Finite Group Databasebeta

← Group #278310

Character table — Group #278310

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488882244444444488884444888888888888888888888888844884488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1111-1-1-1-1-1-111111111-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111-1-1111-1-1-1-1-1-111111111-1-11111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1
χ71111111111111111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ81111111111111111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-111
χ9111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-1111-11-1
χ10111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-111-11-11
χ11111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-111-1-1-11-11
χ12111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-1-1-1111111-1-11-11-1
χ13111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-11111-1-1-1-1-1-1111111-1-1-111-1
χ14111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-111-1-1111111-1-1-1-111-1-11-1-11
χ15111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-11111-1-1111-1-11
χ16111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-1111111-1-1-1-1-1-111-111-1
χ17222222-22222-2222222-2-2-2-2-2-2-22222-2-200002200000000-2-2-200000000000000000000
χ18222222-22222-22222-2-2-2-2-22222-2-222-2-20000-2-200000000-22200000000000000000000
χ19222222-22222-2-2-2-2-222-2-2-2-2-2-2-222-2-2220000-2-20000000022200000000000000000000
χ20222222-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222000022000000002-2-200000000000000000000
χ212222-2-222-22-220000222-2-222-2-2-2-2000000000022-2-200000000000000000002-2000000
χ222222-2-222-22-220000222-2-222-2-2-2-20000000000-2-2220000000000000000000-22000000
χ232222-2-222-22-220000-2-22-2-2-2-22222000000000022-2-20000000000000000000-22000000
χ242222-2-222-22-220000-2-22-2-2-2-222220000000000-2-22200000000000000000002-2000000
χ252222-2-22-22-222222200-22-2000000-2-22200000000002222-200-2-2-2-20000000000000000
χ262222-2-22-22-222222200-22-2000000-2-2220000000000-2-2-2-2-20022220000000000000000
χ272222-2-22-22-222-2-2-2-200-22-200000022-2-2000000000022-2-2200-2-2220000000000000000
χ282222-2-22-22-222-2-2-2-200-22-200000022-2-20000000000-2-22220022-2-20000000000000000
χ292222-2-2-22-22-2-2000022-222-2-222-2-200002i2i−2i−2i0000000000000000000000000002i−2i0000
χ302222-2-2-22-22-2-2000022-222-2-222-2-20000−2i−2i2i2i000000000000000000000000000−2i2i0000
χ312222-2-2-22-22-2-20000-2-2-22222-2-22200002i2i−2i−2i000000000000000000000000000−2i2i0000
χ322222-2-2-22-22-2-20000-2-2-22222-2-2220000−2i−2i2i2i0000000000000000000000000002i−2i0000
χ332222-2-2-2-22-22-22222002-22000000-2-2-2-20000000000000020000002i2i−2i−2i2i2i−2i−2i00000000
χ342222-2-2-2-22-22-22222002-22000000-2-2-2-2000000000000002000000−2i−2i2i2i−2i−2i2i2i00000000
χ352222-2-2-2-22-22-2-2-2-2-2002-22000000222200000000000000-20000002i2i−2i−2i−2i−2i2i2i00000000
χ362222-2-2-2-22-22-2-2-2-2-2002-22000000222200000000000000-2000000−2i−2i2i2i2i2i−2i−2i00000000
χ372-2-222-20-222-2022-2-22-200000002-22-20000002-20000i2−i2i2−i2000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ382-2-222-20-222-2022-2-22-200000002-22-20000002-20000−i2i2−i2i2000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ392-2-222-20-222-2022-2-2-220000000-222-2000000-220000i2−i2i2−i2000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ402-2-222-20-222-2022-2-2-220000000-222-2000000-220000−i2i2−i2i2000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ412-2-222-20-222-20-2-2222-200000002-2-22000000-220000i2−i2−i2i2000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ422-2-222-20-222-20-2-2222-200000002-2-22000000-220000−i2i2i2−i2000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ432-2-222-20-222-20-2-222-220000000-22-220000002-20000i2−i2−i2i2000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ442-2-222-20-222-20-2-222-220000000-22-220000002-20000−i2i2i2−i2000−i2i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ452-2-22-22022-2-2022-2-2000002i−2i2i−2i00-22000000000000i2−i2i2−i202i−2i−i2i2−i2i22−2−222−2−2200000000
χ462-2-22-22022-2-2022-2-2000002i−2i2i−2i00-22000000000000−i2i2−i2i202i−2ii2−i2i2−i2−222−2−222−200000000
χ472-2-22-22022-2-2022-2-200000−2i2i−2i2i00-22000000000000i2−i2i2−i20−2i2i−i2i2−i2i2−222−2−222−200000000
χ482-2-22-22022-2-2022-2-200000−2i2i−2i2i00-22000000000000−i2i2−i2i20−2i2ii2−i2i2−i22−2−222−2−2200000000
χ492-2-22-22022-2-20-2-222000002i−2i2i−2i002-2000000000000i2−i2−i2i20−2i2i−i2i2i2−i22−2−22−222−200000000
χ502-2-22-22022-2-20-2-222000002i−2i2i−2i002-2000000000000−i2i2i2−i20−2i2ii2−i2−i2i2−222−22−2−2200000000
χ512-2-22-22022-2-20-2-22200000−2i2i−2i2i002-2000000000000i2−i2−i2i202i−2i−i2i2i2−i2−222−22−2−2200000000
χ522-2-22-22022-2-20-2-22200000−2i2i−2i2i002-2000000000000−i2i2i2−i202i−2ii2−i2−i2i22−2−22−222−200000000
χ534444444-4-4-4-44000000-4-4400000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-400000044-400000000000000000000000000000000000000000000000
χ5544-4-40040000-422−2222−22000000000000022−222-22-2000022−22000000000000000000000000000
χ5644-4-40040000-422−2222−22000000000000022−22-22-220000−2222000000000000000000000000000
χ5744-4-40040000-4−2222−22220000000000000−22222-22-20000−2222000000000000000000000000000
χ5844-4-40040000-4−2222−22220000000000000−2222-22-22000022−22000000000000000000000000000
χ5944-4-400-40000422−2222−220000000000000−22222i−2i−2i2i002i2−2i200000000000000000000000000000
χ6044-4-400-40000422−2222−220000000000000−2222−2i2i2i−2i00−2i22i200000000000000000000000000000
χ6144-4-400-400004−2222−2222000000000000022−222i−2i−2i2i00−2i22i200000000000000000000000000000
χ6244-4-400-400004−2222−2222000000000000022−22−2i2i2i−2i002i2−2i200000000000000000000000000000
χ634-4-444-404-4-4400000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ644-4-444-404-4-440000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ654-4-44-440-4-444000004-40000000-4400000000000000000000000000000000000000000
χ664-4-44-440-4-44400000-4400000004-400000000000000000000000000000000000000000
χ678-88-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-88-800000000−424242−420000000000000000000000000000000000000000000000000000

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