Finite Group Databasebeta

← Group #258374

Character table — Group #258374

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422444444444888888888888888844444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111111
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ911111111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-111-1-1
χ1011111111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-11111-1-111
χ1111111111-1-1-1-111111111-1-1-1-1111111-1-111-1-111-1-1-11111-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-111
χ1211111111-1-1-1-111111111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-11-1-1-1-1111-1-111-1-111-11111-1-1-1-11111-1-1-1-1111-1-1-1-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-11-1-1-1-1111-1-111-1-111-1-1-1-1-11111-1-1-1-11111111-111-1-1-1-111-1-1
χ1511111111-1-1-1-111111111-1-1-1-11-1-1-1-11-1-11111-1-111-11111-1-1-1-1-1-1-1-11111-1-1-11-1-1111111-1-1
χ1611111111-1-1-1-111111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1-1-1-111111111-1-1-1-1-1-1-111111-1-1-1-111
χ17222222222222222-2-2-2-2222-2-2-20000-22222000000-20000000000000000-200-20000000000
χ18222222222222222-2-2-2-2222-2-2-20000-2-2-2-2-2000000-2000000000000000020020000000000
χ19222222222222-2-2-22222-2-2-222-22222-20000-2-2-2-222-2000000000000000000000000000000
χ20222222222222-2-2-22222-2-2-222-2-2-2-2-2-200002222-2-2-2000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-220000200000000002000000000000000002-20002-2000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22000020000000000200000000000000000-22000-22000000
χ2322222222-2-2-2-2222-2-2-2-22-2-222-20000-222-2-200000020000000000000000-20020000000000
χ2422222222-2-2-2-2222-2-2-2-22-2-222-20000-2-2-22200000020000000000000000200-20000000000
χ2522222222-2-2-2-2-2-2-22222-222-2-2-22222-2000022-2-2-2-22000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-22222-222-2-2-2-2-2-2-2-20000-2-222222000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222000020000000000-2000000000000000002-2000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222000020000000000-200000000000000000-220002-2000000
χ292222-2-2-2-222-2-222-20000-22-2000000002-22-2000000022−2−222−2−222−2−222−2−200000000000000
χ302222-2-2-2-222-2-222-20000-22-2000000002-22-20000000−2−222−2−222−2−222−2−22200000000000000
χ312222-2-2-2-222-2-222-20000-22-200000000-22-22000000022−2−222−2−2−2−222−2−22200000000000000
χ322222-2-2-2-222-2-222-20000-22-200000000-22-220000000−2−222−2−22222−2−222−2−200000000000000
χ332222-2-2-2-2-2-22222-20000-2-22000000002-2-22000000022−2−2−2−22222−2−2−2−22200000000000000
χ342222-2-2-2-2-2-22222-20000-2-22000000002-2-220000000−2−22222−2−2−2−22222−2−200000000000000
χ352222-2-2-2-2-2-22222-20000-2-2200000000-222-2000000022−2−2−2−222−2−22222−2−200000000000000
χ362222-2-2-2-2-2-22222-20000-2-2200000000-222-20000000−2−22222−2−222−2−2−2−22200000000000000
χ3722-2-22-2-222i−2i2i−2i0002-22-20002i−2i022-2-20000000002i−2i000000000i2−i2i2−i22−22−20000000000i2−i22−2
χ3822-2-22-2-222i−2i2i−2i0002-22-20002i−2i022-2-20000000002i−2i000000000−i2i2−i2i2−22−220000000000−i2i2−22
χ3922-2-22-2-222i−2i2i−2i0002-22-20002i−2i0-2-222000000000−2i2i000000000i2−i2i2−i22−22−20000000000−i2i2−22
χ4022-2-22-2-222i−2i2i−2i0002-22-20002i−2i0-2-222000000000−2i2i000000000−i2i2−i2i2−22−220000000000i2−i22−2
χ4122-2-22-2-22−2i2i−2i2i0002-22-2000−2i2i022-2-2000000000−2i2i000000000i2−i2i2−i2−22−220000000000i2−i2−22
χ4222-2-22-2-22−2i2i−2i2i0002-22-2000−2i2i022-2-2000000000−2i2i000000000−i2i2−i2i22−22−20000000000−i2i22−2
χ4322-2-22-2-22−2i2i−2i2i0002-22-2000−2i2i0-2-2220000000002i−2i000000000i2−i2i2−i2−22−220000000000−i2i22−2
χ4422-2-22-2-22−2i2i−2i2i0002-22-2000−2i2i0-2-2220000000002i−2i000000000−i2i2−i2i22−22−20000000000i2−i2−22
χ452-2-222-22-200002-22-222-2-20000-22i−2i2i−2i20000002i−2i00000002-22-200000000000000002i−2i0000
χ462-2-222-22-200002-22-222-2-20000-22i−2i2i−2i20000002i−2i0000000-22-220000000000000000−2i2i0000
χ472-2-222-22-200002-22-222-2-20000-2−2i2i−2i2i2000000−2i2i00000002-22-20000000000000000−2i2i0000
χ482-2-222-22-200002-22-222-2-20000-2−2i2i−2i2i2000000−2i2i0000000-22-2200000000000000002i−2i0000
χ492-2-222-22-20000-22-2-222-22000022i−2i2i−2i-2000000−2i2i0002i−2i2i−2i00000000000000002-200000000
χ502-2-222-22-20000-22-2-222-22000022i−2i2i−2i-2000000−2i2i000−2i2i−2i2i0000000000000000-2200000000
χ512-2-222-22-20000-22-2-222-2200002−2i2i−2i2i-20000002i−2i0002i−2i2i−2i0000000000000000-2200000000
χ522-2-222-22-20000-22-2-222-2200002−2i2i−2i2i-20000002i−2i000−2i2i−2i2i00000000000000002-200000000
χ534444-4-4-4-444-4-4-4-4400004-440000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-444-4-44000044-40000000000000000000000000000000000000000000000000
χ5544-4-44-4-444i−4i4i−4i000-44-44000−4i4i00000000000000000000000000000000000000000000000
χ5644-4-44-4-44−4i4i−4i4i000-44-440004i−4i00000000000000000000000000000000000000000000000
χ5744-4-4-444-44i−4i−4i4i00000000000000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ5844-4-4-444-44i−4i−4i4i0000000000000000000000000000000000000−2i2i2i−2i-222-200000000000000
χ5944-4-4-444-4−4i4i4i−4i00000000000000000000000000000000000002i−2i−2i2i-222-200000000000000
χ6044-4-4-444-4−4i4i4i−4i0000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ614-44-444-4-4000000044-4-40000000000000004-400000000000000000000000000000000000
χ624-44-444-4-4000000044-4-4000000000000000-4400000000000000000000000000000000000
χ634-44-444-4-40000000-4-4440000004i−4i−4i4i000000000000000000000000000000000000000000
χ644-44-444-4-40000000-4-444000000−4i4i4i−4i000000000000000000000000000000000000000000
χ654-4-444-44-400004-444-4-44-4000040000-400000000000000000000000000000000000000000
χ664-4-444-44-40000-44-44-4-4440000-40000400000000000000000000000000000000000000000
χ674-4-44-44-4400004-4-400004000000000000000000000000022−22−22220000000000000000000000
χ684-4-44-44-4400004-4-4000040000000000000000000000000−222222−220000000000000000000000
χ694-4-44-44-440000-4440000-40000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ704-4-44-44-440000-4440000-4000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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