Finite Group Databasebeta

← Group #281177

Character table — Group #281177

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822224444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111111-1-1-111-1-11-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-11111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1111-1-111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11-1-1-111-1-1111-1
χ17222222222-22-2-222-2-20000-22222-2-2-2-200220000220000000000000000-200-200000000
χ18222222222-22-2-222-2-20000-22222-2-2-2-200-2-20000-2-20000000000000000200200000000
χ19222222222-22-2-222-2-20000-2-2-2-2-2222200220000-2-20000000000000000200-200000000
χ20222222222-22-2-222-2-20000-2-2-2-2-2222200-2-20000220000000000000000-200200000000
χ2122222222-22-222-2-22-22222-2000000002200-2-2-2-20022-2-2000000000000000000000000
χ2222222222-22-222-2-22-22222-200000000-2-200-2-22200-2-222000000000000000000000000
χ2322222222-22-222-2-22-2-2-2-2-2-200000000220022-2-200-2-222000000000000000000000000
χ2422222222-22-222-2-22-2-2-2-2-2-200000000-2-20022220022-2-2000000000000000000000000
χ2522-22-2-22-20-202-200202i2i−2i−2i022−2−222−2−20000002i−2i00002-2i2i2−i2−i2i2i2−i2−i222−2−2000000000000
χ2622-22-2-22-20-202-200202i2i−2i−2i022−2−222−2−2000000−2i2i0000-22i2i2−i2−i2−i2−i2i2i2−2−222000000000000
χ2722-22-2-22-20-202-200202i2i−2i−2i0−2−222−2−2220000002i−2i00002-2−i2−i2i2i2−i2−i2i2i2−2−222000000000000
χ2822-22-2-22-20-202-200202i2i−2i−2i0−2−222−2−222000000−2i2i0000-22−i2−i2i2i2i2i2−i2−i222−2−2000000000000
χ2922-22-2-22-20-202-20020−2i−2i2i2i022−2−222−2−20000002i−2i0000-22−i2−i2i2i2i2i2−i2−i2−2−222000000000000
χ3022-22-2-22-20-202-20020−2i−2i2i2i022−2−222−2−2000000−2i2i00002-2−i2−i2i2i2−i2−i2i2i222−2−2000000000000
χ3122-22-2-22-20-202-20020−2i−2i2i2i0−2−222−2−2220000002i−2i0000-22i2i2−i2−i2−i2−i2i2i222−2−2000000000000
χ3222-22-2-22-20-202-20020−2i−2i2i2i0−2−222−2−222000000−2i2i00002-2i2i2−i2−i2i2i2−i2−i2−2−222000000000000
χ332-22-22-22-222-2-2-22-22-22i−2i2i−2i20000000000002i−2i0000000000002i−2i2i−2i2-22-2000000000000
χ342-22-22-22-222-2-2-22-22-22i−2i2i−2i20000000000002i−2i000000000000−2i2i−2i2i-22-22000000000000
χ352-22-22-22-222-2-2-22-22-2−2i2i−2i2i2000000000000−2i2i0000000000002i−2i2i−2i-22-22000000000000
χ362-22-22-22-222-2-2-22-22-2−2i2i−2i2i2000000000000−2i2i000000000000−2i2i−2i2i2-22-2000000000000
χ372-22-22-22-2-222-2-2-22222i−2i2i−2i-22-22-22-22-20000−2i2i000000002i−2i2i−2i00000000000000000000
χ382-22-22-22-2-222-2-2-22222i−2i2i−2i-2-22-22-22-220000−2i2i00000000−2i2i−2i2i00000000000000000000
χ392-22-22-22-2-222-2-2-2222−2i2i−2i2i-22-22-22-22-200002i−2i00000000−2i2i−2i2i00000000000000000000
χ402-22-22-22-2-222-2-2-2222−2i2i−2i2i-2-22-22-22-2200002i−2i000000002i−2i2i−2i00000000000000000000
χ412-22-22-22-2-2-2222-22-2-2000022-22-2-22-220000000000000000000000000002i−2i02i−2i000000
χ422-22-22-22-2-2-2222-22-2-2000022-22-2-22-22000000000000000000000000000−2i2i0−2i2i000000
χ432-22-22-22-2-2-2222-22-2-200002-22-222-22-20000000000000000000000000002i−2i0−2i2i000000
χ442-22-22-22-2-2-2222-22-2-200002-22-222-22-2000000000000000000000000000−2i2i02i−2i000000
χ452-2-2-2-22220-20-2200202-2-2202−2−222−2−222-2000000002-2002−2−222−2−222−2−22000000000000
χ462-2-2-2-22220-20-2200202-2-2202−2−222−2−22-2200000000-22002−2−22−222−2−222−2000000000000
χ472-2-2-2-22220-20-2200202-2-220−222−2−222−22-2000000002-200−222−2−222−2−222−2000000000000
χ482-2-2-2-22220-20-2200202-2-220−222−2−222−2-2200000000-2200−222−22−2−222−2−22000000000000
χ492-2-2-2-22220-20-220020-222-202−2−222−2−222-200000000-2200−222−22−2−22−222−2000000000000
χ502-2-2-2-22220-20-220020-222-202−2−222−2−22-22000000002-200−222−2−222−22−2−22000000000000
χ512-2-2-2-22220-20-220020-222-20−222−2−222−22-200000000-22002−2−22−222−22−2−22000000000000
χ522-2-2-2-22220-20-220020-222-20−222−2−222−2-22000000002-2002−2−222−2−22−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ5444-44-4-44-4040-4400-40000002222−22−22−22−22222200000000000000000000000000000000000000
χ5544-44-4-44-4040-4400-4000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5644-4-444-4-440400-4-4000000000000000000000000000000000000000000000000022−2200
χ5744-4-444-4-440400-4-40000000000000000000000000000000000000000000000000−222200
χ5844-4-444-4-4-40-40044000000000000000000000004i−4i0000000000000000000000000000
χ5944-4-444-4-4-40-4004400000000000000000000000−4i4i0000000000000000000000000000
χ604-44-44-44-44-4-4444-4-440000-40000000000000000000000000000000000000000000000
χ614-4-444-4-4440-400-44000000000000000004-40000000000000000000000000000000000
χ624-4-444-4-4440-400-4400000000000000000-440000000000000000000000000000000000
χ634-4-444-4-44-404004-40000000000000000000000000000000000000000000000022−220000
χ644-4-444-4-44-404004-400000000000000000000000000000000000000000000000−22220000
χ654-4-4-4-44440404-400-400000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-4-4-44440404-400-4000000−222222−2222−22−222200000000000000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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