Finite Group Databasebeta

← Group #311619

Character table — Group #311619

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11-1-11-1-1-1-1-1-111
χ3111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-11-1-111111-1-1-1-1
χ51111111111111111111111-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-111-11111-1-1-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-111-1-1-1-1-1-1-111
χ9111111111111111111-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-111-11
χ11111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-111111-1-1-1-11-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1-111111-1
χ13111111111111111111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-11-1
χ14111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-111111-1
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111111-1-1-1-1-111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111-111-1-111-11
χ17222222222-22-2-222-2-2-2000000222200-2-2-2-20022-2-20000000000000000000000
χ18222222222-22-2-222-2-2-200000022-2-200-2-22200-2-2220000000000000000000000
χ19222222222-22-2-222-2-2-2000000-2-2220022-2-200-2-2220000000000000000000000
χ20222222222-22-2-222-2-2-2000000-2-2-2-20022220022-2-20000000000000000000000
χ2122222222-22-222-2-22-2-22222220000220000-2-200000000000000-200-200000000
χ2222222222-22-222-2-22-2-22222-2-20000-2-20000-2-200000000000000200200000000
χ2322222222-22-222-2-22-2-2-2-2-2-2220000-2-200002200000000000000200-200000000
χ2422222222-22-222-2-22-2-2-2-2-2-2-2-200002200002200000000000000-200200000000
χ2522-2-2-222-222-2-2-22-22-222i2i−2i−2i0000000000002i−2i0000000000002i−2i02-2000000000
χ2622-2-2-222-222-2-2-22-22-222i2i−2i−2i0000000000002i−2i000000000000−2i2i0-22000000000
χ2722-2-2-222-222-2-2-22-22-22−2i−2i2i2i000000000000−2i2i0000000000002i−2i0-22000000000
χ2822-2-2-222-222-2-2-22-22-22−2i−2i2i2i000000000000−2i2i000000000000−2i2i02-2000000000
χ2922-2-2-222-2-222-2-2-2222-22i2i−2i−2i00002i−2i00002i−2i−2i2i00000000000000000000002-200
χ3022-2-2-222-2-222-2-2-2222-22i2i−2i−2i0000−2i2i0000−2i2i−2i2i0000000000000000000000-2200
χ3122-2-2-222-2-222-2-2-2222-2−2i−2i2i2i00002i−2i00002i−2i2i−2i0000000000000000000000-2200
χ3222-2-2-222-2-222-2-2-2222-2−2i−2i2i2i0000−2i2i0000−2i2i2i−2i00000000000000000000002-200
χ3322-2-2-222-2-2-2222-22-2-22000000002i−2i0000−2i2i0000002i2i−2i−2i22-2-200000000000000
χ3422-2-2-222-2-2-2222-22-2-22000000002i−2i0000−2i2i000000−2i−2i2i2i-2-22200000000000000
χ3522-2-2-222-2-2-2222-22-2-2200000000−2i2i00002i−2i0000002i2i−2i−2i-2-22200000000000000
χ3622-2-2-222-2-2-2222-22-2-2200000000−2i2i00002i−2i000000−2i−2i2i2i22-2-200000000000000
χ372-222-22-2-20-202-2002002i−2i2i−2i2-200002i−2i0000002−22−20000i2−i2i2−i2000000i2−i22−20000
χ382-222-22-2-20-202-2002002i−2i2i−2i2-200002i−2i000000−22−220000−i2i2−i2i2000000−i2i2−220000
χ392-222-22-2-20-202-2002002i−2i2i−2i-220000−2i2i0000002−22−20000i2−i2i2−i2000000−i2i2−220000
χ402-222-22-2-20-202-2002002i−2i2i−2i-220000−2i2i000000−22−220000−i2i2−i2i2000000i2−i22−20000
χ412-222-22-2-20-202-200200−2i2i−2i2i2-20000−2i2i0000002−22−20000−i2i2−i2i2000000−i2i22−20000
χ422-222-22-2-20-202-200200−2i2i−2i2i2-20000−2i2i000000−22−220000i2−i2i2−i2000000i2−i2−220000
χ432-222-22-2-20-202-200200−2i2i−2i2i-2200002i−2i0000002−22−20000−i2i2−i2i2000000i2−i2−220000
χ442-222-22-2-20-202-200200−2i2i−2i2i-2200002i−2i000000−22−220000i2−i2i2−i2000000−i2i22−20000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-4-4-4440400-4-40000000000000004-4000000000000000000000000000000
χ47444-4-4-4-4440400-4-4000000000000000-44000000000000000000000000000000
χ48444-4-4-4-44-40-4004400000000000000000000000002i2−2i22i2−2i2000000000000000000
χ49444-4-4-4-44-40-400440000000000000000000000000−2i22i2−2i22i2000000000000000000
χ5044-444-4-4-440-400-44000000000000000000000000022−22−2222000000000000000000
χ5144-444-4-4-440-400-440000000000000000000000000−222222−22000000000000000000
χ5244-444-4-4-4-404004-40000000004-4000000000000000000000000000000000000
χ5344-444-4-4-4-404004-4000000000-44000000000000000000000000000000000000
χ5444-4-4-444-44-4-4444-4-44-400000000000000000000000000000000000000000000
χ554-444-44-4-4040-4400-40000000000000000000022−22−22220000000000000000000000
χ564-444-44-4-4040-4400-400000000000000000000−222222−220000000000000000000000
χ574-4-4-444-440404-400-400000000000000000000000000002i2−2i2−2i22i200000000000000
χ584-4-4-444-440404-400-40000000000000000000000000000−2i22i22i2−2i200000000000000
χ594-4-4-444-440-40-44004004-4-440000000000000000000000000000000000000000
χ604-4-4-444-440-40-4400400-444-40000000000000000000000000000000000000000
χ618-88-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-88-8-888000000000000000000000000000000000000000000000000000000

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