Finite Group Databasebeta

← Group #140270

Character table — Group #140270

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222222244444488888888881616161616161616161616161616161632323232
order1222224444444444888888888888888888888816161616161616164444
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-111-1-111-1-11-11-11-11-1ii−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ101111-1-111-1-111-1-11-11-11-11-1ii−i−iii−i−i11-1-1ii−i−i-1-111−i−iii-11−ii
χ111111-1-111-1-111-1-11-11-11-11-1ii−i−iii−i−i-1-111−i−iii11-1-1ii−i−i-11−ii
χ121111-1-111-1-111-1-11-11-11-11-1ii−i−iii−i−i-1-111−i−iii-1-111−i−iii1-1i−i
χ131111-1-111-1-111-1-11-11-11-11-1−i−iii−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ141111-1-111-1-111-1-11-11-11-11-1−i−iii−i−iii11-1-1−i−iii-1-111ii−i−i-11i−i
χ151111-1-111-1-111-1-11-11-11-11-1−i−iii−i−iii-1-111ii−i−i11-1-1−i−iii-11i−i
χ161111-1-111-1-111-1-11-11-11-11-1−i−iii−i−iii-1-111ii−i−i-1-111ii−i−i1-1−ii
χ172222222222222222-2-2-2-2-2-22222-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2222200000000000000000000
χ1922222222-2-2-2-222-2-22222-2-20000000000002-22-2000000000000
χ2022222222-2-2-2-222-2-22222-2-2000000000000-22-22000000000000
χ2122222222-2-2-2-222-2-2-2-2-2-222000000002i−2i2i−2i0000000000000000
χ2222222222-2-2-2-222-2-2-2-2-2-22200000000−2i2i−2i2i0000000000000000
χ23222222-2-222-2-2-2-22-20000002-22-2000000000000i2−i2i2−i2i2−i2i2−i20000
χ24222222-2-222-2-2-2-22-20000002-22-2000000000000−i2i2−i2i2−i2i2−i2i20000
χ25222222-2-222-2-2-2-22-2000000-22-22000000000000i2−i2i2−i2−i2i2−i2i20000
χ26222222-2-222-2-2-2-22-2000000-22-22000000000000−i2i2−i2i2i2−i2i2−i20000
χ272222-2-22222-2-2-2-2-222-22-2-220000000000002i−2i−2i2i000000000000
χ282222-2-22222-2-2-2-2-222-22-2-22000000000000−2i2i2i−2i000000000000
χ292222-2-22222-2-2-2-2-22-22-222-2000000002i−2i−2i2i0000000000000000
χ302222-2-22222-2-2-2-2-22-22-222-200000000−2i2i2i−2i0000000000000000
χ312222-2-222-2-222-2-22-2-22-22-222i2i−2i−2i−2i−2i2i2i00000000000000000000
χ322222-2-222-2-222-2-22-2-22-22-22−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ332222-2-2-2-2-2-2-2-222220000002i−2i−2i2i000000000000i2−i2−i2i2−222−20000
χ342222-2-2-2-2-2-2-2-222220000002i−2i−2i2i000000000000−i2i2i2−i22−2−220000
χ352222-2-2-2-2-2-2-2-22222000000−2i2i2i−2i000000000000i2−i2−i2i22−2−220000
χ362222-2-2-2-2-2-2-2-22222000000−2i2i2i−2i000000000000−i2i2i2−i2−222−20000
χ37444444-4-4-4-444-4-4-440000000000000000000000000000000000
χ384444-4-4-4-4444444-4-40000000000000000000000000000000000
χ3944-4-44-44-400004-400000000000022−2222−2200000000000000000000
χ4044-4-44-44-400004-4000000000000−2222−222200000000000000000000
χ4144-4-44-4-440000-44004-4-44000000000000000000000000000000
χ4244-4-44-4-440000-4400-444-4000000000000000000000000000000
χ4344-4-4-444-40000-440000000000002i2−2i2−2i22i200000000000000000000
χ4444-4-4-444-40000-44000000000000−2i22i22i2−2i200000000000000000000
χ4544-4-4-44-4400004-40044-4-4000000000000000000000000000000
χ4644-4-4-44-4400004-400-4-444000000000000000000000000000000
χ478-88-80000008-800000000000000000000000000000000000000
χ488-88-8000000-8800000000000000000000000000000000000000
χ498-8-8800008-80000000000000000000000000000000000000000
χ508-8-880000-880000000000000000000000000000000000000000

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