2i2i2−i2−i200000000−2200000
χ32222-2-2-2-220-202-20020−2i−2i2i2i0−2−22200000000-22−222i−2i00i2i2−i2−i2−i2−i2i2i2000000002−200000
χ332-2-222-2-2222-2-2-22-2220000-2000000002i−2i2i−2i000000002i−2i2i−2i00000000002-20000000
χ342-2-222-2-2222-2-2-22-2220000-2000000002i−2i2i−2i00000000−2i2i−2i2i0000000000-220000000
χ352-2-222-2-2222-2-2-22-2220000-200000000−2i2i−2i2i000000002i−2i2i−2i0000000000-220000000
χ362-2-222-2-2222-2-2-22-2220000-200000000−2i2i−2i2i00000000−2i2i−2i2i00000000002-20000000
χ372-2-222-2-222-2-2222-2-2-22-22-2200002-2002i−2i−2i2i00000000000000002i−2i0000000000000
χ382-2-222-2-222-2-2222-2-2-22-22-2200002-200−2i2i2i−2i0000000000000000−2i2i0000000000000
χ392-2-222-2-222-2-2222-2-2-2-22-2220000-22002i−2i−2i2i0000000000000000−2i2i0000000000000
χ402-2-222-2-222-2-2222-2-2-2-22-2220000-2200−2i2i2i−2i00000000000000002i−2i0000000000000
χ412-2-222-2-22-2-2222-22-222-22-2-20000-22000000000000000000000000002i−2i0000002i−2i0
χ422-2-222-2-22-2-2222-22-222-22-2-20000-2200000000000000000000000000−2i2i000000−2i2i0
χ432-2-222-2-22-2-2222-22-22-22-22-200002-2000000000000000000000000002i−2i000000−2i2i0
χ442-2-222-2-22-2-2222-22-22-22-22-200002-200000000000000000000000000−2i2i0000002i−2i0
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-4-44040-4400-40000002222−22−220000000000−2222000000000000000000000000000
χ47444-4-4-4-44040-4400-4000000−22−222222000000000022−22000000000000000000000000000
χ4844-44-44-4-440400-4-400000000000000000000000000000000000000000000022−22000
χ4944-44-44-4-440400-4-4000000000000000000000000000000000000000000000−2222000
χ5044-44-44-4-4-40-4004400000000000004i−4i00000000000000000000000000000000000
χ5144-44-44-4-4-40-400440000000000000−4i4i00000000000000000000000000000000000
χ524-444-4-44-440-400-4400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ534-444-4-44-440-400-440000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ544-444-4-44-4-404004-400000004i−4i4i−4i000000000000000000000000000000000000000
χ554-444-4-44-4-404004-40000000−4i4i−4i4i000000000000000000000000000000000000000
χ564-44-444-4-4000000000000002i2−2i2−2i22i2000000000000002i2−2i200002-2-22000000000000000
χ574-44-444-4-4000000000000002i2−2i2−2i22i200000000000000−2i22i20000-222-2000000000000000
χ584-44-444-4-400000000000000−2i22i22i2−2i2000000000000002i2−2i20000-222-2000000000000000
χ594-44-444-4-400000000000000−2i22i22i2−2i200000000000000−2i22i200002-2-22000000000000000
χ604-4-444-4-44-444-4-4-444-4000040000000000000000000000000000000000000000000
χ614-4-4-4-44440404-400-404i−4i−4i4i00000000000000000000000000000000000000000000
χ624-4-4-4-44440404-400-40−4i4i4i−4i00000000000000000000000000000000000000000000
χ634-4-4-4-44440-40-440040000000000000000000000000022−22−22220000000000000000000
χ644-4-4-4-44440-40-4400400000000000000000000000000−222222−220000000000000000000
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000

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