Finite Group Databasebeta

← Group #243451

Character table — Group #243451

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444422444444888888888888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ911111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ1011111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-111-1-1
χ1111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ1311111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-111-1-111
χ1511111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ1611111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-111-1-1
χ172222222222222222-222-2-222-2-2-2-2-2-2-200000000222200000000-2-2-2-200000000000000000000
χ182222222222222222-222-2-222-2-2-2-2-2-2-200000000-2-2-2-200000000222200000000000000000000
χ19222222222222-2-2-2-22-2-222-2-2222-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ20222222222222-2-2-2-22-2-222-2-2222-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000002i−2i2i−2i
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-2-2-222222-2-222-2-22-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ2422222222-2-2-2-222222-2-222-2-22-2-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ2722222222-2-2-2-2-2-2-2-2-222-2-222-222-2-2220000000022-2-200000000-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-222-2-222-222-2-22200000000-2-2220000000022-2-200000000000000000000
χ29222-2-2-2-222i2i−2i−2i2i2i−2i−2i02-2002-20000000000000002i−2i2-2i2i2−i2−i222−2−2000022−2−2i2i2−i2−i2000000000000
χ30222-2-2-2-222i2i−2i−2i2i2i−2i−2i02-2002-20000000000000002i−2i2-2−i2−i2i2i2−2−2220000−2−222−i2−i2i2i2000000000000
χ31222-2-2-2-222i2i−2i−2i2i2i−2i−2i02-2002-2000000000000000−2i2i-22i2i2−i2−i2−2−222000022−2−2−i2−i2i2i2000000000000
χ32222-2-2-2-222i2i−2i−2i2i2i−2i−2i02-2002-2000000000000000−2i2i-22−i2−i2i2i222−2−20000−2−222i2i2−i2−i2000000000000
χ33222-2-2-2-22−2i−2i2i2i−2i−2i2i2i02-2002-20000000000000002i−2i-22i2i2−i2−i222−2−20000−2−222−i2−i2i2i2000000000000
χ34222-2-2-2-22−2i−2i2i2i−2i−2i2i2i02-2002-20000000000000002i−2i-22−i2−i2i2i2−2−222000022−2−2i2i2−i2−i2000000000000
χ35222-2-2-2-22−2i−2i2i2i−2i−2i2i2i02-2002-2000000000000000−2i2i2-2i2i2−i2−i2−2−2220000−2−222i2i2−i2−i2000000000000
χ36222-2-2-2-22−2i−2i2i2i−2i−2i2i2i02-2002-2000000000000000−2i2i2-2−i2−i2i2i222−2−2000022−2−2−i2−i2i2i2000000000000
χ372-2222-2-2-22-22-22-22-20-2-200220000000000000000000i2−i2i2−i2i2−i2i2−i22-22-2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-2222-2-2-22-22-22-22-20-2-200220000000000000000000i2−i2i2−i2−i2i2−i2i2-22-22i2−i2i2−i2−i2i2−i2i2000000000000
χ392-2222-2-2-22-22-22-22-20-2-200220000000000000000000−i2i2−i2i2i2−i2i2−i2-22-22−i2i2−i2i2i2−i2i2−i2000000000000
χ402-2222-2-2-22-22-22-22-20-2-200220000000000000000000−i2i2−i2i2−i2i2−i2i22-22-2−i2i2−i2i2−i2i2−i2i2000000000000
χ412-2222-2-2-2-22-22-22-220-2-200220000000000000000000i2−i2i2−i2i2−i2i2−i22-2-22−i2i2−i2i2−i2i2−i2i2000000000000
χ422-2222-2-2-2-22-22-22-220-2-200220000000000000000000i2−i2i2−i2−i2i2−i2i2-222-2−i2i2−i2i2i2−i2i2−i2000000000000
χ432-2222-2-2-2-22-22-22-220-2-200220000000000000000000−i2i2−i2i2i2−i2i2−i2-222-2i2−i2i2−i2−i2i2−i2i2000000000000
χ442-2222-2-2-2-22-22-22-220-2-200220000000000000000000−i2i2−i2i2−i2i2−i2i22-2-22i2−i2i2−i2i2−i2i2−i2000000000000
χ452-22-2-222-22i−2i−2i2i2i−2i−2i2i2-22-2-22-222i−2i2-22i−2i00000000000000002i−2i−2i2i00000000-222-2000000000000
χ462-22-2-222-22i−2i−2i2i2i−2i−2i2i2-22-2-22-222i−2i2-22i−2i0000000000000000−2i2i2i−2i000000002-2-22000000000000
χ472-22-2-222-22i−2i−2i2i2i−2i−2i2i-2-22222-2-2−2i2i-22−2i2i0000000000002-2-2200000000−2i2i2i−2i0000000000000000
χ482-22-2-222-22i−2i−2i2i2i−2i−2i2i-2-22222-2-2−2i2i-22−2i2i000000000000-222-2000000002i−2i−2i2i0000000000000000
χ492-22-2-222-22i−2i−2i2i−2i2i2i−2i22-2-2-2-2222i−2i-22−2i2i00000000000000000000000000000000002-2002i−2i0000
χ502-22-2-222-22i−2i−2i2i−2i2i2i−2i22-2-2-2-2222i−2i-22−2i2i0000000000000000000000000000000000-2200−2i2i0000
χ512-22-2-222-22i−2i−2i2i−2i2i2i−2i-22-222-22-2−2i2i2-22i−2i000000000000000000000000000000002-2002i−2i000000
χ522-22-2-222-22i−2i−2i2i−2i2i2i−2i-22-222-22-2−2i2i2-22i−2i00000000000000000000000000000000-2200−2i2i000000
χ532-22-2-222-2−2i2i2i−2i2i−2i−2i2i22-2-2-2-222−2i2i-222i−2i00000000000000000000000000000000002-200−2i2i0000
χ542-22-2-222-2−2i2i2i−2i2i−2i−2i2i22-2-2-2-222−2i2i-222i−2i0000000000000000000000000000000000-22002i−2i0000
χ552-22-2-222-2−2i2i2i−2i2i−2i−2i2i-22-222-22-22i−2i2-2−2i2i000000000000000000000000000000002-200−2i2i000000
χ562-22-2-222-2−2i2i2i−2i2i−2i−2i2i-22-222-22-22i−2i2-2−2i2i00000000000000000000000000000000-22002i−2i000000
χ572-22-2-222-2−2i2i2i−2i−2i2i2i−2i2-22-2-22-22−2i2i2-2−2i2i00000000000000002i−2i−2i2i000000002-2-22000000000000
χ582-22-2-222-2−2i2i2i−2i−2i2i2i−2i2-22-2-22-22−2i2i2-2−2i2i0000000000000000−2i2i2i−2i00000000-222-2000000000000
χ592-22-2-222-2−2i2i2i−2i−2i2i2i−2i-2-22222-2-22i−2i-222i−2i0000000000002-2-22000000002i−2i−2i2i0000000000000000
χ602-22-2-222-2−2i2i2i−2i−2i2i2i−2i-2-22222-2-22i−2i-222i−2i000000000000-222-200000000−2i2i2i−2i0000000000000000
χ61444-4-4-4-444i4i−4i−4i−4i−4i4i4i0-4400-44000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44−4i−4i4i4i4i4i−4i−4i0-4400-44000000000000000000000000000000000000000000000000000
χ6344-44-44-4-4000000004004-400-40000004-4000000000000000000000000000000000000000000
χ6444-44-44-4-4000000004004-400-4000000-44000000000000000000000000000000000000000000
χ6544-44-44-4-400000000-400-44004000000004i−4i0000000000000000000000000000000000000000
χ6644-44-44-4-400000000-400-4400400000000−4i4i0000000000000000000000000000000000000000
χ674-4444-4-4-44-44-4-44-4404400-4-4000000000000000000000000000000000000000000000000000
χ684-4444-4-4-4-44-444-44-404400-4-4000000000000000000000000000000000000000000000000000
χ694-4-4-444-4400000000400-4400-400000000004i−4i00000000000000000000000000000000000000
χ704-4-4-444-4400000000400-4400-40000000000−4i4i00000000000000000000000000000000000000
χ714-4-4-444-4400000000-4004-40040000000000004-4000000000000000000000000000000000000
χ724-4-4-444-4400000000-4004-4004000000000000-44000000000000000000000000000000000000
χ7388-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000

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