Finite Group Databasebeta

← Group #499243

Character table — Group #499243

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order122222444444444444888888888824448888161616161616161616161616161616162222444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11111-1-11-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-111-11-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-11-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-11-1111-11-1-11-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-1-11-111-111-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-11-11-1-1111-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1111-11-111-1-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1111111-1-1
χ1511111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-11-1-11-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111-111-111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ1922222222-2-2-2-2-2-2-2-222222222-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ21222222-2-22222-2-2-2-2-2-200000000002-2-22000022−2−222−2−222−2−222−2−20000000000000000
χ22222222-2-22222-2-2-2-2-2-200000000002-2-220000−2−222−2−222−2−222−2−2220000000000000000
χ23222222-2-22222-2-2-2-2-2-20000000000-222-2000022−2−222−2−2−2−222−2−2220000000000000000
χ24222222-2-22222-2-2-2-2-2-20000000000-222-20000−2−222−2−22222−2−222−2−20000000000000000
χ25222222-2-2-2-2-2-22222-2-200000000002-22-2000022−2−2−2−22222−2−2−2−2220000000000000000
χ26222222-2-2-2-2-2-22222-2-200000000002-22-20000−2−22222−2−2−2−22222−2−20000000000000000
χ27222222-2-2-2-2-2-22222-2-20000000000-22-22000022−2−2−2−222−2−22222−2−20000000000000000
χ28222222-2-2-2-2-2-22222-2-20000000000-22-220000−2−22222−2−222−2−2−2−2220000000000000000
χ292222-2-2-2-222-2-222-2-2222222-2-222-2-20000000000000000000000002000-2-20020000000
χ302222-2-2-2-222-2-222-2-2222222-2-222-2-2000000000000000000000000-20002200-20000000
χ312222-2-2-2-222-2-222-2-222-2-2-2-222-2-2220000000000000000000000000200002-20-2000000
χ322222-2-2-2-222-2-222-2-222-2-2-2-222-2-2220000000000000000000000000-20000-2202000000
χ332222-2-2-2-2-2-222-2-222222222-2-2-2-222000000000000000000000000020000-2-202000000
χ342222-2-2-2-2-2-222-2-222222222-2-2-2-2220000000000000000000000000-20000220-2000000
χ352222-2-2-2-2-2-222-2-22222-2-2-2-22222-2-20000000000000000000000002000-2200-20000000
χ362222-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2000000000000000000000000-20002-20020000000
χ3722-2-22-22-22i−2i2i−2i2i−2i2i−2i2-2000000000000002i−2i2-22−22−2i2−i2i2−i2i2−i2i2−i22−22−20000000000000000
χ3822-2-22-22-22i−2i2i−2i2i−2i2i−2i2-2000000000000002i−2i2-2−22−22−i2i2−i2i2−i2i2−i2i2−22−220000000000000000
χ3922-2-22-22-22i−2i2i−2i2i−2i2i−2i2-200000000000000−2i2i-222−22−2i2−i2i2−i2−i2i2−i2i2−22−220000000000000000
χ4022-2-22-22-22i−2i2i−2i2i−2i2i−2i2-200000000000000−2i2i-22−22−22−i2i2−i2i2i2−i2i2−i22−22−20000000000000000
χ4122-2-22-22-2−2i2i−2i2i−2i2i−2i2i2-2000000000000002i−2i-222−22−2−i2i2−i2i2i2−i2i2−i2−22−220000000000000000
χ4222-2-22-22-2−2i2i−2i2i−2i2i−2i2i2-2000000000000002i−2i-22−22−22i2−i2i2−i2−i2i2−i2i22−22−20000000000000000
χ4322-2-22-22-2−2i2i−2i2i−2i2i−2i2i2-200000000000000−2i2i2-22−22−2−i2i2−i2i2−i2i2−i2i22−22−20000000000000000
χ4422-2-22-22-2−2i2i−2i2i−2i2i−2i2i2-200000000000000−2i2i2-2−22−22i2−i2i2−i2i2−i2i2−i2−22−220000000000000000
χ4522-2-22-2-222i−2i2i−2i−2i2i−2i2i-222i2i−2i−2i2i−2i2-22-200000000000000002i−2i−2i2i2-2-220000000000000000
χ4622-2-22-2-222i−2i2i−2i−2i2i−2i2i-222i2i−2i−2i2i−2i2-22-20000000000000000−2i2i2i−2i-222-20000000000000000
χ4722-2-22-2-222i−2i2i−2i−2i2i−2i2i-22−2i−2i2i2i−2i2i-22-22000000002-2-222i−2i−2i2i000000000000000000000000
χ4822-2-22-2-222i−2i2i−2i−2i2i−2i2i-22−2i−2i2i2i−2i2i-22-2200000000-222-2−2i2i2i−2i000000000000000000000000
χ4922-2-22-2-22−2i2i−2i2i2i−2i2i−2i-222i2i−2i−2i2i−2i-22-22000000002-2-22−2i2i2i−2i000000000000000000000000
χ5022-2-22-2-22−2i2i−2i2i2i−2i2i−2i-222i2i−2i−2i2i−2i-22-2200000000-222-22i−2i−2i2i000000000000000000000000
χ5122-2-22-2-22−2i2i−2i2i2i−2i2i−2i-22−2i−2i2i2i−2i2i2-22-200000000000000002i−2i−2i2i-222-20000000000000000
χ5222-2-22-2-22−2i2i−2i2i2i−2i2i−2i-22−2i−2i2i2i−2i2i2-22-20000000000000000−2i2i2i−2i2-2-220000000000000000
χ5322-2-2-222-22i−2i−2i2i−2i2i2i−2i-222i2i−2i−2i−2i2i2-2-220000000000000000000000000000000000002-22i−2i
χ5422-2-2-222-22i−2i−2i2i−2i2i2i−2i-222i2i−2i−2i−2i2i2-2-22000000000000000000000000000000000000-22−2i2i
χ5522-2-2-222-22i−2i−2i2i−2i2i2i−2i-22−2i−2i2i2i2i−2i-222-2000000000000000000000000002-20000002i−2i0000
χ5622-2-2-222-22i−2i−2i2i−2i2i2i−2i-22−2i−2i2i2i2i−2i-222-200000000000000000000000000-22000000−2i2i0000
χ5722-2-2-222-2−2i2i2i−2i2i−2i−2i2i-222i2i−2i−2i−2i2i-222-2000000000000000000000000002-2000000−2i2i0000
χ5822-2-2-222-2−2i2i2i−2i2i−2i−2i2i-222i2i−2i−2i−2i2i-222-200000000000000000000000000-220000002i−2i0000
χ5922-2-2-222-2−2i2i2i−2i2i−2i−2i2i-22−2i−2i2i2i2i−2i2-2-220000000000000000000000000000000000002-2−2i2i
χ6022-2-2-222-2−2i2i2i−2i2i−2i−2i2i-22−2i−2i2i2i2i−2i2-2-22000000000000000000000000000000000000-222i−2i
χ614444-4-44444-4-4-4-444-4-400000000000000000000000000000000000000000000000000
χ624444-4-444-4-44444-4-4-4-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-444i−4i−4i4i4i−4i−4i4i4-400000000000000000000000000000000000000000000000000
χ6444-4-4-44-44−4i4i4i−4i−4i4i4i−4i4-400000000000000000000000000000000000000000000000000
χ658-88-8000000000000004i2−4i24i2−4i20000000000000000000000000000000000000000000000
χ668-88-800000000000000−4i24i2−4i24i20000000000000000000000000000000000000000000000
χ678-8-880000000000000042−42−42420000000000000000000000000000000000000000000000
χ688-8-8800000000000000−424242−420000000000000000000000000000000000000000000000

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