Finite Group Databasebeta

← Group #318700

Character table — Group #318700

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888884444444488888888888844444444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222-2-2-222-200000000-2-2-2-2-2-22200000000000022-2-2-2-222000000000000000000000000
χ1822222222222222-2-2-222-200000000-2-2-2-2-2-222000000000000-2-22222-2-2000000000000000000000000
χ19222222222222-2-2222-2-2222222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2222-2-22-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-222-2-2-222-200000000-2-22222-2-20000000000002222-2-2-2-2000000000000000000000000
χ2422222222-2-2-2-222-2-2-222-200000000-2-22222-2-2000000000000-2-2-2-22222000000000000000000000000
χ2522222222-2-2-2-2-2-2222-2-2222222222-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-22-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ292222-2-2-2-222-2-20022-200-22222-2-2-2-2002-20000000022-2-200000000000000000000000000002−22−22−22−2
χ302222-2-2-2-222-2-20022-200-22222-2-2-2-2002-20000000022-2-20000000000000000000000000000−22−22−22−22
χ312222-2-2-2-222-2-20022-200-2-2-2-2-22222002-200000000-2-22200000000000000000000000000002−22−2−22−22
χ322222-2-2-2-222-2-20022-200-2-2-2-2-22222002-200000000-2-2220000000000000000000000000000−22−222−22−2
χ332222-2-2-2-2-2-2220022-200-22222-2-2-2-200-2200000000-2-22200000000000000000000000000002−2−222−2−22
χ342222-2-2-2-2-2-2220022-200-22222-2-2-2-200-2200000000-2-2220000000000000000000000000000−222−2−222−2
χ352222-2-2-2-2-2-2220022-200-2-2-2-2-2222200-220000000022-2-200000000000000000000000000002−2−22−222−2
χ362222-2-2-2-2-2-2220022-200-2-2-2-2-2222200-220000000022-2-20000000000000000000000000000−222−22−2−22
χ3722-2-22-22-20000222-22-2-2-222-2-222-2-22-200000022-2-20000000000000000000000002-22-2000000000000
χ3822-2-22-22-20000222-22-2-2-222-2-222-2-22-200000022-2-2000000000000000000000000-22-22000000000000
χ3922-2-22-22-20000222-22-2-2-2-2-222-2-2222-2000000-2-2220000000000000000000000002-2-22000000000000
χ4022-2-22-22-20000222-22-2-2-2-2-222-2-2222-2000000-2-222000000000000000000000000-222-2000000000000
χ4122-2-22-22-20000-2-22-2222-222-2-222-2-2-22000000-2-22200000000000000000000000000002i−2i2i−2i00000000
χ4222-2-22-22-20000-2-22-2222-222-2-222-2-2-22000000-2-2220000000000000000000000000000−2i2i−2i2i00000000
χ4322-2-22-22-20000-2-22-2222-2-2-222-2-222-2200000022-2-200000000000000000000000000002i−2i−2i2i00000000
χ4422-2-22-22-20000-2-22-2222-2-2-222-2-222-2200000022-2-20000000000000000000000000000−2i2i2i−2i00000000
χ452-22-2-222-22i−2i2i−2i2-20002-202−22−22−22−20000002i−2i2−22−2i2−i2i2−i2i2i2−i2−i2002-22i−2i00i2−i2i2−i22−22−20000000000000000
χ462-22-2-222-22i−2i2i−2i2-20002-202−22−22−22−20000002i−2i2−22−2i2−i2i2−i2i2i2−i2−i200-22−2i2i00−i2i2−i2i2−22−220000000000000000
χ472-22-2-222-22i−2i2i−2i2-20002-20−22−22−22−220000002i−2i−22−22−i2i2−i2i2−i2−i2i2i2002-22i−2i00−i2i2−i2i2−22−220000000000000000
χ482-22-2-222-22i−2i2i−2i2-20002-20−22−22−22−220000002i−2i−22−22−i2i2−i2i2−i2−i2i2i200-22−2i2i00i2−i2i2−i22−22−20000000000000000
χ492-22-2-222-22i−2i2i−2i-22000-2202−22−22−22−2000000−2i2i−22−22i2−i2i2−i2−i2−i2i2i22-200002i−2i2−2−22−i2i2i2−i20000000000000000
χ502-22-2-222-22i−2i2i−2i-22000-2202−22−22−22−2000000−2i2i−22−22i2−i2i2−i2−i2−i2i2i2-220000−2i2i−222−2i2−i2−i2i20000000000000000
χ512-22-2-222-22i−2i2i−2i-22000-220−22−22−22−22000000−2i2i2−22−2−i2i2−i2i2i2i2−i2−i22-200002i−2i−222−2i2−i2−i2i20000000000000000
χ522-22-2-222-22i−2i2i−2i-22000-220−22−22−22−22000000−2i2i2−22−2−i2i2−i2i2i2i2−i2−i2-220000−2i2i2−2−22−i2i2i2−i20000000000000000
χ532-22-2-222-2−2i2i−2i2i2-20002-202−22−22−22−2000000−2i2i2−22−2−i2i2−i2i2−i2−i2i2i2002-2−2i2i00−i2i2−i2i22−22−20000000000000000
χ542-22-2-222-2−2i2i−2i2i2-20002-202−22−22−22−2000000−2i2i2−22−2−i2i2−i2i2−i2−i2i2i200-222i−2i00i2−i2i2−i2−22−220000000000000000
χ552-22-2-222-2−2i2i−2i2i2-20002-20−22−22−22−22000000−2i2i−22−22i2−i2i2−i2i2i2−i2−i2002-2−2i2i00i2−i2i2−i2−22−220000000000000000
χ562-22-2-222-2−2i2i−2i2i2-20002-20−22−22−22−22000000−2i2i−22−22i2−i2i2−i2i2i2−i2−i200-222i−2i00−i2i2−i2i22−22−20000000000000000
χ572-22-2-222-2−2i2i−2i2i-22000-2202−22−22−22−20000002i−2i−22−22−i2i2−i2i2i2i2−i2−i22-20000−2i2i2−2−22i2−i2−i2i20000000000000000
χ582-22-2-222-2−2i2i−2i2i-22000-2202−22−22−22−20000002i−2i−22−22−i2i2−i2i2i2i2−i2−i2-2200002i−2i−222−2−i2i2i2−i20000000000000000
χ592-22-2-222-2−2i2i−2i2i-22000-220−22−22−22−220000002i−2i2−22−2i2−i2i2−i2−i2−i2i2i22-20000−2i2i−222−2−i2i2i2−i20000000000000000
χ602-22-2-222-2−2i2i−2i2i-22000-220−22−22−22−220000002i−2i2−22−2i2−i2i2−i2−i2−i2i2i2-2200002i−2i2−2−22i2−i2−i2i20000000000000000
χ614444-4-4-4-444-4-400-4-440040000000000-44000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-44400-4-4400400000000004-4000000000000000000000000000000000000000000000000
χ6344-4-44-44-4000044-44-4-4-4400000000-4400000000000000000000000000000000000000000000000000
χ6444-4-44-44-40000-4-4-44-4444000000004-400000000000000000000000000000000000000000000000000
χ6544-4-4-44-440000004-4-400444-4-4-4-4440000000000000000000000000000000000000000000000000000
χ6644-4-4-44-440000004-4-4004-4-44444-4-40000000000000000000000000000000000000000000000000000
χ6744-4-4-44-44000000-44400-40000000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ6844-4-4-44-44000000-44400-4000000000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ694-44-44-4-444i−4i−4i4i0000000022−2222−22−2222−22220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ704-44-44-4-444i−4i−4i4i00000000−2222−222222−2222−22000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ714-44-44-4-44−4i4i4i−4i0000000022−2222−22−2222−2222000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ724-44-44-4-44−4i4i4i−4i00000000−2222−222222−2222−220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ734-4-4444-4-400000000000022−22−2222−222222−2200004-4000000000022−22−222200000000000000000000000000000000
χ744-4-4444-4-400000000000022−22−2222−222222−220000-440000000000−222222−2200000000000000000000000000000000
χ754-4-4444-4-4000000000000−222222−2222−22−222200004-40000000000−222222−2200000000000000000000000000000000
χ764-4-4444-4-4000000000000−222222−2222−22−22220000-44000000000022−22−222200000000000000000000000000000000
χ774-4-44-4-44400004-4000-44022−22−222222−22−22220000000022−22−22220000000000000000000000000000000000000000
χ784-4-44-4-44400004-4000-440−222222−22−222222−2200000000−222222−220000000000000000000000000000000000000000
χ794-4-44-4-4440000-440004-4022−22−222222−22−222200000000−222222−220000000000000000000000000000000000000000
χ804-4-44-4-4440000-440004-40−222222−22−222222−220000000022−22−22220000000000000000000000000000000000000000

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