Finite Group Databasebeta

← Group #240959

Character table — Group #240959

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222444444444444442444448888888888888888888888882224444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-111111-1-1-1-1
χ9111111-1-11-1-1-1-1-1-1-1-111111-11-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111-1-11-1-1-1-1-1-1-1-111111-11-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ11111111-1-11-1-1-1-1-1-1-1-111111-11-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ12111111-1-11-1-1-1-1-1-1-1-111111-11-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ13111111-1-11-1-1-1-1-1-1-1-111111-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-1-111
χ14111111-1-11-1-1-1-1-1-1-1-111111-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-111-1-1-11111-1-1
χ15111111-1-11-1-1-1-1-1-1-1-111111-11-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11-1-11-1-11111-1-1
χ16111111-1-11-1-1-1-1-1-1-1-111111-11-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-111-111-1-1-1-111
χ172222222222222-2-2-2-2-2-22-2-222-2-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ182222222222222-2-2-2-2-2-22-2-222-2-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ1922222222-2-2-2-2-22222-2-2-2-2-22-2-2-222000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2022222222-2-2-2-2-22222-2-2-2-2-22-2-2-22200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2122222222-2-2-2-2-2-2-2-2-222-2222-222-2-222-2-222-2-200000000000000000000000000000000
χ2222222222-2-2-2-2-2-2-2-2-222-2222-222-2-2-2-222-2-22200000000000000000000000000000000
χ23222222-2-22-2-2-2-22222-2-22-2-2-2222-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ24222222-2-22-2-2-2-22222-2-22-2-2-2222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ25222222-2-2-22222222222-222-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ26222222-2-2-22222222222-222-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ27222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ28222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ292222-2-222222-2-222-2-2222-2-2-2-22-2-22000000000000000000000000000000002-22-20000
χ302222-2-222222-2-222-2-2222-2-2-2-22-2-2200000000000000000000000000000000-22-220000
χ312222-2-222222-2-2-2-222-2-2222-2-2-222-2000000000000000000000000002-2-200200000000
χ322222-2-222222-2-2-2-222-2-2222-2-2-222-200000000000000000000000000-22200-200000000
χ332222-2-222-2-2-22222-2-2-2-2-222-22-22-220000000000000000000000002-20002-2000000000
χ342222-2-222-2-2-22222-2-2-2-2-222-22-22-22000000000000000000000000-22000-22000000000
χ352222-2-222-2-2-222-2-22222-2-2-2-222-22-20000000000000000000000000000000000002i−2i2i−2i
χ362222-2-222-2-2-222-2-22222-2-2-2-222-22-2000000000000000000000000000000000000−2i2i−2i2i
χ372222-2-2-2-22-2-22222-2-2-2-22222-22-22-2000000000000000000000000002-2200-200000000
χ382222-2-2-2-22-2-22222-2-2-2-22222-22-22-200000000000000000000000000-22-200200000000
χ392222-2-2-2-22-2-222-2-222222-2-22-2-22-22000000000000000000000000000000002-2-220000
χ402222-2-2-2-22-2-222-2-222222-2-22-2-22-2200000000000000000000000000000000-222-20000
χ412222-2-2-2-2-222-2-222-2-222-2-2-222-222-20000000000000000000000000000000000002i−2i−2i2i
χ422222-2-2-2-2-222-2-222-2-222-2-2-222-222-2000000000000000000000000000000000000−2i2i2i−2i
χ432222-2-2-2-2-222-2-2-2-222-2-2-222222-2-220000000000000000000000002-2000-22000000000
χ442222-2-2-2-2-222-2-2-2-222-2-2-222222-2-22000000000000000000000000-220002-2000000000
χ4522-2-22-20002i−2i2i−2i2i−2i2i−2i2-202-2000000002-22i−2i00i2−i2i2−i22−22−2i2−i2i2−i22−22−20000000000000000
χ4622-2-22-20002i−2i2i−2i2i−2i2i−2i2-202-2000000002-22i−2i00−i2i2−i2i2−22−22−i2i2−i2i2−22−220000000000000000
χ4722-2-22-20002i−2i2i−2i2i−2i2i−2i2-202-200000000-22−2i2i00i2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ4822-2-22-20002i−2i2i−2i2i−2i2i−2i2-202-200000000-22−2i2i00−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ4922-2-22-20002i−2i2i−2i−2i2i−2i2i-220-220000002-200002i−2i2−2−22i2−i2−i2i22−2−22−i2i2i2−i20000000000000000
χ5022-2-22-20002i−2i2i−2i−2i2i−2i2i-220-220000002-200002i−2i−222−2−i2i2i2−i2−222−2i2−i2−i2i20000000000000000
χ5122-2-22-20002i−2i2i−2i−2i2i−2i2i-220-22000000-220000−2i2i2−2−22i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
χ5222-2-22-20002i−2i2i−2i−2i2i−2i2i-220-22000000-220000−2i2i−222−2−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
χ5322-2-22-2000−2i2i−2i2i2i−2i2i−2i-220-220000002-20000−2i2i2−2−22−i2i2i2−i22−2−22i2−i2−i2i20000000000000000
χ5422-2-22-2000−2i2i−2i2i2i−2i2i−2i-220-220000002-20000−2i2i−222−2i2−i2−i2i2−222−2−i2i2i2−i20000000000000000
χ5522-2-22-2000−2i2i−2i2i2i−2i2i−2i-220-22000000-2200002i−2i2−2−22−i2i2i2−i2−222−2−i2i2i2−i20000000000000000
χ5622-2-22-2000−2i2i−2i2i2i−2i2i−2i-220-22000000-2200002i−2i−222−2i2−i2−i2i22−2−22i2−i2−i2i20000000000000000
χ5722-2-22-2000−2i2i−2i2i−2i2i−2i2i2-202-2000000002-2−2i2i00i2−i2i2−i2−22−22i2−i2i2−i2−22−220000000000000000
χ5822-2-22-2000−2i2i−2i2i−2i2i−2i2i2-202-2000000002-2−2i2i00−i2i2−i2i22−22−2−i2i2−i2i22−22−20000000000000000
χ5922-2-22-2000−2i2i−2i2i−2i2i−2i2i2-202-200000000-222i−2i00i2−i2i2−i2−22−22−i2i2−i2i22−22−20000000000000000
χ6022-2-22-2000−2i2i−2i2i−2i2i−2i2i2-202-200000000-222i−2i00−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000000000000
χ6144-4-4-440004i−4i−4i4i4i−4i−4i4i4-40-440000000000000000000000000000000000000000000000
χ6244-4-4-440004i−4i−4i4i−4i4i4i−4i-4404-40000000000000000000000000000000000000000000000
χ6344-4-4-44000−4i4i4i−4i4i−4i−4i4i-4404-40000000000000000000000000000000000000000000000
χ6444-4-4-44000−4i4i4i−4i−4i4i4i−4i4-40-440000000000000000000000000000000000000000000000
χ658-88-8000080000000000-8000000000000000000000000000000000000000000000000
χ668-88-80000-800000000008000000000000000000000000000000000000000000000000
χ678-8-88008-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8800-88000000000000000000000000000000000000000000000000000000000000

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