Finite Group Databasebeta

← Group #274859

Character table — Group #274859

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444224444224444444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-11-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ9111111111-1-1-1-11111111-1-111-1-111-111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ10111111111-1-1-1-11111111-1-111-1-111-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-11
χ11111111111-1-1-1-11111111-1-111-1-111-111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111-11
χ12111111111-1-1-1-11111111-1-111-1-111-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1111-1
χ13111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-11
χ14111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ15111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-11-1
χ16111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111111-1-111-1-111-1-1-11
χ172222222222222-2-222-2-2222-2-2-2-222-2-2-222-2-2000000000000000000000000000000
χ182222222222222-2-222-2-2222-2-2-2-2-2-2-222-2-222000000000000000000000000000000
χ19222222222-2-2-2-2-2-222-2-22-2-2-2-222222-2-2-2-222000000000000000000000000000000
χ20222222222-2-2-2-2-2-222-2-22-2-2-2-222-2-222222-2-2000000000000000000000000000000
χ2122222222-2222222-2-222-2-2-2-2-22200-20000002222-2-2-2-20000000000000000000000
χ2222222222-2222222-2-222-2-2-2-2-22200-2000000-2-2-2-222220000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-222-2-20020000000000000000000000000000002i−2i2i−2i00
χ2422222222-22222-2-2-2-2-2-2-2-2-222-2-2002000000000000000000000000000000−2i2i−2i2i00
χ2522222222-2-2-2-2-222-2-222-222-2-2-2-200200000022-2-2-2-2220000000000000000000000
χ2622222222-2-2-2-2-222-2-222-222-2-2-2-2002000000-2-22222-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200-20000000000000000000000000000002i−2i−2i2i00
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200-2000000000000000000000000000000−2i2i2i−2i00
χ2922-22-2-22-202i2i−2i−2i2-2002-2000002i−2i0000000002-22i−2i0000i2i2−i2−i222−2−20000i2−i22−2000000
χ3022-22-2-22-202i2i−2i−2i2-2002-2000002i−2i0000000002-22i−2i0000−i2−i2i2i2−2−2220000−i2i2−22000000
χ3122-22-2-22-202i2i−2i−2i2-2002-2000002i−2i000000000-22−2i2i0000i2i2−i2−i222−2−20000−i2i2−22000000
χ3222-22-2-22-202i2i−2i−2i2-2002-2000002i−2i000000000-22−2i2i0000−i2−i2i2i2−2−2220000i2−i22−2000000
χ3322-22-2-22-20−2i−2i2i2i2-2002-200000−2i2i0000000002-2−2i2i0000i2i2−i2−i2−2−2220000i2−i2−22000000
χ3422-22-2-22-20−2i−2i2i2i2-2002-200000−2i2i0000000002-2−2i2i0000−i2−i2i2i222−2−20000−i2i22−2000000
χ3522-22-2-22-20−2i−2i2i2i2-2002-200000−2i2i000000000-222i−2i0000i2i2−i2−i2−2−2220000−i2i22−2000000
χ3622-22-2-22-20−2i−2i2i2i2-2002-200000−2i2i000000000-222i−2i0000−i2−i2i2i222−2−20000i2−i2−22000000
χ372-2-222-2-22200002-22-2-22-2002-200000002-22-2000000002i−2i2i−2i0000002i−2i0000000000
χ382-2-222-2-22200002-22-2-22-2002-200000002-22-200000000−2i2i−2i2i000000−2i2i0000000000
χ392-2-222-2-22200002-22-2-22-2002-20000000-22-22000000002i−2i2i−2i000000−2i2i0000000000
χ402-2-222-2-22200002-22-2-22-2002-20000000-22-2200000000−2i2i−2i2i0000002i−2i0000000000
χ412-2-222-2-2220000-222-22-2-200-2200000002-2-220000000000002i−2i2i−2i2i−2i000000000000
χ422-2-222-2-2220000-222-22-2-200-2200000002-2-22000000000000−2i2i−2i2i−2i2i000000000000
χ432-2-222-2-2220000-222-22-2-200-220000000-222-20000000000002i−2i2i−2i−2i2i000000000000
χ442-2-222-2-2220000-222-22-2-200-220000000-222-2000000000000−2i2i−2i2i2i−2i000000000000
χ45444-44-4-4-444-44-400-4-40044-40000000000000000000000000000000000000000000
χ46444-44-4-4-44-44-4400-4-4004-440000000000000000000000000000000000000000000
χ47444-44-4-4-4-44-44-4004400-4-440000000000000000000000000000000000000000000
χ48444-44-4-4-4-4-44-44004400-44-40000000000000000000000000000000000000000000
χ4944-44-4-44-404i4i−4i−4i-4400-4400000−4i4i000000000000000000000000000000000000000
χ5044-44-4-44-40−4i−4i4i4i-4400-44000004i−4i000000000000000000000000000000000000000
χ5144-4-4-44-4404i−4i−4i4i0000000000000000000000000022−222i2−2i20000000000000000000000
χ5244-4-4-44-4404i−4i−4i4i00000000000000000000000000−2222−2i22i20000000000000000000000
χ5344-4-4-44-440−4i4i4i−4i0000000000000000000000000022−22−2i22i20000000000000000000000
χ5444-4-4-44-440−4i4i4i−4i00000000000000000000000000−22222i2−2i20000000000000000000000
χ554-444-44-4-4000004400-4-400000000000000000000000022−22−2222000000000000000000
χ564-444-44-4-4000004400-4-4000000000000000000000000−222222−22000000000000000000
χ574-444-44-4-400000-4-4004400000000000000000000000000002i2−2i2−2i22i200000000000000
χ584-444-44-4-400000-4-400440000000000000000000000000000−2i22i22i2−2i200000000000000
χ594-4-444-4-44-400004-4-44-44400-4400000000000000000000000000000000000000000
χ604-4-444-4-44-40000-44-444-44004-400000000000000000000000000000000000000000
χ614-4-4-4444-44000000-4400-40000000004i−4i0000000000000000000000000000000000
χ624-4-4-4444-44000000-4400-4000000000−4i4i0000000000000000000000000000000000
χ634-4-4-4444-4-40000004-40040000004-40000000000000000000000000000000000000
χ644-4-4-4444-4-40000004-4004000000-440000000000000000000000000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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