Finite Group Databasebeta

← Group #311235

Character table — Group #311235

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888884444444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-11-111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111111-11-1-1-1-1-11-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-111-1-1111-1
χ71111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1111-1-1-1-11-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-1-1-11111-11
χ91111111111111111-1-1-1-11111111111-1-1111111-1-1-1-111111-1-1-1-1-11-11111-1-1-1-1
χ101111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-1-111111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1111-1-11111-1-1-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-111-1-111-1-111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-11-1-111-1-11-1
χ17222222222-22-2-222-22222-2-200000000-2-20022-2-2000000000200000-200000000
χ18222222222-22-2-222-22222-2-200000000-2-200-2-222000000000-200000200000000
χ19222222222-22-2-222-2-2-2-2-2-2-200000000220022-2-2000000000-200000200000000
χ20222222222-22-2-222-2-2-2-2-2-2-2000000002200-2-222000000000200000-200000000
χ2122222222-22-222-2-220000-2-22222222200-2-2000000000000-200000-2000000000
χ2222222222-22-222-2-220000-2-22222-2-2-2-200-2-20000000000002000002000000000
χ2322222222-22-222-2-220000-2-2-2-2-2-222-2-20022000000000000200000-2000000000
χ2422222222-22-222-2-220000-2-2-2-2-2-2-2-2220022000000000000-2000002000000000
χ2522-22-22-2-20-202-20020000002i2i−2i−2i2-22i−2i00002−22−20000i2i2−i2−i200000000i2−i22−20000
χ2622-22-22-2-20-202-20020000002i2i−2i−2i2-22i−2i0000−22−220000−i2−i2i2i200000000−i2i2−220000
χ2722-22-22-2-20-202-20020000002i2i−2i−2i-22−2i2i00002−22−20000i2i2−i2−i200000000−i2i2−220000
χ2822-22-22-2-20-202-20020000002i2i−2i−2i-22−2i2i0000−22−220000−i2−i2i2i200000000i2−i22−20000
χ2922-22-22-2-20-202-2002000000−2i−2i2i2i2-2−2i2i00002−22−20000−i2−i2i2i200000000−i2i22−20000
χ3022-22-22-2-20-202-2002000000−2i−2i2i2i2-2−2i2i0000−22−220000i2i2−i2−i200000000i2−i2−220000
χ3122-22-22-2-20-202-2002000000−2i−2i2i2i-222i−2i00002−22−20000−i2−i2i2i200000000i2−i2−220000
χ3222-22-22-2-20-202-2002000000−2i−2i2i2i-222i−2i0000−22−220000i2i2−i2−i200000000−i2i22−20000
χ332-222-2-22-222-2-2-22-220000-222i−2i2i−2i0000002i−2i000000000000002i−2i2-20000000000
χ342-222-2-22-222-2-2-22-220000-222i−2i2i−2i0000002i−2i00000000000000−2i2i-220000000000
χ352-222-2-22-222-2-2-22-220000-22−2i2i−2i2i000000−2i2i000000000000002i−2i-220000000000
χ362-222-2-22-222-2-2-22-220000-22−2i2i−2i2i000000−2i2i00000000000000−2i2i2-20000000000
χ372-222-2-22-2-222-2-2-2222i2i−2i−2i2-22i−2i2i−2i00002i−2i−2i2i000022-2-200000000000000000000
χ382-222-2-22-2-222-2-2-2222i2i−2i−2i2-2−2i2i−2i2i00002i−2i2i−2i0000-2-22200000000000000000000
χ392-222-2-22-2-222-2-2-222−2i−2i2i2i2-22i−2i2i−2i0000−2i2i−2i2i0000-2-22200000000000000000000
χ402-222-2-22-2-222-2-2-222−2i−2i2i2i2-2−2i2i−2i2i0000−2i2i2i−2i000022-2-200000000000000000000
χ412-222-2-22-2-2-2222-22-22i2i−2i−2i-2200000000−2i2i00000000002-22-20000000000002i−2i00
χ422-222-2-22-2-2-2222-22-22i2i−2i−2i-2200000000−2i2i0000000000-22-22000000000000−2i2i00
χ432-222-2-22-2-2-2222-22-2−2i−2i2i2i-22000000002i−2i00000000002-22-2000000000000−2i2i00
χ442-222-2-22-2-2-2222-22-2−2i−2i2i2i-22000000002i−2i0000000000-22-220000000000002i−2i00
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ46444-44-4-4-440-400-440000000000000000000000022−2222−2200000000000000000000
χ47444-44-4-4-440-400-4400000000000000000000000−2222−222200000000000000000000
χ48444-44-4-4-4-404004-404-44-4000000000000000000000000000000000000000000
χ49444-44-4-4-4-404004-40-44-44000000000000000000000000000000000000000000
χ5044-44-44-4-4040-4400-400000000000000000022−22−2222000000000000000000000000
χ5144-44-44-4-4040-4400-4000000000000000000−222222−22000000000000000000000000
χ524-444-4-44-44-4-4444-4-400004-40000000000000000000000000000000000000000
χ534-44-4-44-4440400-4-404i−4i−4i4i000000000000000000000000000000000000000000
χ544-44-4-44-4440400-4-40−4i4i4i−4i000000000000000000000000000000000000000000
χ554-44-4-44-44-40-400440000000000000000000000022−22−222200000000000000000000
χ564-44-4-44-44-40-4004400000000000000000000000−222222−2200000000000000000000
χ574-4-444-4-440404-400-4000000000000000000000000002i2−2i2−2i22i20000000000000000
χ584-4-444-4-440404-400-400000000000000000000000000−2i22i22i2−2i20000000000000000
χ594-4-444-4-440-40-440040000004-4-44000000000000000000000000000000000000
χ604-4-444-4-440-40-44004000000-444-4000000000000000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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