Finite Group Databasebeta

← Group #277448

Character table — Group #277448

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
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-11-1
χ911111111111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111
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
χ172222222222-2-22-22-2-22222-20000000022-2-20000-2-2220000-2-200000000000000000000
χ182222222222-2-22-22-2-22222-200000000-2-2-2-2000022-2-200002200000000000000000000
χ192222222222-2-22-22-2-2-2-2-2-2-20000000022220000-2-2-2-200002200000000000000000000
χ202222222222-2-22-22-2-2-2-2-2-2-200000000-2-222000022220000-2-200000000000000000000
χ2122222222-2-222-22-22-20000-22222-2-2-2-200002222000000000000000000-2-20000000000
χ2222222222-2-222-22-22-20000-22222-2-2-2-20000-2-2-2-2000000000000000000220000000000
χ2322222222-2-222-22-22-20000-2-2-2-2-22222000022-2-2000000000000000000-220000000000
χ2422222222-2-222-22-22-20000-2-2-2-2-222220000-2-2220000000000000000002-20000000000
χ25222-2-2-2-222-200-202002i2i−2i−2i022−2−222−2−22-2000000002i−2ii2i2−i2−i20022−2−2i2i2−i2−i2000000000000
χ26222-2-2-2-222-200-202002i2i−2i−2i022−2−222−2−2-2200000000−2i2ii2i2−i2−i200−2−222−i2−i2i2i2000000000000
χ27222-2-2-2-222-200-202002i2i−2i−2i0−2−222−2−2222-2000000002i−2i−i2−i2i2i200−2−222−i2−i2i2i2000000000000
χ28222-2-2-2-222-200-202002i2i−2i−2i0−2−222−2−222-2200000000−2i2i−i2−i2i2i20022−2−2i2i2−i2−i2000000000000
χ29222-2-2-2-222-200-20200−2i−2i2i2i022−2−222−2−22-200000000−2i2i−i2−i2i2i20022−2−2−i2−i2i2i2000000000000
χ30222-2-2-2-222-200-20200−2i−2i2i2i022−2−222−2−2-22000000002i−2i−i2−i2i2i200−2−222i2i2−i2−i2000000000000
χ31222-2-2-2-222-200-20200−2i−2i2i2i0−2−222−2−2222-200000000−2i2ii2i2−i2−i200−2−222i2i2−i2−i2000000000000
χ32222-2-2-2-222-200-20200−2i−2i2i2i0−2−222−2−222-22000000002i−2ii2i2−i2−i20022−2−2−i2−i2i2i2000000000000
χ332-2222-2-2-2-2200-202002i−2i2i−2i02−22−22−22−2000000002i−2i00i2−i2i2−i22-2i2−i2i2−i22−22−2000000000000
χ342-2222-2-2-2-2200-202002i−2i2i−2i02−22−22−22−200000000−2i2i00i2−i2i2−i2-22−i2i2−i2i2−22−22000000000000
χ352-2222-2-2-2-2200-202002i−2i2i−2i0−22−22−22−22000000002i−2i00−i2i2−i2i22-2−i2i2−i2i2−22−22000000000000
χ362-2222-2-2-2-2200-202002i−2i2i−2i0−22−22−22−2200000000−2i2i00−i2i2−i2i2-22i2−i2i2−i22−22−2000000000000
χ372-2222-2-2-2-2200-20200−2i2i−2i2i02−22−22−22−2000000002i−2i00−i2i2−i2i2-22i2−i2i2−i2−22−22000000000000
χ382-2222-2-2-2-2200-20200−2i2i−2i2i02−22−22−22−200000000−2i2i00−i2i2−i2i22-2−i2i2−i2i22−22−2000000000000
χ392-2222-2-2-2-2200-20200−2i2i−2i2i0−22−22−22−22000000002i−2i00i2−i2i2−i2-22−i2i2−i2i22−22−2000000000000
χ402-2222-2-2-2-2200-20200−2i2i−2i2i0−22−22−22−2200000000−2i2i00i2−i2i2−i22-2i2−i2i2−i2−22−22000000000000
χ412-22-2-222-222-2-2-22-2220000-22-2-22-222-200000000000000000000000000002i−2i2i−2i000000
χ422-22-2-222-222-2-2-22-2220000-22-2-22-222-20000000000000000000000000000−2i2i−2i2i000000
χ432-22-2-222-222-2-2-22-2220000-2-222-22-2-2200000000000000000000000000002i−2i−2i2i000000
χ442-22-2-222-222-2-2-22-2220000-2-222-22-2-220000000000000000000000000000−2i2i2i−2i000000
χ452-22-2-222-2-2-2222-22-222-2-22-200000000002-2000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ462-22-2-222-2-2-2222-22-222-2-22-200000000002-200000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ472-22-2-222-2-2-2222-22-22-222-2-20000000000-22000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ482-22-2-222-2-2-2222-22-22-222-2-20000000000-2200000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ492-22-2-222-2-2-2-2-22222-22-2-2222-2-222-2-2200-22000000002-2-220000000000000000000000
χ502-22-2-222-2-2-2-2-22222-22-2-222-222-2-222-200-2200000000-222-20000000000000000000000
χ512-22-2-222-2-2-2-2-22222-2-222-222-2-222-2-22002-200000000-222-20000000000000000000000
χ522-22-2-222-2-2-2-2-22222-2-222-22-222-2-222-2002-2000000002-2-220000000000000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-4-4-44-440040-400000002222−22−22−22−22222200000000000000000000000000000000000000
χ55444-4-4-4-44-440040-40000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5644-44-44-4-4004-4040-4000000000000000000004-4000000000000000000000000000000
χ5744-44-44-4-4004-4040-400000000000000000000-44000000000000000000000000000000
χ5844-44-44-4-400-440-4040000000000000000000000000000000000000000000000002i2−2i200
χ5944-44-44-4-400-440-404000000000000000000000000000000000000000000000000−2i22i200
χ604-4444-4-4-44-40040-4000000022−2222−22−2222−222200000000000000000000000000000000000000
χ614-4444-4-4-44-40040-40000000−2222−222222−2222−2200000000000000000000000000000000000000
χ624-44-4-444-44444-4-4-4-4-4000040000000000000000000000000000000000000000000000
χ634-4-4-444-44004-40-404000000000000000000000000000000000000000000000022−220000
χ644-4-4-444-44004-40-4040000000000000000000000000000000000000000000000−22220000
χ654-4-4-444-4400-44040-40000000000000000004i−4i00000000000000000000000000000000
χ664-4-4-444-4400-44040-4000000000000000000−4i4i00000000000000000000000000000000
χ6788-8-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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