Finite Group Databasebeta

← Group #315344

Character table — Group #315344

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888844444444444488888888888888888844884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ81111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ9111111111111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1
χ10111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-11-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111-1-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-11-11-1
χ17222222222-22-2-222-2-2-222220000-2-2-2-200220000-2-2000000000000000000002-2000000
χ18222222222-22-2-222-2-2-222220000-2-2-2-200-2-200002200000000000000000000-22000000
χ19222222222-22-2-222-2-2-2-2-2-2-20000222200220000-2-200000000000000000000-22000000
χ20222222222-22-2-222-2-2-2-2-2-2-20000222200-2-2000022000000000000000000002-2000000
χ2122222222-22-222-2-22-2-2000022220000220022-2-200-2-2-2-2000000000000000000000000
χ2222222222-22-222-2-22-2-2000022220000-2-200-2-2220022-2-2000000000000000000000000
χ2322222222-22-222-2-22-2-20000-2-2-2-200002200-2-22200-2-222000000000000000000000000
χ2422222222-22-222-2-22-2-20000-2-2-2-20000-2-20022-2-2002222000000000000000000000000
χ25222-2-2-2-2222-2-2-22-22-2200002i2i−2i−2i00000000000000002i−2i22-2-22i2i−2i−2i0000000000000000
χ26222-2-2-2-2222-2-2-22-22-2200002i2i−2i−2i00000000000000002i−2i-2-222−2i−2i2i2i0000000000000000
χ27222-2-2-2-2222-2-2-22-22-220000−2i−2i2i2i0000000000000000−2i2i22-2-2−2i−2i2i2i0000000000000000
χ28222-2-2-2-2222-2-2-22-22-220000−2i−2i2i2i0000000000000000−2i2i-2-2222i2i−2i−2i0000000000000000
χ29222-2-2-2-22-222-2-2-2222-222-2-22i2i−2i−2i22-2-2000000000000−2i2i0000000000002i2i−2i−2i00000000
χ30222-2-2-2-22-222-2-2-2222-222-2-2−2i−2i2i2i22-2-20000000000002i−2i000000000000−2i−2i2i2i00000000
χ31222-2-2-2-22-222-2-2-2222-2-2-2222i2i−2i−2i-2-222000000000000−2i2i000000000000−2i−2i2i2i00000000
χ32222-2-2-2-22-222-2-2-2222-2-2-222−2i−2i2i2i-2-2220000000000002i−2i0000000000002i2i−2i−2i00000000
χ33222-2-2-2-22-2-2222-22-2-2222-2-20000-2-22200000000000000000000002i2i−2i−2i0000002i−2i0000
χ34222-2-2-2-22-2-2222-22-2-2222-2-20000-2-2220000000000000000000000−2i−2i2i2i000000−2i2i0000
χ35222-2-2-2-22-2-2222-22-2-22-2-222000022-2-200000000000000000000002i2i−2i−2i000000−2i2i0000
χ36222-2-2-2-22-2-2222-22-2-22-2-222000022-2-20000000000000000000000−2i−2i2i2i0000002i−2i0000
χ372-2-22-22-220202-200-2002−22−22-22-22−22−22i−2i002i−2i00000000i2−i2i2−i2i2−i2i2−i200002−22−200000000
χ382-2-22-22-220202-200-2002−22−22-22-22−22−2−2i2i00−2i2i00000000−i2i2−i2i2−i2i2−i2i200002−22−200000000
χ392-2-22-22-220202-200-2002−22−2-22-222−22−22i−2i00−2i2i00000000−i2i2−i2i2i2−i2i2−i20000−22−2200000000
χ402-2-22-22-220202-200-2002−22−2-22-222−22−2−2i2i002i−2i00000000i2−i2i2−i2−i2i2−i2i20000−22−2200000000
χ412-2-22-22-220202-200-200−22−222-22-2−22−222i−2i002i−2i00000000−i2i2−i2i2−i2i2−i2i20000−22−2200000000
χ422-2-22-22-220202-200-200−22−222-22-2−22−22−2i2i00−2i2i00000000i2−i2i2−i2i2−i2i2−i20000−22−2200000000
χ432-2-22-22-220202-200-200−22−22-22-22−22−222i−2i00−2i2i00000000i2−i2i2−i2−i2i2−i2i200002−22−200000000
χ442-2-22-22-220202-200-200−22−22-22-22−22−22−2i2i002i−2i00000000−i2i2−i2i2i2−i2i2−i200002−22−200000000
χ452-2-2-22-222020-2200-2002−2−222i−2i−2i2i2−2−220000002i−2i002-200i2−i2−i2i2−222−20000i2−i2−i2i200000000
χ462-2-2-22-222020-2200-2002−2−222i−2i−2i2i2−2−22000000−2i2i00-2200−i2i2i2−i22−2−220000i2−i2−i2i200000000
χ472-2-2-22-222020-2200-2002−2−22−2i2i2i−2i2−2−220000002i−2i00-2200i2−i2−i2i22−2−220000−i2i2i2−i200000000
χ482-2-2-22-222020-2200-2002−2−22−2i2i2i−2i2−2−22000000−2i2i002-200−i2i2i2−i2−222−20000−i2i2i2−i200000000
χ492-2-2-22-222020-2200-200−222−22i−2i−2i2i−222−20000002i−2i002-200−i2i2i2−i22−2−220000−i2i2i2−i200000000
χ502-2-2-22-222020-2200-200−222−22i−2i−2i2i−222−2000000−2i2i00-2200i2−i2−i2i2−222−20000−i2i2i2−i200000000
χ512-2-2-22-222020-2200-200−222−2−2i2i2i−2i−222−20000002i−2i00-2200−i2i2i2−i2−222−20000i2−i2−i2i200000000
χ522-2-2-22-222020-2200-200−222−2−2i2i2i−2i−222−2000000−2i2i002-200i2−i2−i2i22−2−220000i2−i2−i2i200000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ54444-4-4-4-444-4-4444-4-44-400000000000000000000000000000000000000000000000000
χ5544-444-4-4-440-400-44000000000000000000000000000000000000022−2222−22000000000000
χ5644-444-4-4-440-400-440000000000000000000000000000000000000−2222−2222000000000000
χ5744-444-4-4-4-404004-4000000000000000004-40000000000000000000000000000000000
χ5844-444-4-4-4-404004-400000000000000000-440000000000000000000000000000000000
χ5944-4-4-444-440400-4-4000000000000000000000004-40000000000000000000000000000
χ6044-4-4-444-440400-4-400000000000000000000000-440000000000000000000000000000
χ6144-4-4-444-4-40-4004400000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ6244-4-4-444-4-40-400440000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ634-4-44-44-440-40-440040022−2222−220000−2222−222200000000000000000000000000000000000000
χ644-4-44-44-440-40-4400400−2222−2222000022−2222−2200000000000000000000000000000000000000
χ654-4-4-44-4440-404-40040022−22−22220000−222222−2200000000000000000000000000000000000000
χ664-4-4-44-4440-404-400400−222222−22000022−22−222200000000000000000000000000000000000000
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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