Finite Group Databasebeta

← Group #288184

Character table — Group #288184

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-111-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-11-1-11111-1-11-1
χ911111111111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-111111-1-1-111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1111-1-111-1-1-11
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
χ17222222222-2-22-222-2-20000-22222-2-2-2-200002222000000000000000000-2-20000000000
χ18222222222-2-22-222-2-20000-22222-2-2-2-20000-2-2-2-2000000000000000000220000000000
χ19222222222-2-22-222-2-20000-2-2-2-2-22222000022-2-2000000000000000000-220000000000
χ20222222222-2-22-222-2-20000-2-2-2-2-222220000-2-2220000000000000000002-20000000000
χ2122222222-222-22-2-22-22222-20000000022-2-20000-2-22200000000-2-20000000000000000
χ2222222222-222-22-2-22-22222-200000000-2-2-2-2000022-2-200000000220000000000000000
χ2322222222-222-22-2-22-2-2-2-2-2-20000000022220000-2-2-2-200000000220000000000000000
χ2422222222-222-22-2-22-2-2-2-2-2-200000000-2-2220000222200000000-2-20000000000000000
χ25222-2-2-2-2202-20-200202i2i−2i−2i022−2−222−2−22-2000000002i−2ii2i2−i2−i222−2−200i2i2−i2−i2000000000000
χ26222-2-2-2-2202-20-200202i2i−2i−2i022−2−222−2−2-2200000000−2i2ii2i2−i2−i2−2−22200−i2−i2i2i2000000000000
χ27222-2-2-2-2202-20-200202i2i−2i−2i0−2−222−2−2222-2000000002i−2i−i2−i2i2i2−2−22200−i2−i2i2i2000000000000
χ28222-2-2-2-2202-20-200202i2i−2i−2i0−2−222−2−222-2200000000−2i2i−i2−i2i2i222−2−200i2i2−i2−i2000000000000
χ29222-2-2-2-2202-20-20020−2i−2i2i2i022−2−222−2−22-200000000−2i2i−i2−i2i2i222−2−200−i2−i2i2i2000000000000
χ30222-2-2-2-2202-20-20020−2i−2i2i2i022−2−222−2−2-22000000002i−2i−i2−i2i2i2−2−22200i2i2−i2−i2000000000000
χ31222-2-2-2-2202-20-20020−2i−2i2i2i0−2−222−2−2222-200000000−2i2ii2i2−i2−i2−2−22200i2i2−i2−i2000000000000
χ32222-2-2-2-2202-20-20020−2i−2i2i2i0−2−222−2−222-22000000002i−2ii2i2−i2−i222−2−200−i2−i2i2i2000000000000
χ332-2-22-22-2202-20200-202-22-202−22−22−22−2000000002i−2i002−22−2i2−i2i2−i22i−2ii2−i2i2−i2000000000000
χ342-2-22-22-2202-20200-202-22-202−22−22−22−200000000−2i2i002−22−2−i2i2−i2i2−2i2i−i2i2−i2i2000000000000
χ352-2-22-22-2202-20200-202-22-20−22−22−22−22000000002i−2i00−22−22−i2i2−i2i22i−2i−i2i2−i2i2000000000000
χ362-2-22-22-2202-20200-202-22-20−22−22−22−2200000000−2i2i00−22−22i2−i2i2−i2−2i2ii2−i2i2−i2000000000000
χ372-2-22-22-2202-20200-20-22-2202−22−22−22−2000000002i−2i00−22−22i2−i2i2−i2−2i2i−i2i2−i2i2000000000000
χ382-2-22-22-2202-20200-20-22-2202−22−22−22−200000000−2i2i00−22−22−i2i2−i2i22i−2ii2−i2i2−i2000000000000
χ392-2-22-22-2202-20200-20-22-220−22−22−22−22000000002i−2i002−22−2−i2i2−i2i2−2i2ii2−i2i2−i2000000000000
χ402-2-22-22-2202-20200-20-22-220−22−22−22−2200000000−2i2i002−22−2i2−i2i2−i22i−2i−i2i2−i2i2000000000000
χ412-2-2-22-222222-2-22-2-2-22i−2i−2i2i200000000002i−2i0000000000002i−2i−2i2i00-222-2000000000000
χ422-2-2-22-222222-2-22-2-2-22i−2i−2i2i200000000002i−2i000000000000−2i2i2i−2i002-2-22000000000000
χ432-2-2-22-222222-2-22-2-2-2−2i2i2i−2i20000000000−2i2i0000000000002i−2i−2i2i002-2-22000000000000
χ442-2-2-22-222222-2-22-2-2-2−2i2i2i−2i20000000000−2i2i000000000000−2i2i2i−2i00-222-2000000000000
χ452-2-2-22-222-2222-2-22-222i−2i−2i2i-22-2-222-2-2200−2i2i000000002i−2i−2i2i0000000000000000000000
χ462-2-2-22-222-2222-2-22-222i−2i−2i2i-2-222-2-222-200−2i2i00000000−2i2i2i−2i0000000000000000000000
χ472-2-2-22-222-2222-2-22-22−2i2i2i−2i-22-2-222-2-22002i−2i00000000−2i2i2i−2i0000000000000000000000
χ482-2-2-22-222-2222-2-22-22−2i2i2i−2i-2-222-2-222-2002i−2i000000002i−2i−2i2i0000000000000000000000
χ492-2-2-22-222-2-2-222-222-2000022-2-22-222-200000000000000000000000000002-22-2000000
χ502-2-2-22-222-2-2-222-222-2000022-2-22-222-20000000000000000000000000000-22-22000000
χ512-2-2-22-222-2-2-222-222-200002-222-22-2-2200000000000000000000000000002-2-22000000
χ522-2-2-22-222-2-2-222-222-200002-222-22-2-220000000000000000000000000000-222-2000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-4-4-440-440400-40000002222−22−22−22−22222200000000000000000000000000000000000000
χ55444-4-4-4-440-440400-4000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5644-44-4-44-440040-4-40000000000000000000004-4000000000000000000000000000000
χ5744-44-4-44-440040-4-4000000000000000000000-44000000000000000000000000000000
χ5844-44-4-44-4-400-404400000000000000000000000000000000000000000000000002i2−2i200
χ5944-44-4-44-4-400-40440000000000000000000000000000000000000000000000000−2i22i200
χ604-44-4-444-4400-40-44000000000000000000000000000000000000000000000002i2−2i20000
χ614-44-4-444-4400-40-4400000000000000000000000000000000000000000000000−2i22i20000
χ624-44-4-444-4-400404-400000000000000000004i−4i00000000000000000000000000000000
χ634-44-4-444-4-400404-40000000000000000000−4i4i00000000000000000000000000000000
χ644-4-44-44-440-440-400400000022−2222−22−2222−222200000000000000000000000000000000000000
χ654-4-44-44-440-440-4004000000−2222−222222−2222−2200000000000000000000000000000000000000
χ664-4-4-44-4444-4-4-444-4440000-40000000000000000000000000000000000000000000000
χ6788-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000000000000000000000000000000000000000000000000000000000

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