Finite Group Databasebeta

← Group #292550

Character table — Group #292550

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444422444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ91111111111111111-1-1-1-1-1-111111-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-111111-1-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-111-11
χ121111111111111111-1-1-1-1-1-111111-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1111-1
χ1722222222222-2-2-2-222222-2-20000-2-2-2-2220000-2-2000000000000000000-220000000000
χ1822222222222-2-2-2-222222-2-20000-2-2-2-2-2-20000220000000000000000002-20000000000
χ1922222222222-2-2-2-22-2-2-2-2220000-222-222000022000000000000000000-2-20000000000
χ2022222222222-2-2-2-22-2-2-2-2220000-222-2-2-20000-2-2000000000000000000220000000000
χ2122222222-2-2-22222-222-2-2222222-2-2-2-200-2-2-2-200220000000000000000000000000000
χ2222222222-2-2-22222-222-2-222-2-2-2-2-2-2-2-200222200-2-20000000000000000000000000000
χ2322222222-2-2-22222-2-2-222-2-22222-222-200-2-22200-2-20000000000000000000000000000
χ2422222222-2-2-22222-2-2-222-2-2-2-2-2-2-222-20022-2-200220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-20000222200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-2000022220000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200002-2-2200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200002-2-220000000000000000000000000000-222-2000000
χ29222-2-2-2-2222-22-22-2-20000002i2i−2i−2i-2002002i−2i0000002i2i−2i−2i000022-2-20000000000000000
χ30222-2-2-2-2222-22-22-2-20000002i2i−2i−2i-2002002i−2i000000−2i−2i2i2i0000-2-2220000000000000000
χ31222-2-2-2-2222-22-22-2-2000000−2i−2i2i2i-200200−2i2i0000002i2i−2i−2i0000-2-2220000000000000000
χ32222-2-2-2-2222-22-22-2-2000000−2i−2i2i2i-200200−2i2i000000−2i−2i2i2i000022-2-20000000000000000
χ33222-2-2-2-22-2-222-22-220000002i2i−2i−2i200-200−2i2i000000000022-2-200002i2i−2i−2i000000000000
χ34222-2-2-2-22-2-222-22-220000002i2i−2i−2i200-200−2i2i0000000000-2-2220000−2i−2i2i2i000000000000
χ35222-2-2-2-22-2-222-22-22000000−2i−2i2i2i200-2002i−2i000000000022-2-20000−2i−2i2i2i000000000000
χ36222-2-2-2-22-2-222-22-22000000−2i−2i2i2i200-2002i−2i0000000000-2-22200002i2i−2i−2i000000000000
χ372-2222-2-2-2000-2-22202-2002-22i−2i2i−2i0000000000002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ382-2222-2-2-2000-2-22202-2002-22i−2i2i−2i0000000000002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ392-2222-2-2-2000-2-22202-2002-2−2i2i−2i2i000000000000−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ402-2222-2-2-2000-2-22202-2002-2−2i2i−2i2i000000000000−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ412-2222-2-2-2000-2-2220-2200-222i−2i2i−2i000000000000−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ422-2222-2-2-2000-2-2220-2200-222i−2i2i−2i000000000000−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ432-2222-2-2-2000-2-2220-2200-22−2i2i−2i2i0000000000002i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ442-2222-2-2-2000-2-2220-2200-22−2i2i−2i2i0000000000002i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ452-22-2-222-2000-222-20002i−2i002-2-2202i−2i000002i−2i00002−2−22i2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ462-22-2-222-2000-222-20002i−2i002-2-2202i−2i000002i−2i0000−222−2−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ472-22-2-222-2000-222-20002i−2i00-222-202i−2i00000−2i2i00002−2−22i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ482-22-2-222-2000-222-20002i−2i00-222-202i−2i00000−2i2i0000−222−2−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ492-22-2-222-2000-222-2000−2i2i002-2-220−2i2i00000−2i2i00002−2−22−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ502-22-2-222-2000-222-2000−2i2i002-2-220−2i2i00000−2i2i0000−222−2i2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ512-22-2-222-2000-222-2000−2i2i00-222-20−2i2i000002i−2i00002−2−22−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ522-22-2-222-2000-222-2000−2i2i00-222-20−2i2i000002i−2i0000−222−2i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ53444-4-4-4-4444-4-44-44-40000000000400-400000000000000000000000000000000000000
χ54444-4-4-4-44-4-44-44-4440000000000-400400000000000000000000000000000000000000
χ5544-44-44-4-44-440000-4000000000000004-4000000000000000000000000000000000000
χ5644-44-44-4-44-440000-400000000000000-44000000000000000000000000000000000000
χ5744-44-44-4-4-44-400004000000000000000000004i−4i000000000000000000000000000000
χ5844-44-44-4-4-44-40000400000000000000000000−4i4i000000000000000000000000000000
χ5944-4-44-44-44-4-40000400000000000000000000000000000000000000000000002i2−2i20000
χ6044-4-44-44-44-4-4000040000000000000000000000000000000000000000000000−2i22i20000
χ6144-4-44-44-4-4440000-400000000000000000000000000000000000000000000000022−2200
χ6244-4-44-44-4-4440000-4000000000000000000000000000000000000000000000000−222200
χ634-4444-4-4-400044-4-404-400-440000000000000000000000000000000000000000000000
χ644-4444-4-4-400044-4-40-44004-40000000000000000000000000000000000000000000000
χ654-44-4-444-40004-4-440004i−4i0000000−4i4i000000000000000000000000000000000000000
χ664-44-4-444-40004-4-44000−4i4i00000004i−4i000000000000000000000000000000000000000
χ678-8-88-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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