Finite Group Databasebeta

← Group #278300

Character table — Group #278300

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488882244444444488884444888888888888888888888888824882288
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1111-1-1-1-1-1-1111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ71111111111111111-1-1111-1-1-1-1-1-11111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ81111111111111111-1-1111-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ9111111111111-1-1-1-111111111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111-11-1
χ10111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-11-11
χ11111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-1-11-11
χ12111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1111111-1-11-11-1
χ13111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-11111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-111-1
χ14111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-11-1-11
χ15111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1111-1-11
χ16111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1111111-1-1-1-1-1-111-111-1
χ172222222-222-22222222-2-2-2-2-2-2-222-2-2220000-2-2-2000022000000000000000000000000
χ182222222-222-222222-2-2-2-2-22222-2-2-2-2220000-2220000-2-2000000000000000000000000
χ192222222-222-22-2-2-2-222-2-2-2-2-2-2-22222-2-200002220000-2-2000000000000000000000000
χ202222222-222-22-2-2-2-2-2-2-2-2-22222-2-222-2-200002-2-2000022000000000000000000000000
χ212222-2-222-2-2220000222-2-222-2-2-2-20000000000000000022-2-20000000000002-2000000
χ222222-2-222-2-2220000222-2-222-2-2-2-200000000000000000-2-222000000000000-22000000
χ232222-2-222-2-2220000-2-22-2-2-2-222220000000000000000022-2-2000000000000-22000000
χ242222-2-222-2-2220000-2-22-2-2-2-2222200000000000000000-2-2220000000000002-2000000
χ252222-2-22-2-2-2-22000022-222-2-222-2-200002i2i−2i−2i0000000000000000000000000002i−2i0000
χ262222-2-22-2-2-2-22000022-222-2-222-2-20000−2i−2i2i2i000000000000000000000000000−2i2i0000
χ272222-2-22-2-2-2-220000-2-2-22222-2-22200002i2i−2i−2i000000000000000000000000000−2i2i0000
χ282222-2-22-2-2-2-220000-2-2-22222-2-2220000−2i−2i2i2i0000000000000000000000000002i−2i0000
χ292222-2-2-22222-2222200-22-200000022-2-20000-2002222000000-2-2-2-20000000000000000
χ302222-2-2-22222-2222200-22-200000022-2-20000-200-2-2-2-200000022220000000000000000
χ312222-2-2-22222-2-2-2-2-200-22-2000000-2-222000020022-2-2000000-2-2220000000000000000
χ322222-2-2-22222-2-2-2-2-200-22-2000000-2-2220000200-2-22200000022-2-20000000000000000
χ332222-2-2-2-222-2-22222002-22000000-2-2-2-20000200000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ342222-2-2-2-222-2-22222002-22000000-2-2-2-2000020000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ352222-2-2-2-222-2-2-2-2-2-2002-2200000022220000-200000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ362222-2-2-2-222-2-2-2-2-2-2002-2200000022220000-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ372-2-222-220-220-222-2-2000002i−2i2i−2i00002-2000002i−2i2−22−20000002−22−2i2−i2i2−i2i2−i2i2−i200000000
χ382-2-222-220-220-222-2-2000002i−2i2i−2i00002-2000002i−2i−22−22000000−22−22−i2i2−i2i2−i2i2−i2i200000000
χ392-2-222-220-220-222-2-200000−2i2i−2i2i00002-200000−2i2i2−22−20000002−22−2−i2i2−i2i2−i2i2−i2i200000000
χ402-2-222-220-220-222-2-200000−2i2i−2i2i00002-200000−2i2i−22−22000000−22−22i2−i2i2−i2i2−i2i2−i200000000
χ412-2-222-220-220-2-2-222000002i−2i2i−2i0000-2200000−2i2i2−2−220000002−2−22i2−i2i2−i2−i2i2−i2i200000000
χ422-2-222-220-220-2-2-222000002i−2i2i−2i0000-2200000−2i2i−222−2000000−222−2−i2i2−i2i2i2−i2i2−i200000000
χ432-2-222-220-220-2-2-22200000−2i2i−2i2i0000-22000002i−2i2−2−220000002−2−22−i2i2−i2i2i2−i2i2−i200000000
χ442-2-222-220-220-2-2-22200000−2i2i−2i2i0000-22000002i−2i−222−2000000−222−2i2−i2i2−i2−i2i2−i2i200000000
χ452-2-22-22-20-220222-2-22-200000002-200-2200000002−22−22-20000−22−222−2−222−2−2200000000
χ462-2-22-22-20-220222-2-22-200000002-200-220000000−22−222-200002−22−2−222−2−222−200000000
χ472-2-22-22-20-220222-2-2-220000000-2200-2200000002−22−2-220000−22−22−222−2−222−200000000
χ482-2-22-22-20-220222-2-2-220000000-2200-220000000−22−22-2200002−22−22−2−222−2−2200000000
χ492-2-22-22-20-2202-2-2222-200000002-2002-200000002−2−22-220000−222−22−2−22−222−200000000
χ502-2-22-22-20-2202-2-2222-200000002-2002-20000000−222−2-2200002−2−22−222−22−2−2200000000
χ512-2-22-22-20-2202-2-222-220000000-22002-200000002−2−222-20000−222−2−222−22−2−2200000000
χ522-2-22-22-20-2202-2-222-220000000-22002-20000000−222−22-200002−2−222−2−22−222−200000000
χ53444444-44-4-44-4000000-4-4400000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-400000044-400000000000000000000000000000000000000000000000
χ5544-4-4000400-4022−2222−220000000000022−22002i−2i2i−2i000000000002i2−2i200000000000000000000
χ5644-4-4000400-4022−2222−220000000000022−2200−2i2i−2i2i00000000000−2i22i200000000000000000000
χ5744-4-4000400-40−2222−222200000000000−2222002i−2i2i−2i00000000000−2i22i200000000000000000000
χ5844-4-4000400-40−2222−222200000000000−222200−2i2i−2i2i000000000002i2−2i200000000000000000000
χ5944-4-4000-4004022−2222−2200000000000−2222002-2-2200000000022−220000000000000000000000
χ6044-4-4000-4004022−2222−2200000000000−222200-222-2000000000−22220000000000000000000000
χ6144-4-4000-40040−2222−22220000000000022−22002-2-22000000000−22220000000000000000000000
χ6244-4-4000-40040−2222−22220000000000022−2200-222-200000000022−220000000000000000000000
χ634-4-444-4-404-40400004-40000000-4400000000000000000000000000000000000000000
χ644-4-444-4-404-4040000-4400000004-400000000000000000000000000000000000000000
χ654-4-44-44404-40-40000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ664-4-44-44404-40-4000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ678-88-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-88-800000000−424242−420000000000000000000000000000000000000000000000000000

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