Finite Group Databasebeta

← Group #129786

Character table — Group #129786

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222244444444444488888888888816161616161616161616161616161616161616161616
order12222244442244444444442244444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ41111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111-1-1-1-1111111111-1-1-1-1-1-1111-1-11-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111-1-1-1-1111111111-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-111-1111111-1-1-1-11111-1-1-1-1
χ81111111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-11111
χ91111111111-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-11111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1111ii−i−i−i−iii−i−iiiii−i−i
χ121111111111-1-1-11111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1111−i−iiiii−i−iii−i−i−i−iii
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1-1-111ii−i−iii−i−i−i−iii−i−iii
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1-1-111−i−iii−i−iiiii−i−iii−i−i
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1722222222222222222-2-2-2-2200-2-2-2-2-2-222000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2200-2-22222-2-2000000000000000000000000
χ192222222222-2-2-222222222-200-2-2-2-222-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-22222-200-2-222-2-222000000000000000000000000
χ21222222-2-2-2-222-2000022-2-2-2002-20000000002-202-20000000000000000
χ22222222-2-2-2-222-2000022-2-2-2002-2000000000-220-220000000000000000
χ23222222-2-2-2-222-20000-2-222-222-2200000022-200-2000000000000000000
χ24222222-2-2-2-222-20000-2-222-2-2-2-22000000-2-22002000000000000000000
χ25222222-2-2-2-2-2-22000022-2-2222-22000000-2-2-2002000000000000000000
χ26222222-2-2-2-2-2-22000022-2-22-2-2-2200000022200-2000000000000000000
χ27222222-2-2-2-2-2-220000-2-2222002-20000000002-20-220000000000000000
χ28222222-2-2-2-2-2-220000-2-2222002-2000000000-2202-20000000000000000
χ292-2-222-222-2-200022-2-22i−2i2i−2i00000002i−2i00000000001+i−1−i1−i−1+i000000001+i−1−i1−i−1+i
χ302-2-222-222-2-200022-2-22i−2i2i−2i00000002i−2i0000000000−1−i1+i−1+i1−i00000000−1−i1+i−1+i1−i
χ312-2-222-222-2-200022-2-2−2i2i−2i2i0000000−2i2i00000000001−i−1+i1+i−1−i000000001−i−1+i1+i−1−i
χ322-2-222-222-2-200022-2-2−2i2i−2i2i0000000−2i2i0000000000−1+i1−i−1−i1+i00000000−1+i1−i−1−i1+i
χ332-2-222-222-2-2000-2-2222i−2i2i−2i0000000−2i2i00000000001+i−1−i1−i−1+i00000000−1−i1+i−1+i1−i
χ342-2-222-222-2-2000-2-2222i−2i2i−2i0000000−2i2i0000000000−1−i1+i−1+i1−i000000001+i−1−i1−i−1+i
χ352-2-222-222-2-2000-2-222−2i2i−2i2i00000002i−2i00000000001−i−1+i1+i−1−i00000000−1+i1−i−1−i1+i
χ362-2-222-222-2-2000-2-222−2i2i−2i2i00000002i−2i0000000000−1+i1−i−1−i1+i000000001−i−1+i1+i−1−i
χ372-2-22-222-22-22-222-22-20000-2000000002-2000000000000i2−i2i2−i2i2−i2i2−i20000
χ382-2-22-222-22-22-222-22-20000-2000000002-2000000000000−i2i2−i2i2−i2i2−i2i20000
χ392-2-22-222-22-22-22-22-220000-200000000-22000000000000i2−i2i2−i2−i2i2−i2i20000
χ402-2-22-222-22-22-22-22-220000-200000000-22000000000000−i2i2−i2i2i2−i2i2−i20000
χ412-2-22-222-22-2-22-22-22-20000200000000-220000000000002−2−222−2−220000
χ422-2-22-222-22-2-22-22-22-20000200000000-22000000000000−222−2−222−20000
χ432-2-22-222-22-2-22-2-22-2200002000000002-20000000000002−2−22−222−20000
χ442-2-22-222-22-2-22-2-22-2200002000000002-2000000000000−222−22−2−220000
χ454444-4-44-4-440004-4-44000000000000000000000000000000000000000
χ464444-4-44-4-44000-444-4000000000000000000000000000000000000000
χ474444-4-4-444-400000000000000004-40000000000000000000000000000
χ484444-4-4-444-40000000000000000-440000000000000000000000000000
χ494-4-444-4-4-44400000004i−4i−4i4i00000000000000000000000000000000000
χ504-4-444-4-4-4440000000−4i4i4i−4i00000000000000000000000000000000000
χ514-4-44-44-44-444-4-40000000040000000000000000000000000000000000
χ524-4-44-44-44-44-44400000000-40000000000000000000000000000000000
χ5388-8-80000000000000000004-400000000000000000000000000000000
χ5488-8-8000000000000000000-4400000000000000000000000000000000
χ558-88-800000000000000000000000000004-40000000000000000000000
χ568-88-80000000000000000000000000000-440000000000000000000000

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