Finite Group Databasebeta

← Group #285800

Character table — Group #285800

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444488888888888888882244444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ91111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-11111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-11
χ101111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-1
χ111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-11
χ121111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-11111-1-1111111-1-1-1-11-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1111-1
χ141111111111111111-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-11
χ151111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-11-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-111-11
χ17222222222-2-2-2222-222-2-2-2-2-2-20000000000000000222-2-222-2-20000000000000000000000
χ18222222222-2-2-2222-222-2-2-2-2-2-20000000000000000-2-2222-2-2220000000000000000000000
χ19222222222-2-2-2222-2-2-2-2-22222000000000000000022-222-2-2-2-20000000000000000000000
χ20222222222-2-2-2222-2-2-2-2-222220000000000000000-2-2-2-2-222220000000000000000000000
χ2122222222-2222-2-2-2222-2-2-2-222222222220000000000-2000000-2-2-2-2000000000000000000
χ2222222222-2222-2-2-2222-2-2-2-222-2-2-2-2-2-2-2-20000000000-20000002222000000000000000000
χ2322222222-2222-2-2-22-2-2-2-222-2-22222-2-2-2-200000000002000000-2-222000000000000000000
χ2422222222-2222-2-2-22-2-2-2-222-2-2-2-2-2-222220000000000200000022-2-2000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-2000000002i2i2i2i−2i−2i−2i−2i00-200000000002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2222222-2-200000000−2i−2i−2i−2i2i2i2i2i00-20000000000−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-222000000002i2i2i2i−2i−2i−2i−2i0020000000000−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-22200000000−2i−2i−2i−2i2i2i2i2i00200000000002i2i−2i−2i00000000000000
χ29222-2-2-2-2222-2-22-2-22002-200000000000022-2-222-2-2000000000000000002i−2i002i−2i00000000
χ30222-2-2-2-2222-2-22-2-22002-200000000000022-2-222-2-200000000000000000−2i2i00−2i2i00000000
χ31222-2-2-2-2222-2-22-2-22002-2000000000000-2-222-2-222000000000000000002i−2i00−2i2i00000000
χ32222-2-2-2-2222-2-22-2-22002-2000000000000-2-222-2-22200000000000000000−2i2i002i−2i00000000
χ33222-2-2-2-22-2-222-222-2002-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000000002i−2i00002-20000
χ34222-2-2-2-22-2-222-222-2002-20000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000−2i2i0000-220000
χ35222-2-2-2-22-2-222-222-2002-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000002i−2i0000-220000
χ36222-2-2-2-22-2-222-222-2002-2000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000−2i2i00002-20000
χ3722-2-22-22-22000-2-22000002i−2i2i−2i22−2−2i2i2−i2−i22−22−22−22−2000002-22i−2i2−2i2−i2i2−i2i2−i200000000000000
χ3822-2-22-22-22000-2-22000002i−2i2i−2i22−2−2i2i2−i2−i2−22−22−22−2200000-22−2i2i2−2i2−i2−i2i2−i2i200000000000000
χ3922-2-22-22-22000-2-22000002i−2i2i−2i−2−222−i2−i2i2i22−22−22−22−200000-22−2i2i−22−i2i2i2−i2i2−i200000000000000
χ4022-2-22-22-22000-2-22000002i−2i2i−2i−2−222−i2−i2i2i2−22−22−22−22000002-22i−2i−22−i2i2−i2i2−i2i200000000000000
χ4122-2-22-22-22000-2-2200000−2i2i−2i2i22−2−2−i2−i2i2i22−22−22−22−2000002-2−2i2i2−2−i2i2−i2i2−i2i200000000000000
χ4222-2-22-22-22000-2-2200000−2i2i−2i2i22−2−2−i2−i2i2i2−22−22−22−2200000-222i−2i2−2−i2i2i2−i2i2−i200000000000000
χ4322-2-22-22-22000-2-2200000−2i2i−2i2i−2−222i2i2−i2−i22−22−22−22−200000-222i−2i−22i2−i2−i2i2−i2i200000000000000
χ4422-2-22-22-22000-2-2200000−2i2i−2i2i−2−222i2i2−i2−i2−22−22−22−22000002-2−2i2i−22i2−i2i2−i2i2−i200000000000000
χ4522-2-22-22-2-200022-2000002i−2i−2i2i22−2−2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i22-202i−2i0000−22i2−i2−222−200000000000000
χ4622-2-22-22-2-200022-2000002i−2i−2i2i22−2−2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i2-220−2i2i0000−22i2−i22−2−2200000000000000
χ4722-2-22-22-2-200022-2000002i−2i−2i2i−2−222i2i2−i2−i2i2−i2i2−i2−i2i2−i2i2-220−2i2i00002−2−i2i2−222−200000000000000
χ4822-2-22-22-2-200022-2000002i−2i−2i2i−2−222i2i2−i2−i2−i2i2−i2i2i2−i2i2−i22-202i−2i00002−2−i2i22−2−2200000000000000
χ4922-2-22-22-2-200022-200000−2i2i2i−2i22−2−2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i2-2202i−2i0000−22−i2i22−2−2200000000000000
χ5022-2-22-22-2-200022-200000−2i2i2i−2i22−2−2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i22-20−2i2i0000−22−i2i2−222−200000000000000
χ5122-2-22-22-2-200022-200000−2i2i2i−2i−2−222−i2−i2i2i2i2−i2i2−i2−i2i2−i2i22-20−2i2i00002−2i2−i22−2−2200000000000000
χ5222-2-22-22-2-200022-200000−2i2i2i−2i−2−222−i2−i2i2i2−i2i2−i2i2i2−i2i2−i2-2202i−2i00002−2i2−i2−222−200000000000000
χ53444-4-4-4-444-4444-4-4-400-44000000000000000000000000000000000000000000000000000
χ54444-4-4-4-44-44-4-4-444400-44000000000000000000000000000000000000000000000000000
χ5544-44-44-4-44000-44-40000000000000000022−22−222222−22−22220000000000000000000000000000000
χ5644-44-44-4-44000-44-400000000000000000−222222−22−222222−220000000000000000000000000000000
χ5744-44-44-4-4-40004-44000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000
χ5844-44-44-4-4-40004-4400000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000
χ594-44-4-444-4000000004-40000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000
χ604-44-4-444-4000000004-4000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000
χ614-44-4-444-400000000-440000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000
χ624-44-4-444-400000000-44000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000
χ634-4-44-4-444044-4000-4000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ644-4-44-4-444044-4000-400000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ654-4-44-4-4440-4-4400040000000000004-4-44000000000000000000000000000000000000000
χ664-4-44-4-4440-4-440004000000000000-444-4000000000000000000000000000000000000000
χ674-4-4-444-4404-44000-4000000000000000000000000000000000000000000000002i2−2i2000000
χ684-4-4-444-4404-44000-400000000000000000000000000000000000000000000000−2i22i2000000
χ694-4-4-444-440-44-4000400000000000000000000000000000000000000000000000000022−2200
χ704-4-4-444-440-44-40004000000000000000000000000000000000000000000000000000−222200
χ718-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000

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