Finite Group Databasebeta

← Group #324893

Character table — Group #324893

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444444444488888888888888888888888888888888444488882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-11-11-1
χ1011111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-11-11
χ1111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-11-11
χ1211111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1111-11-1
χ1311111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-11-1-1-1111-1-11
χ1411111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-11-1111-1-1-111-1
χ1511111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-11-1-1-111-111-1
χ1611111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-11-1111-1-11-1-11
χ17222222222222222222-2-2-2-222-2-2-2-2-2-20000000000000000000000000000000022-2-200000000
χ18222222222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000000000000000-2-22200000000
χ19222222222222-2-2-2-2-2-22222-2-2-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ20222222222222-2-2-2-2-2-22222-2-2-2-222-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000002i−2i2i−2i0000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000−2i2i−2i2i0000
χ2322222222-2-2-2-22222-2-22222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-22222-2-22222-2-2-2-2-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000002i−2i−2i2i0000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000−2i2i2i−2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222000000000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2222200000000000000000000000000000000-222-200000000
χ29222-2-22-2-2000000002-2-2-2222-22-200002i2i−2i−2i2i2i−2i−2i0000000000002i2i−2i−2i000022-2-2000000000000
χ30222-2-22-2-2000000002-2-2-2222-22-200002i2i−2i−2i2i2i−2i−2i000000000000−2i−2i2i2i0000-2-222000000000000
χ31222-2-22-2-2000000002-2-2-2222-22-20000−2i−2i2i2i−2i−2i2i2i0000000000002i2i−2i−2i0000-2-222000000000000
χ32222-2-22-2-2000000002-2-2-2222-22-20000−2i−2i2i2i−2i−2i2i2i000000000000−2i−2i2i2i000022-2-2000000000000
χ33222-2-22-2-200000000-22-2-222-22-2200002i2i−2i−2i−2i−2i2i2i000000002i2i−2i−2i000022-2-20000000000000000
χ34222-2-22-2-200000000-22-2-222-22-2200002i2i−2i−2i−2i−2i2i2i00000000−2i−2i2i2i0000-2-2220000000000000000
χ35222-2-22-2-200000000-22-2-222-22-220000−2i−2i2i2i2i2i−2i−2i000000002i2i−2i−2i0000-2-2220000000000000000
χ36222-2-22-2-200000000-22-2-222-22-220000−2i−2i2i2i2i2i−2i−2i00000000−2i−2i2i2i000022-2-20000000000000000
χ3722-22-2-22-200002i2i−2i−2i002-22-20000002i−2i00002i−2i2i−2i22-2-20000i2−i2i2−i22−22−22−22−2i2−i2i2−i2000000000000
χ3822-22-2-22-200002i2i−2i−2i002-22-20000002i−2i00002i−2i2i−2i22-2-20000−i2i2−i2i2−22−22−22−22−i2i2−i2i2000000000000
χ3922-22-2-22-200002i2i−2i−2i002-22-20000002i−2i0000−2i2i−2i2i-2-2220000i2−i2i2−i22−22−2−22−22−i2i2−i2i2000000000000
χ4022-22-2-22-200002i2i−2i−2i002-22-20000002i−2i0000−2i2i−2i2i-2-2220000−i2i2−i2i2−22−222−22−2i2−i2i2−i2000000000000
χ4122-22-2-22-20000−2i−2i2i2i002-22-2000000−2i2i00002i−2i2i−2i-2-2220000i2−i2i2−i2−22−222−22−2−i2i2−i2i2000000000000
χ4222-22-2-22-20000−2i−2i2i2i002-22-2000000−2i2i00002i−2i2i−2i-2-2220000−i2i2−i2i22−22−2−22−22i2−i2i2−i2000000000000
χ4322-22-2-22-20000−2i−2i2i2i002-22-2000000−2i2i0000−2i2i−2i2i22-2-20000i2−i2i2−i2−22−22−22−22i2−i2i2−i2000000000000
χ4422-22-2-22-20000−2i−2i2i2i002-22-2000000−2i2i0000−2i2i−2i2i22-2-20000−i2i2−i2i22−22−22−22−2−i2i2−i2i2000000000000
χ4522-2-22-2-222i2i−2i−2i000000-222-200002i−2i0000002-2-2200002i2i−2i−2i2−2−22i2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ4622-2-22-2-222i2i−2i−2i000000-222-200002i−2i0000002-2-2200002i2i−2i−2i−222−2−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ4722-2-22-2-222i2i−2i−2i000000-222-200002i−2i000000-222-20000−2i−2i2i2i2−2−22i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ4822-2-22-2-222i2i−2i−2i000000-222-200002i−2i000000-222-20000−2i−2i2i2i−222−2−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ4922-2-22-2-22−2i−2i2i2i000000-222-20000−2i2i0000002-2-220000−2i−2i2i2i2−2−22−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ5022-2-22-2-22−2i−2i2i2i000000-222-20000−2i2i0000002-2-220000−2i−2i2i2i−222−2i2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ5122-2-22-2-22−2i−2i2i2i000000-222-20000−2i2i000000-222-200002i2i−2i−2i2−2−22−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ5222-2-22-2-22−2i−2i2i2i000000-222-20000−2i2i000000-222-200002i2i−2i−2i−222−2i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ53444-4-44-4-4000000004-444-4-44-4-44000000000000000000000000000000000000000000000000
χ54444-4-44-4-400000000-4444-4-4-444-4000000000000000000000000000000000000000000000000
χ5544-44-4-44-400004i4i−4i−4i00-44-44000000−4i4i00000000000000000000000000000000000000000000
χ5644-44-4-44-40000−4i−4i4i4i00-44-440000004i−4i00000000000000000000000000000000000000000000
χ5744-4-44-4-444i4i−4i−4i0000004-4-440000−4i4i0000000000000000000000000000000000000000000000
χ5844-4-44-4-44−4i−4i4i4i0000004-4-4400004i−4i0000000000000000000000000000000000000000000000
χ594-444-4-4-4400004i−4i4i−4i0000000000000022−2222−22000000002i2−2i22i2−2i20000000000000000000000000000
χ604-444-4-4-4400004i−4i4i−4i00000000000000−2222−222200000000−2i22i2−2i22i20000000000000000000000000000
χ614-444-4-4-440000−4i4i−4i4i0000000000000022−2222−2200000000−2i22i2−2i22i20000000000000000000000000000
χ624-444-4-4-440000−4i4i−4i4i00000000000000−2222−2222000000002i2−2i22i2−2i20000000000000000000000000000
χ634-44-44-44-44i−4i4i−4i0000000000000000002i2−2i2−2i22i2000022−2222−2200000000000000000000000000000000
χ644-44-44-44-44i−4i4i−4i000000000000000000−2i22i22i2−2i20000−2222−222200000000000000000000000000000000
χ654-44-44-44-4−4i4i−4i4i0000000000000000002i2−2i2−2i22i20000−2222−222200000000000000000000000000000000
χ664-44-44-44-4−4i4i−4i4i000000000000000000−2i22i22i2−2i2000022−2222−2200000000000000000000000000000000
χ674-4-4444-4-44-4-444-4-44440000-4-400000000000000000000000000000000000000000000000000
χ684-4-4444-4-44-4-44-444-4-4-400004400000000000000000000000000000000000000000000000000
χ694-4-4444-4-4-444-44-4-44-4-400004400000000000000000000000000000000000000000000000000
χ704-4-4444-4-4-444-4-444-4440000-4-400000000000000000000000000000000000000000000000000
χ714-4-4-4-4444000000004-40000-440000000000000022−22−2222−222222−220000000000000000000000000000
χ724-4-4-4-4444000000004-40000-4400000000000000−222222−2222−22−22220000000000000000000000000000
χ734-4-4-4-444400000000-4400004-40000000000000022−22−222222−22−22220000000000000000000000000000
χ744-4-4-4-444400000000-4400004-400000000000000−222222−22−222222−220000000000000000000000000000

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