Finite Group Databasebeta

← Group #313205

Character table — Group #313205

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444224444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-11-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-11-1-1-11-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1111-1-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1111-1-11111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-11111111-1-1-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11-11111-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-11-1-1-1-111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-1-1-11111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111-1-1-1-1-11111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-11-1-111-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111-1-1-1-1-111-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-111111-1-1-1-1-11
χ17222222222-22-22-22-2-2-222220000-2-2-2-20000000000002222000000-2000-200000000000
χ18222222222-22-22-22-2-2-222220000-2-2-2-2000000000000-2-2-2-20000002000200000000000
χ19222222222-22-22-22-2-2-2-2-2-2-20000222200000000000022-2-20000002000-200000000000
χ20222222222-22-22-22-2-2-2-2-2-2-200002222000000000000-2-222000000-2000200000000000
χ2122222222-22-22-22-22-2-2000022220000-2-2-2-200000000000022-2-20002000-20000000000
χ2222222222-22-22-22-22-2-2000022220000-2-2-2-2000000000000-2-222000-200020000000000
χ2322222222-22-22-22-22-2-20000-2-2-2-20000222200000000000022-2-2000-200020000000000
χ2422222222-22-22-22-22-2-20000-2-2-2-200002222000000000000-2-2220002000-20000000000
χ2522-22-2-2-2222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i00000000000000002i−2i2i−2i00000000002-2000000
χ2622-22-2-2-2222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i0000000000000000−2i2i−2i2i0000000000-22000000
χ2722-22-2-2-2222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i00000000000000002i−2i2i−2i0000000000-22000000
χ2822-22-2-2-2222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i0000000000000000−2i2i−2i2i00000000002-2000000
χ2922-22-2-2-222-2-222-2-222-22i2i−2i−2i0000−2i−2i2i2i000000000000000000002-2002i−2i000000000000
χ3022-22-2-2-222-2-222-2-222-22i2i−2i−2i0000−2i−2i2i2i00000000000000000000-2200−2i2i000000000000
χ3122-22-2-2-222-2-222-2-222-2−2i−2i2i2i00002i2i−2i−2i000000000000000000002-200−2i2i000000000000
χ3222-22-2-2-222-2-222-2-222-2−2i−2i2i2i00002i2i−2i−2i00000000000000000000-22002i−2i000000000000
χ3322-22-2-2-22-222-2-222-22-200000000000000002i2i2i2i−2i−2i−2i−2i00002i−2i−2i2i000000000000002-200
χ3422-22-2-2-22-222-2-222-22-200000000000000002i2i2i2i−2i−2i−2i−2i0000−2i2i2i−2i00000000000000-2200
χ3522-22-2-2-22-222-2-222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i00002i−2i−2i2i00000000000000-2200
χ3622-22-2-2-22-222-2-222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i0000−2i2i2i−2i000000000000002-200
χ3722-2-22-22-2-202020-20002-22-2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-22-2000000000000i2−i200i2−i20000
χ3822-2-22-22-2-202020-20002-22-2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-22-22000000000000−i2i200−i2i20000
χ3922-2-22-22-2-202020-20002-22-2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-22-2000000000000−i2i200−i2i20000
χ4022-2-22-22-2-202020-20002-22-2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-22-22000000000000i2−i200i2−i20000
χ4122-2-22-22-2-202020-2000-22-22i2i2−i2−i20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22-2-22000000000000i2−i200−i2i20000
χ4222-2-22-22-2-202020-2000-22-22i2i2−i2−i20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-222-2000000000000−i2i200i2−i20000
χ4322-2-22-22-2-202020-2000-22-22−i2−i2i2i20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22-2-22000000000000−i2i200i2−i20000
χ4422-2-22-22-2-202020-2000-22-22−i2−i2i2i20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-222-2000000000000i2−i200−i2i20000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-44040-40-400000000000000000002222−22−22−22−22222200000000000000000000000000
χ47444-4-44-4-44040-40-40000000000000000000−22−2222222222−22−2200000000000000000000000000
χ48444-4-44-4-4-40-404040004i−4i−4i4i0000000000000000000000000000000000000000000000
χ49444-4-44-4-4-40-40404000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ5044-44-4-4-44-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ5144-4-44-44-440-40-40400000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ5244-4-44-44-440-40-4040000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ534-444-4-44-4000000000000002i2−2i22i2−2i222−2222−2200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ544-444-4-44-4000000000000002i2−2i22i2−2i2−2222−22220000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ554-444-4-44-400000000000000−2i22i2−2i22i222−2222−220000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ564-444-4-44-400000000000000−2i22i2−2i22i2−2222−222200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ574-44-44-4-4404040-40-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000
χ584-44-44-4-4404040-40-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000
χ594-44-44-4-440-40-40404000000000000004-44-40000000000000000000000000000000000
χ604-44-44-4-440-40-4040400000000000000-44-440000000000000000000000000000000000
χ614-4-4444-4-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i22-22-2-22-2200000000000000000000000000
χ624-4-4444-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2-22-222-22-200000000000000000000000000
χ634-4-4444-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2-22-222-22-200000000000000000000000000
χ644-4-4444-4-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i22-22-2-22-2200000000000000000000000000
χ654-4-4-4-4444040-40-40400000000000000000022−22−222222−22−222200000000000000000000000000
χ664-4-4-4-4444040-40-404000000000000000000−222222−22−222222−2200000000000000000000000000
χ674-4-4-4-44440-404040-40000004-4-44000000000000000000000000000000000000000000
χ684-4-4-4-44440-404040-4000000-444-4000000000000000000000000000000000000000000

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