Finite Group Databasebeta

← Group #317596

Character table — Group #317596

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888844444444448888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ10111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ12111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ172222222222-2-2-222-2-2-2222200000000-2-222-2-222-2-20000000000000000000000000000
χ182222222222-2-2-222-2-2-2222200000000-2-2-2-222-2-2220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-2000000002222-2-2-2-2220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-20000000022-2-22222-2-20000000000000000000000000000
χ2122222222-2-2222-2-22-2-222-2-22222-2-2-2-22-20000000022-2-2000000000000000000000000
χ2222222222-2-2222-2-22-2-222-2-2-2-2-2-222222-200000000-2-222000000000000000000000000
χ2322222222-2-2222-2-22-2-2-2-2222222-2-2-2-2-2200000000-2-222000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-222-2-2-2-22222-220000000022-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000-220000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000-22000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-222000000002-20000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-222000000002-2000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-2-2-22-22-22-2-22-222-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000002-22i−2i0000000000
χ30222-2-2-22-22-22-2-22-222-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000-22−2i2i0000000000
χ31222-2-2-22-22-22-2-22-222-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-2−2i2i0000000000
χ32222-2-2-22-22-22-2-22-222-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000-222i−2i0000000000
χ33222-2-2-22-2-222-2-2-222-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000002-200002i−2i00000000
χ34222-2-2-22-2-222-2-2-222-2200002i2i−2i−2i−2i−2i2i2i0000000000000000000000-220000−2i2i00000000
χ35222-2-2-22-2-222-2-2-222-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000002-20000−2i2i00000000
χ36222-2-2-22-2-222-2-2-222-220000−2i−2i2i2i2i2i−2i−2i0000000000000000000000-2200002i−2i00000000
χ372-2-22-2-22222000-2-20002-22-22−22−22−22−2002i−2i002i−2i002−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-2-22-2-22222000-2-20002-22-22−22−22−22−200−2i2i00−2i2i002−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-2-22-2-22222000-2-20002-22-2−22−22−22−22002i−2i002i−2i00−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-2-22-2-22222000-2-20002-22-2−22−22−22−2200−2i2i00−2i2i00−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-2-22-2-22222000-2-2000-22-222−22−22−22−2002i−2i00−2i2i00−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ422-2-22-2-22222000-2-2000-22-222−22−22−22−200−2i2i002i−2i00−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ432-2-22-2-22222000-2-2000-22-22−22−22−22−22002i−2i00−2i2i002−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ442-2-22-2-22222000-2-2000-22-22−22−22−22−2200−2i2i002i−2i002−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ452-2-22-2-222-2-2000220002-2-222−22−2−22−2200002-2002-22−2−222−2−222−2−220000000000000000
χ462-2-22-2-222-2-2000220002-2-222−22−2−22−220000-2200-222−2−22−222−2−222−20000000000000000
χ472-2-22-2-222-2-2000220002-2-22−22−222−22−200002-2002-2−222−2−222−2−222−20000000000000000
χ482-2-22-2-222-2-2000220002-2-22−22−222−22−20000-2200-22−222−22−2−222−2−220000000000000000
χ492-2-22-2-222-2-200022000-222-22−22−2−22−2200002-200-22−222−22−2−22−222−20000000000000000
χ502-2-22-2-222-2-200022000-222-22−22−2−22−220000-22002-2−222−2−222−22−2−220000000000000000
χ512-2-22-2-222-2-200022000-222-2−22−222−22−200002-200-222−2−22−222−22−2−220000000000000000
χ522-2-22-2-222-2-200022000-222-2−22−222−22−20000-22002-22−2−222−2−22−222−20000000000000000
χ53444-4-4-44-44-4-4444-4-4-4400000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-44-444-44-44-400000000000000000000000000000000000000000000000000
χ5544-444-4-4-40044-400-40000000000000000000000000000000000000000000022−22000000
χ5644-444-4-4-40044-400-400000000000000000000000000000000000000000000−2222000000
χ5744-444-4-4-400-4-4400400000000000000000000000000000000000000000000002i2−2i20000
χ5844-444-4-4-400-4-440040000000000000000000000000000000000000000000000−2i22i20000
χ5944-4-4-44-44004-4400-40000000000000000000000000000000000000000000000002i2−2i200
χ6044-4-4-44-44004-4400-4000000000000000000000000000000000000000000000000−2i22i200
χ6144-4-4-44-4400-44-40040000000000000000000000000000000000000000000000000022−22
χ6244-4-4-44-4400-44-400400000000000000000000000000000000000000000000000000−2222
χ634-4-4-4444-44-4000-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ644-4-4-4444-44-4000-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ654-4-4-4444-4-440004-400000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ664-4-4-4444-4-440004-40000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ678-888-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-88-8-88000000000000000000000000000000000000000000000000000000000000

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