Finite Group Databasebeta

← Group #165751

Character table — Group #165751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111111111111144444444444488888888888888888888888888888888888816161616161616161616
order12222222444444442244444444442244444444448888888888888888888888882244444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1
χ51111111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-11-1
χ61111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111111-1
χ71111111111111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-11
χ81111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-11-1-1-1-1-1-1-11
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-1-11
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1-1-111-11
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1111-1
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-111-1-11-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-11-1-111-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1111-1-1-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-11-1-11111
χ17222222222222222222-2-2-2-22-2-2-2-2222000000002200000000000000000000000000-2-2000000
χ18222222222222222222-2-2-2-22-2-2-2-22-2-200000000-2-20000000000000000000000000022000000
χ192222222222222222-2-222-2-2-222-2-2-20000002222000000000000000000000000000-20000000-2
χ202222222222222222-2-222-2-2-222-2-2-2000000-2-2-2-2000000000000000000000000000200000002
χ212222222222222222-2-2-2-222-2-2-222-2002222000000000000000000000000000000-20000000-20
χ222222222222222222-2-2-2-222-2-2-222-200-2-2-2-20000000000000000000000000000002000000020
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-2-222-20022-2-2000000000000000000000000000000-2000000020
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-2-222-200-2-22200000000000000000000000000000020000000-20
χ2522222222-2-2-2-2-2-2-2-222-2-222-222-2-2-200000022-2-200000000000000000000000000020000000-2
χ2622222222-2-2-2-2-2-2-2-222-2-222-222-2-2-2000000-2-222000000000000000000000000000-200000002
χ2722222222-2-2-2-2-2-2-2-2-2-222222-2-2-2-222200000000-2-200000000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222-2-2-2-22-2-20000000022000000000000000000000000002-2000000
χ2922-22-22-2-22i2i2i2i−2i−2i−2i−2i00002i−2i0002-20002i−2i2-2000000i2i2−i2−i222−2−20000000022−2−2i2i2−i2−i20000000000
χ3022-22-22-2-22i2i2i2i−2i−2i−2i−2i00002i−2i0002-20002i−2i2-2000000−i2−i2i2i2−2−22200000000−2−222−i2−i2i2i20000000000
χ3122-22-22-2-22i2i2i2i−2i−2i−2i−2i00002i−2i0002-2000−2i2i-22000000i2i2−i2−i222−2−200000000−2−222−i2−i2i2i20000000000
χ3222-22-22-2-22i2i2i2i−2i−2i−2i−2i00002i−2i0002-2000−2i2i-22000000−i2−i2i2i2−2−2220000000022−2−2i2i2−i2−i20000000000
χ3322-22-22-2-2−2i−2i−2i−2i2i2i2i2i0000−2i2i0002-20002i−2i-22000000i2i2−i2−i2−2−2220000000022−2−2−i2−i2i2i20000000000
χ3422-22-22-2-2−2i−2i−2i−2i2i2i2i2i0000−2i2i0002-20002i−2i-22000000−i2−i2i2i222−2−200000000−2−222i2i2−i2−i20000000000
χ3522-22-22-2-2−2i−2i−2i−2i2i2i2i2i0000−2i2i0002-2000−2i2i2-2000000i2i2−i2−i2−2−22200000000−2−222i2i2−i2−i20000000000
χ3622-22-22-2-2−2i−2i−2i−2i2i2i2i2i0000−2i2i0002-2000−2i2i2-2000000−i2−i2i2i222−2−20000000022−2−2−i2−i2i2i20000000000
χ3722-2-22-22-22i2i−2i−2i2i2i−2i−2i002i−2i0002-20000000002-22i−2i0000000000i2i2−i2−i222−2−2i2−i2i2−i22−22−20000000000
χ3822-2-22-22-22i2i−2i−2i2i2i−2i−2i002i−2i0002-20000000002-22i−2i0000000000−i2−i2i2i2−2−222−i2i2−i2i2−22−220000000000
χ3922-2-22-22-22i2i−2i−2i2i2i−2i−2i002i−2i0002-2000000000-22−2i2i0000000000i2i2−i2−i222−2−2−i2i2−i2i2−22−220000000000
χ4022-2-22-22-22i2i−2i−2i2i2i−2i−2i002i−2i0002-2000000000-22−2i2i0000000000−i2−i2i2i2−2−222i2−i2i2−i22−22−20000000000
χ4122-2-22-22-2−2i−2i2i2i−2i−2i2i2i00−2i2i0002-20000000002-2−2i2i0000000000i2i2−i2−i2−2−222i2−i2i2−i2−22−220000000000
χ4222-2-22-22-2−2i−2i2i2i−2i−2i2i2i00−2i2i0002-20000000002-2−2i2i0000000000−i2−i2i2i222−2−2−i2i2−i2i22−22−20000000000
χ4322-2-22-22-2−2i−2i2i2i−2i−2i2i2i00−2i2i0002-2000000000-222i−2i0000000000i2i2−i2−i2−2−222−i2i2−i2i22−22−20000000000
χ4422-2-22-22-2−2i−2i2i2i−2i−2i2i2i00−2i2i0002-2000000000-222i−2i0000000000−i2−i2i2i222−2−2i2−i2i2−i2−22−220000000000
χ452-2-222-2-222-22-22-22-22-2000020000-22-2000000002-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ462-2-222-2-222-22-22-22-22-2000020000-22-2000000002-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ472-2-222-2-222-22-22-22-22-2000020000-2-2200000000-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ482-2-222-2-222-22-22-22-22-2000020000-2-2200000000-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ492-2-222-2-22-22-22-22-22-22000020000-22-200000000-22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ502-2-222-2-22-22-22-22-22-22000020000-22-200000000-22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ512-2-222-2-22-22-22-22-22-22000020000-2-22000000002-2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ522-2-222-2-22-22-22-22-22-22000020000-2-22000000002-2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ53444-4-4-4-4444-4-4-4-44400000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ54444-4-4-4-4444-4-4-4-4440000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ55444-4-4-4-44-4-44444-4-400000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ56444-4-4-4-44-4-44444-4-40000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ5744-44-44-4-44i4i4i4i−4i−4i−4i−4i0000−4i4i000-4400000000000000000000000000000000000000000000000
χ5844-44-44-4-4−4i−4i−4i−4i4i4i4i4i00004i−4i000-4400000000000000000000000000000000000000000000000
χ5944-4-44-44-44i4i−4i−4i4i4i−4i−4i00−4i4i000-440000000000000000000000000000000000000000000000000
χ6044-4-44-44-4−4i−4i4i4i−4i−4i4i4i004i−4i000-440000000000000000000000000000000000000000000000000
χ614-444-4-44-44i−4i4i−4i−4i4i−4i4i0000000000000000000000002-2-22−2i2i2i−2i00000000000000000000000000
χ624-444-4-44-44i−4i4i−4i−4i4i−4i4i000000000000000000000000-222-22i−2i−2i2i00000000000000000000000000
χ634-444-4-44-4−4i4i−4i4i4i−4i4i−4i0000000000000000000000002-2-222i−2i−2i2i00000000000000000000000000
χ644-444-4-44-4−4i4i−4i4i4i−4i4i−4i000000000000000000000000-222-2−2i2i2i−2i00000000000000000000000000
χ654-44-444-4-44i−4i−4i4i4i−4i−4i4i000000000000000000000000000000002-2-22−2i2i2i−2i000000000000000000
χ664-44-444-4-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000-222-22i−2i−2i2i000000000000000000
χ674-44-444-4-4−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000002-2-222i−2i−2i2i000000000000000000
χ684-44-444-4-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000-222-2−2i2i2i−2i000000000000000000
χ694-4-444-4-444-44-44-44-4-440000-4000040000000000000000000000000000000000000000000000
χ704-4-444-4-44-44-44-44-444-40000-4000040000000000000000000000000000000000000000000000
χ714-4-4-4-44444-4-44-444-400000000000000000000000000000000000000000000000000002-22-200
χ724-4-4-4-44444-4-44-444-40000000000000000000000000000000000000000000000000000-22-2200
χ734-4-4-4-4444-444-44-4-4400000000000000000000000000000000000000000000000000002-2-2200
χ744-4-4-4-4444-444-44-4-440000000000000000000000000000000000000000000000000000-222-200

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