Finite Group Databasebeta

← Group #315225

Character table — Group #315225

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444444444444444444441616161616161616161616161616161632323232
order12222222444444444488888888888888888888888844444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-11-11-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-11-11-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1111-1-1-1-1-1-11-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-111-1-11111-11-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1111-1-111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-11111111-11-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-1-1-1-1-11111-1-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1111-1-1-1-1-11111-1-11-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-11-1-111-1-111-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-11-111-1-111-1-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-111111-1-1-1-1111-1-11
χ17222222222-2-22-2-222-2-2000000002222-2-2-2-2000000002200-20-20000000000000
χ18222222222-2-22-2-222-2-2000000002222-2-2-2-200000000-2-2002020000000000000
χ19222222222-2-22-2-222-2-200000000-2-2-2-22222000000002-200-2020000000000000
χ20222222222-2-22-2-222-2-200000000-2-2-2-2222200000000-220020-20000000000000
χ2122222222-222-222-2-2-2-22222-2-2-2-20000000000000000002-2020-2000000000000
χ2222222222-222-222-2-2-2-22222-2-2-2-2000000000000000000-220-202000000000000
χ2322222222-222-222-2-2-2-2-2-2-2-222220000000000000000002-20-202000000000000
χ2422222222-222-222-2-2-2-2-2-2-2-22222000000000000000000-22020-2000000000000
χ252-2-222-22-22-2-2-2222-2-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000002-22i−2i0000
χ262-2-222-22-22-2-2-2222-2-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000-22−2i2i0000
χ272-2-222-22-22-2-2-2222-2-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002-2−2i2i0000
χ282-2-222-22-22-2-2-2222-2-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000-222i−2i0000
χ292-2-222-22-2-2222-2-2-22-220000000022-2-222-2-200000000000000002i−2i2i−2i00000000
χ302-2-222-22-2-2222-2-2-22-220000000022-2-222-2-20000000000000000−2i2i−2i2i00000000
χ312-2-222-22-2-2222-2-2-22-2200000000-2-222-2-22200000000000000002i−2i−2i2i00000000
χ322-2-222-22-2-2222-2-2-22-2200000000-2-222-2-2220000000000000000−2i2i2i−2i00000000
χ332-2-222-22-2-2-2-2222-222-22i2i−2i−2i−2i−2i2i2i22-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000000000000
χ342-2-222-22-2-2-2-2222-222-22i2i−2i−2i−2i−2i2i2i-2-22222-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ352-2-222-22-2-2-2-2222-222-2−2i−2i2i2i2i2i−2i−2i22-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ362-2-222-22-2-2-2-2222-222-2−2i−2i2i2i2i2i−2i−2i-2-22222-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ38444-4-4-44-4400400-4-400000000004-44-400000000000000000000000000000000
χ39444-4-4-44-4400400-4-40000000000-44-4400000000000000000000000000000000
χ40444-4-4-44-4-400-400440000000000000000002i22i2−2i2−2i22i22i2−2i2−2i200000000000000000000
χ41444-4-4-44-4-400-40044000000000000000000−2i2−2i22i22i2−2i2−2i22i22i200000000000000000000
χ4244-44-44-4-40000000000000022−2222−22000022−2222−222-22-22-22-200000000000000000000
χ4344-44-44-4-40000000000000022−2222−220000−2222−2222-22-22-22-2200000000000000000000
χ4444-44-44-4-400000000000000−2222−2222000022−2222−22-22-22-22-2200000000000000000000
χ4544-44-44-4-400000000000000−2222−22220000−2222−22222-22-22-22-200000000000000000000
χ4644-4-44-4-4404-404-4000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000
χ4744-4-44-4-4404-404-400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000
χ4844-4-44-4-440-440-4400004i−4i4i−4i0000000000000000000000000000000000000000
χ4944-4-44-4-440-440-440000−4i4i−4i4i0000000000000000000000000000000000000000
χ504-444-4-4-44000000000000002i2−2i2−2i22i2000022−22−22222i−2i2i−2i−2i2i−2i2i00000000000000000000
χ514-444-4-4-44000000000000002i2−2i2−2i22i20000−222222−22−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ524-444-4-4-4400000000000000−2i22i22i2−2i2000022−22−2222−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ534-444-4-4-4400000000000000−2i22i22i2−2i20000−222222−222i−2i2i−2i−2i2i−2i2i00000000000000000000
χ544-44-444-4-404-40-4400004-4-440000000000000000000000000000000000000000
χ554-44-444-4-404-40-440000-444-40000000000000000000000000000000000000000
χ564-44-444-4-40-4404-40000000000000000000022−22−2222−222222−2200000000000000000000
χ574-44-444-4-40-4404-400000000000000000000−222222−2222−22−222200000000000000000000
χ584-4-444-44-4444-4-4-44-44-400000000000000000000000000000000000000000000
χ594-4-4-4-4444400-400-440000000000000000002222−22−22−22−22222200000000000000000000
χ604-4-4-4-4444400-400-44000000000000000000−22−2222222222−22−2200000000000000000000
χ614-4-4-4-4444-4004004-400000000004-4-4400000000000000000000000000000000
χ624-4-4-4-4444-4004004-40000000000-444-400000000000000000000000000000000

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