Finite Group Databasebeta

← Group #316640

Character table — Group #316640

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888244444888888888822244444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111-1-11-1-11111-1-1-1-111-111-1111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-111-1-1-111-1-1-1-11111-1-111
χ81111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-1
χ9111111111111111111-1-1-1-11111-111-11111-1-11111-1-1-111-111-1-1-1-111-1-1-1-1-1-111
χ10111111111111111111-1-1-1-11111-111-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-1111111-1-111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-111-111-1-1-1-1-111111111-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111-1-11111-1-1-1-1-1-1
χ17222222222-222-2-22-2-2-222222222-200-200-2-2220000-2-200000000000000000000
χ18222222222-222-2-22-2-2-22222-2-2-2-2-200-20022-2-200002200000000000000000000
χ19222222222-222-2-22-2-2-2-2-2-2-22222200200-2-2-2-200002200000000000000000000
χ20222222222-222-2-22-2-2-2-2-2-2-2-2-2-2-220020022220000-2-200000000000000000000
χ2122222222-22-2-222-22-2-222-2-20000-2222-2-20000000000-20020000000000000000
χ2222222222-22-2-222-22-2-222-2-20000-2-2-22220000000000200-20000000000000000
χ2322222222-22-2-222-22-2-2-2-2220000222-2-2-20000000000200-20000000000000000
χ2422222222-22-2-222-22-2-2-2-22200002-2-2-2220000000000-20020000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000200-20000002i2i−2i−2i00000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000200-2000000−2i−2i2i2i0000000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-2220000-20020000002i2i−2i−2i0000000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-222-2-2220000-2002000000−2i−2i2i2i00000000000000002i−2i0000
χ2922-2-222-2-220-2-20020002i−2i2i−2i22-2-2000000002i−2i0000000000000000i2−i22−2002−2i2−i2
χ3022-2-222-2-220-2-20020002i−2i2i−2i22-2-2000000002i−2i0000000000000000−i2i2−2200−22−i2i2
χ3122-2-222-2-220-2-20020002i−2i2i−2i-2-22200000000−2i2i0000000000000000i2−i2−22002−2−i2i2
χ3222-2-222-2-220-2-20020002i−2i2i−2i-2-22200000000−2i2i0000000000000000−i2i22−200−22i2−i2
χ3322-2-222-2-220-2-2002000−2i2i−2i2i22-2-200000000−2i2i0000000000000000i2−i2−2200−22i2−i2
χ3422-2-222-2-220-2-2002000−2i2i−2i2i22-2-200000000−2i2i0000000000000000−i2i22−2002−2−i2i2
χ3522-2-222-2-220-2-2002000−2i2i−2i2i-2-222000000002i−2i0000000000000000i2−i22−200−22−i2i2
χ3622-2-222-2-220-2-2002000−2i2i−2i2i-2-222000000002i−2i0000000000000000−i2i2−22002−2i2−i2
χ372-22-22-22-2222-2-2-2-222-200002i−2i2i−2i0000002i−2i0000000002-202i−2i00000000000000
χ382-22-22-22-2222-2-2-2-222-200002i−2i2i−2i0000002i−2i000000000-220−2i2i00000000000000
χ392-22-22-22-2222-2-2-2-222-20000−2i2i−2i2i000000−2i2i0000000002-20−2i2i00000000000000
χ402-22-22-22-2222-2-2-2-222-20000−2i2i−2i2i000000−2i2i000000000-2202i−2i00000000000000
χ412-22-22-22-22-22-222-2-2-2200002i−2i2i−2i000000−2i2i000000000000002-22i−2i0000000000
χ422-22-22-22-22-22-222-2-2-2200002i−2i2i−2i000000−2i2i00000000000000-22−2i2i0000000000
χ432-22-22-22-22-22-222-2-2-220000−2i2i−2i2i0000002i−2i000000000000002-2−2i2i0000000000
χ442-22-22-22-22-22-222-2-2-220000−2i2i−2i2i0000002i−2i00000000000000-222i−2i0000000000
χ4544-4-444-4-4-404400-40004i−4i−4i4i0000000000000000000000000000000000000000
χ4644-4-444-4-4-404400-4000−4i4i4i−4i0000000000000000000000000000000000000000
χ4744-4-4-4-44404004-40-4000000000000000000002i2−2i22i2−2i20000000000000000000000
χ4844-4-4-4-44404004-40-400000000000000000000−2i22i2−2i22i20000000000000000000000
χ4944-4-4-4-4440-400-44040000000000000000000022−22−22220000000000000000000000
χ5044-4-4-4-4440-400-440400000000000000000000−222222−220000000000000000000000
χ514-44-44-44-4-44-44-4-444-4400000000000000000000000000000000000000000000
χ524-44-44-44-4-4-4-44444-44-400000000000000000000000000000000000000000000
χ534-4-444-4-4440-4400-400000004i−4i−4i4i000000000000000000000000000000000000
χ544-4-444-4-4440-4400-40000000−4i4i4i−4i000000000000000000000000000000000000
χ554-4-444-4-44-404-400400000000000000000000000004-400000000000000000000
χ564-4-444-4-44-404-40040000000000000000000000000-4400000000000000000000
χ574-4-44-444-40400-440-4000000000000004i−4i000000000000000000000000000000
χ584-4-44-444-40400-440-400000000000000−4i4i000000000000000000000000000000
χ594-4-44-444-40-4004-404000000000004-4000000000000000000000000000000000
χ604-4-44-444-40-4004-40400000000000-44000000000000000000000000000000000
χ618888-8-8-8-8000000000000000000000000000000000000000000000000000000
χ628-88-8-88-88000000000000000000000000000000000000000000000000000000

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