Finite Group Databasebeta

← Group #243447

Character table — Group #243447

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444444444444888888888888888888888888444444448888
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
χ911111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-111-1-1
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-111-1-111
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-111-1-1
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
χ19222222222222-2-2-2-22-2-222-2-2222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ20222222222222-2-2-2-22-2-222-2-2222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
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
χ2322222222-2-2-2-222222-2-222-2-22-2-222-2-222-2-222-2-2000000000000000000000000000000000000
χ2422222222-2-2-2-222222-2-222-2-22-2-222-2-2-2-222-2-222000000000000000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000000000002i−2i−2i2i
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000−2i2i2i−2i
χ2722222222-2-2-2-2-2-2-2-2-222-2-222-22222-2-20000000022-2-200000000-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-222-2-222-22222-2-200000000-2-2220000000022-2-200000000000000000000
χ292222-2-2-2-222-2-222-2-202200-2-20000000000000002-22-222−2−222−2−2000022−2−222−2−2000000000000
χ302222-2-2-2-222-2-222-2-202200-2-20000000000000002-22-2−2−222−2−2220000−2−222−2−222000000000000
χ312222-2-2-2-222-2-222-2-202200-2-2000000000000000-22-2222−2−2−2−222000022−2−2−2−222000000000000
χ322222-2-2-2-222-2-222-2-202200-2-2000000000000000-22-22−2−22222−2−20000−2−22222−2−2000000000000
χ332222-2-2-2-2-2-222-2-22202200-2-20000000000000002-2-2222−2−222−2−20000−2−222−2−222000000000000
χ342222-2-2-2-2-2-222-2-22202200-2-20000000000000002-2-22−2−222−2−222000022−2−222−2−2000000000000
χ352222-2-2-2-2-2-222-2-22202200-2-2000000000000000-222-222−2−2−2−2220000−2−22222−2−2000000000000
χ362222-2-2-2-2-2-222-2-22202200-2-2000000000000000-222-2−2−22222−2−2000022−2−2−2−222000000000000
χ3722-2-22-2-222i−2i2i−2i2i−2i2i−2i22-2-2-22-222i−2i2i−2i2-20000000000002i−2i2i−2i000000002-22-20000000000000000
χ3822-2-22-2-222i−2i2i−2i2i−2i2i−2i22-2-2-22-222i−2i2i−2i2-2000000000000−2i2i−2i2i00000000-22-220000000000000000
χ3922-2-22-2-222i−2i2i−2i2i−2i2i−2i-22-2222-2-2−2i2i−2i2i-2200000000000000002-22-2000000002i−2i2i−2i000000000000
χ4022-2-22-2-222i−2i2i−2i2i−2i2i−2i-22-2222-2-2−2i2i−2i2i-220000000000000000-22-2200000000−2i2i−2i2i000000000000
χ4122-2-22-2-222i−2i2i−2i−2i2i−2i2i2-22-2-2-2222i−2i−2i2i-22000000000000000000000000000000002i−2i002-2000000
χ4222-2-22-2-222i−2i2i−2i−2i2i−2i2i2-22-2-2-2222i−2i−2i2i-2200000000000000000000000000000000−2i2i00-22000000
χ4322-2-22-2-222i−2i2i−2i−2i2i−2i2i-2-2222-22-2−2i2i2i−2i2-200000000000000000000000000000000002i−2i002-20000
χ4422-2-22-2-222i−2i2i−2i−2i2i−2i2i-2-2222-22-2−2i2i2i−2i2-20000000000000000000000000000000000−2i2i00-220000
χ4522-2-22-2-22−2i2i−2i2i2i−2i2i−2i2-22-2-2-222−2i2i2i−2i-22000000000000000000000000000000002i−2i00-22000000
χ4622-2-22-2-22−2i2i−2i2i2i−2i2i−2i2-22-2-2-222−2i2i2i−2i-2200000000000000000000000000000000−2i2i002-2000000
χ4722-2-22-2-22−2i2i−2i2i2i−2i2i−2i-2-2222-22-22i−2i−2i2i2-200000000000000000000000000000000002i−2i00-220000
χ4822-2-22-2-22−2i2i−2i2i2i−2i2i−2i-2-2222-22-22i−2i−2i2i2-20000000000000000000000000000000000−2i2i002-20000
χ4922-2-22-2-22−2i2i−2i2i−2i2i−2i2i22-2-2-22-22−2i2i−2i2i2-20000000000002i−2i2i−2i00000000-22-220000000000000000
χ5022-2-22-2-22−2i2i−2i2i−2i2i−2i2i22-2-2-22-22−2i2i−2i2i2-2000000000000−2i2i−2i2i000000002-22-20000000000000000
χ5122-2-22-2-22−2i2i−2i2i−2i2i−2i2i-22-2222-2-22i−2i2i−2i-2200000000000000002-22-200000000−2i2i−2i2i000000000000
χ5222-2-22-2-22−2i2i−2i2i−2i2i−2i2i-22-2222-2-22i−2i2i−2i-220000000000000000-22-22000000002i−2i2i−2i000000000000
χ5322-2-2-222-22i−2i−2i2i2i−2i−2i2i02-200-220000000000000000000i2−i2−i2i22−2−222i−2i2-22−2−22i2−i2−i2i2000000000000
χ5422-2-2-222-22i−2i−2i2i2i−2i−2i2i02-200-220000000000000000000i2−i2−i2i2−222−2−2i2i-222−2−22−i2i2i2−i2000000000000
χ5522-2-2-222-22i−2i−2i2i2i−2i−2i2i02-200-220000000000000000000−i2i2i2−i22−2−22−2i2i-22−222−2i2−i2−i2i2000000000000
χ5622-2-2-222-22i−2i−2i2i2i−2i−2i2i02-200-220000000000000000000−i2i2i2−i2−222−22i−2i2-2−222−2−i2i2i2−i2000000000000
χ5722-2-2-222-2−2i2i2i−2i−2i2i2i−2i02-200-220000000000000000000i2−i2−i2i22−2−222i−2i-22−222−2−i2i2i2−i2000000000000
χ5822-2-2-222-2−2i2i2i−2i−2i2i2i−2i02-200-220000000000000000000i2−i2−i2i2−222−2−2i2i2-2−222−2i2−i2−i2i2000000000000
χ5922-2-2-222-2−2i2i2i−2i−2i2i2i−2i02-200-220000000000000000000−i2i2i2−i22−2−22−2i2i2-22−2−22−i2i2i2−i2000000000000
χ6022-2-2-222-2−2i2i2i−2i−2i2i2i−2i02-200-220000000000000000000−i2i2i2−i2−222−22i−2i-222−2−22i2−i2−i2i2000000000000
χ614444-4-4-4-444-4-4-4-4440-4-40044000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-44444-4-40-4-40044000000000000000000000000000000000000000000000000000
χ6344-4-4-444-44i−4i−4i4i−4i4i4i−4i0-44004-4000000000000000000000000000000000000000000000000000
χ6444-4-4-444-4−4i4i4i−4i4i−4i−4i4i0-44004-4000000000000000000000000000000000000000000000000000
χ654-44-444-4-4000000004004-400-4000000004-40000000000000000000000000000000000000000
χ664-44-444-4-4000000004004-400-400000000-440000000000000000000000000000000000000000
χ674-44-444-4-400000000-400-4400400000000004i−4i00000000000000000000000000000000000000
χ684-44-444-4-400000000-400-440040000000000−4i4i00000000000000000000000000000000000000
χ694-4-444-44-400000000400-4400-40000004-4000000000000000000000000000000000000000000
χ704-4-444-44-400000000400-4400-4000000-44000000000000000000000000000000000000000000
χ714-4-444-44-400000000-4004-40040000000000004i−4i000000000000000000000000000000000000
χ724-4-444-44-400000000-4004-4004000000000000−4i4i000000000000000000000000000000000000
χ738-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000

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