Finite Group Databasebeta

← Group #349751

Character table — Group #349751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444444444444444444444222244444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11-1-111111111-1-1-1-1-1-1-1-111
χ61111111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-11111111111111-1-1-1-11111-1-1
χ81111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1111111-1111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1111111-111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-111-1111111-1-1-1-1-1-111-1-1111-1
χ141111111111111111-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1111111-1-111-1-1-11
χ151111111111111111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ161111111111111111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ1722222222222-2-2-22-222-2000022-2-20000-200000022-2-2000000-2-2-222000000000000000000
χ1822222222222-2-2-22-222-2000022-2-20000-2000000-2-22200000022-2-2-2000000000000000000
χ1922222222222-2-2-22-2-2-2-20000-2-2220000-200000022-2-2000000222-2-2000000000000000000
χ2022222222222-2-2-22-2-2-2-20000-2-2220000-2000000-2-222000000-2-2222000000000000000000
χ2122222222-2-2-2222-2222-22222-2-2222222-20000-2-20000-2-2000000-200000000000000000000
χ2222222222-2-2-2222-2222-2-2-2-2-2-2-222-2-2-2-2-2000022000022000000-200000000000000000000
χ2322222222-2-2-2222-22-2-2-2222222-2-2-2-2-2-2-20000-2-2000022000000200000000000000000000
χ2422222222-2-2-2222-22-2-2-2-2-2-2-222-2-22222-20000220000-2-2000000200000000000000000000
χ2522222222-2-2-2-2-2-2-2-22220000-2-2-2-20000222-2-20000000022-2-200200000000000000000000
χ2622222222-2-2-2-2-2-2-2-22220000-2-2-2-200002-2-22200000000-2-22200200000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22000022220000222-2-200000000-2-22200-200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-220000222200002-2-2220000000022-2-200-200000000000000000000
χ29222-2-22-2-20002-2-2022-202i2i−2i−2i002-22i2i−2i−2i0000000000000000000000i2i2−i2−i2i2i2−i2−i22−22−2000000
χ30222-2-22-2-20002-2-2022-202i2i−2i−2i002-22i2i−2i−2i0000000000000000000000−i2−i2i2i2−i2−i2i2i2−22−22000000
χ31222-2-22-2-20002-2-2022-20−2i−2i2i2i002-2−2i−2i2i2i0000000000000000000000i2i2−i2−i2i2i2−i2−i2−22−22000000
χ32222-2-22-2-20002-2-2022-20−2i−2i2i2i002-2−2i−2i2i2i0000000000000000000000−i2−i2i2i2−i2−i2i2i22−22−2000000
χ33222-2-22-2-20002-2-202-2202i2i−2i−2i00-22−2i−2i2i2i0000000000000000000000i2i2−i2−i2−i2−i2i2i22−2−22000000
χ34222-2-22-2-20002-2-202-2202i2i−2i−2i00-22−2i−2i2i2i0000000000000000000000−i2−i2i2i2i2i2−i2−i2−222−2000000
χ35222-2-22-2-20002-2-202-220−2i−2i2i2i00-222i2i−2i−2i0000000000000000000000i2i2−i2−i2−i2−i2i2i2−222−2000000
χ36222-2-22-2-20002-2-202-220−2i−2i2i2i00-222i2i−2i−2i0000000000000000000000−i2−i2i2i2i2i2−i2−i22−2−22000000
χ372-2222-2-2-222-222-2-2-20022-22-200000000-22-22-22-22-22-200000000000000000000000000000
χ382-2222-2-2-222-222-2-2-20022-22-200000000-2-22-222-2-22-2200000000000000000000000000000
χ392-2222-2-2-222-222-2-2-2002-22-2200000000-22-22-2-22-22-2200000000000000000000000000000
χ402-2222-2-2-222-222-2-2-2002-22-2200000000-2-22-22-222-22-200000000000000000000000000000
χ412-2222-2-2-222-2-2-22-2200-2000000002i−2i2i−2i20000002-2-222i−2i2i−2i2i−2i00000000000000000000000
χ422-2222-2-2-222-2-2-22-2200-2000000002i−2i2i−2i2000000-222-22i−2i−2i2i−2i2i00000000000000000000000
χ432-2222-2-2-222-2-2-22-2200-200000000−2i2i−2i2i20000002-2-22−2i2i−2i2i−2i2i00000000000000000000000
χ442-2222-2-2-222-2-2-22-2200-200000000−2i2i−2i2i2000000-222-2−2i2i2i−2i2i−2i00000000000000000000000
χ452-2222-2-2-2-2-2222-22-200-22-22-20000000020000-220000002i−2i−2i2i2i−2i02i−2i000000000000000000
χ462-2222-2-2-2-2-2222-22-200-22-22-20000000020000-22000000−2i2i2i−2i−2i2i0−2i2i000000000000000000
χ472-2222-2-2-2-2-2222-22-200-2-22-2200000000200002-20000002i−2i−2i2i−2i2i0−2i2i000000000000000000
χ482-2222-2-2-2-2-2222-22-200-2-22-2200000000200002-2000000−2i2i2i−2i2i−2i02i−2i000000000000000000
χ492-2222-2-2-2-2-22-2-2222002000000002i−2i2i−2i-22-2-22000000−2i2i0000−2i2i02i−2i000000000000000000
χ502-2222-2-2-2-2-22-2-2222002000000002i−2i2i−2i-2-222-2000000−2i2i00002i−2i0−2i2i000000000000000000
χ512-2222-2-2-2-2-22-2-222200200000000−2i2i−2i2i-22-2-220000002i−2i00002i−2i0−2i2i000000000000000000
χ522-2222-2-2-2-2-22-2-222200200000000−2i2i−2i2i-2-222-20000002i−2i0000−2i2i02i−2i000000000000000000
χ53444-4-44-4-4000-4440-44-40000000-4400000000000000000000000000000000000000000000
χ54444-4-44-4-4000-4440-4-4400000004-400000000000000000000000000000000000000000000
χ5544-44-4-44-44-44000-40000000000000000000000000000000000000022−2222−2200000000000000
χ5644-44-4-44-44-44000-400000000000000000000000000000000000000−2222−222200000000000000
χ5744-44-4-44-4-44-400040000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ5844-44-4-44-4-44-40004000000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ5944-4-44-4-440000000000000004i−4i00000000000000000000000000002i−2i−2i2i2-2-220000000000
χ6044-4-44-4-440000000000000004i−4i0000000000000000000000000000−2i2i2i−2i-222-20000000000
χ6144-4-44-4-44000000000000000−4i4i00000000000000000000000000002i−2i−2i2i-222-20000000000
χ6244-4-44-4-44000000000000000−4i4i0000000000000000000000000000−2i2i2i−2i2-2-220000000000
χ634-44-4-4-4440004-440-40004i−4i−4i4i000000000000000000000000000000000000000000000000
χ644-44-4-4-4440004-440-4000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ654-44-4-4-444000-44-404000000000004-4-440000000000000000000000000000000000000000
χ664-44-4-4-444000-44-40400000000000-444-40000000000000000000000000000000000000000
χ674-4-44-44-444-4-400040000000000000000000000000000000000000000000000000022−220000
χ684-4-44-44-444-4-4000400000000000000000000000000000000000000000000000000−22220000
χ694-4-44-44-44-444000-400000000000000000000000000000000000000000000000000002i2−2i200
χ704-4-44-44-44-444000-40000000000000000000000000000000000000000000000000000−2i22i200
χ718-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000

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