Finite Group Databasebeta

← Group #281143

Character table — Group #281143

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-11111-1-11-1
χ911111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1111-1-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11-1-1-11111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1111-1-1-1-1111-1
χ17222222222-22-2-222-2-20000-22222-2-2-2-200002222000000000000000000-2-20000000000
χ18222222222-22-2-222-2-20000-22222-2-2-2-20000-2-2-2-2000000000000000000220000000000
χ19222222222-22-2-222-2-20000-2-2-2-2-22222000022-2-2000000000000000000-220000000000
χ20222222222-22-2-222-2-20000-2-2-2-2-222220000-2-2220000000000000000002-20000000000
χ2122222222-22-222-2-22-22222-20000000022-2-20000-2-222-2-2000000000000000000000000
χ2222222222-22-222-2-22-22222-200000000-2-2220000-2-2-2-222000000000000000000000000
χ2322222222-22-222-2-22-2-2-2-2-2-20000000022-2-2000022-2-222000000000000000000000000
χ2422222222-22-222-2-22-2-2-2-2-2-200000000-2-22200002222-2-2000000000000000000000000
χ2522-22-22-2-222-2-2-22-22-22i2i−2i−2i200000000000000002i−2i000000002i2i−2i−2i22-2-2000000000000
χ2622-22-22-2-222-2-2-22-22-22i2i−2i−2i200000000000000002i−2i00000000−2i−2i2i2i-2-222000000000000
χ2722-22-22-2-222-2-2-22-22-2−2i−2i2i2i20000000000000000−2i2i000000002i2i−2i−2i-2-222000000000000
χ2822-22-22-2-222-2-2-22-22-2−2i−2i2i2i20000000000000000−2i2i00000000−2i−2i2i2i22-2-2000000000000
χ2922-22-22-2-2-222-2-2-22222i2i−2i−2i-222-2-222-2-200000000−2i2i00002i2i−2i−2i00000000000000000000
χ3022-22-22-2-2-222-2-2-22222i2i−2i−2i-2-2-222-2-22200000000−2i2i0000−2i−2i2i2i00000000000000000000
χ3122-22-22-2-2-222-2-2-2222−2i−2i2i2i-222-2-222-2-2000000002i−2i0000−2i−2i2i2i00000000000000000000
χ3222-22-22-2-2-222-2-2-2222−2i−2i2i2i-2-2-222-2-222000000002i−2i00002i2i−2i−2i00000000000000000000
χ3322-22-22-2-2-2-2222-22-2-20000222-2-2-2-22200000000000000000000000000002i−2i2i−2i000000
χ3422-22-22-2-2-2-2222-22-2-20000222-2-2-2-2220000000000000000000000000000−2i2i−2i2i000000
χ3522-22-22-2-2-2-2222-22-2-200002-2-22222-2-200000000000000000000000000002i−2i−2i2i000000
χ3622-22-22-2-2-2-2222-22-2-200002-2-22222-2-20000000000000000000000000000−2i2i2i−2i000000
χ372-22-2-22-220202-200-202-22-202−22−22−22−2002i−2i000000002i−2i2−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-22-2-22-220202-200-202-22-202−22−22−22−200−2i2i00000000−2i2i2−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ392-22-2-22-220202-200-202-22-20−22−22−22−22002i−2i000000002i−2i−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ402-22-2-22-220202-200-202-22-20−22−22−22−2200−2i2i00000000−2i2i−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ412-22-2-22-220202-200-20-22-2202−22−22−22−2002i−2i00000000−2i2i−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ422-22-2-22-220202-200-20-22-2202−22−22−22−200−2i2i000000002i−2i−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ432-22-2-22-220202-200-20-22-220−22−22−22−22002i−2i00000000−2i2i2−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ442-22-2-22-220202-200-20-22-220−22−22−22−2200−2i2i000000002i−2i2−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ452-2-2-2222-2020-2200-202i−2i−2i2i02−2−222−2−222-2000000002i−2i00i2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ462-2-2-2222-2020-2200-202i−2i−2i2i02−2−222−2−22-2200000000−2i2i00i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ472-2-2-2222-2020-2200-202i−2i−2i2i0−222−2−222−22-2000000002i−2i00−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ482-2-2-2222-2020-2200-202i−2i−2i2i0−222−2−222−2-2200000000−2i2i00−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ492-2-2-2222-2020-2200-20−2i2i2i−2i02−2−222−2−222-200000000−2i2i00−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ502-2-2-2222-2020-2200-20−2i2i2i−2i02−2−222−2−22-22000000002i−2i00−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ512-2-2-2222-2020-2200-20−2i2i2i−2i0−222−2−222−22-200000000−2i2i00i2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ522-2-2-2222-2020-2200-20−2i2i2i−2i0−222−2−222−2-22000000002i−2i00i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ5444-44-44-4-44-4-4444-4-440000-40000000000000000000000000000000000000000000000
χ554-444-4-44-440-400-44000000000000000000000000000000000000000000000002i2−2i20000
χ564-444-4-44-440-400-4400000000000000000000000000000000000000000000000−2i22i20000
χ574-444-4-44-4-404004-400000000000000000004i−4i00000000000000000000000000000000
χ584-444-4-44-4-404004-40000000000000000000−4i4i00000000000000000000000000000000
χ594-44-4-44-440-40-4400400000022−2222−22−2222−222200000000000000000000000000000000000000
χ604-44-4-44-440-40-44004000000−2222−222222−2222−2200000000000000000000000000000000000000
χ614-4-444-4-4440400-4-40000000000000000000004i−4i000000000000000000000000000000
χ624-4-444-4-4440400-4-4000000000000000000000−4i4i000000000000000000000000000000
χ634-4-444-4-44-40-40044000000000000000000000000000000000000000000000000022−2200
χ644-4-444-4-44-40-400440000000000000000000000000000000000000000000000000−222200
χ654-4-4-4444-40-404-400400000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-4-4444-40-404-4004000000−222222−2222−22−222200000000000000000000000000000000000000
χ67888-88-8-8-8000000000000000000000000000000000000000000000000000000000000
χ6888-8-8-8-888000000000000000000000000000000000000000000000000000000000000

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