Finite Group Databasebeta

← Group #280010

Character table — Group #280010

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882224444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-11111-1-11-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-111-1-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111111-1-111-111-1-1-1
χ91111111111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-111-1-1111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1111111-1-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111111-1-111-1-11-1-1-1-11
χ17222222222-2-22-2-2222222-20000-200002222000022-2-2000000-2-2000000000000000-200000
χ18222222222-2-22-2-2222222-20000-20000-2-2-2-20000-2-2-2-200000022000000000000000200000
χ19222222222-2-22-2-222-2-2-2-2-20000-2000022220000-2-222000000-2-2000000000000000200000
χ20222222222-2-22-2-222-2-2-2-2-20000-20000-2-2-2-20000222200000022000000000000000-200000
χ2122222222-222-222-2-20000-22222-222220000-2-2220000-2-200000000000000-2000000000000
χ2222222222-222-222-2-20000-22222-2-2-2-2-20000-2-2-2-2000022000000000000002000000000000
χ2322222222-222-222-2-20000-2-2-2-2-2-22222000022-2-20000-2-2000000000000002000000000000
χ2422222222-222-222-2-20000-2-2-2-2-2-2-2-2-2-20000222200002200000000000000-2000000000000
χ25222-2-2-2-2202-202-200000002i2i−2i−2i022-2-2i2i2−i2−i2002i−2i0000000000i2−i222−2−2i2i2−i2−i200000000002−20
χ26222-2-2-2-2202-202-200000002i2i−2i−2i022-2-2−i2−i2i2i2002i−2i0000000000−i2i2−2−222−i2−i2i2i20000000000−220
χ27222-2-2-2-2202-202-200000002i2i−2i−2i0-2-222i2i2−i2−i200−2i2i0000000000i2−i222−2−2−i2−i2i2i20000000000−220
χ28222-2-2-2-2202-202-200000002i2i−2i−2i0-2-222−i2−i2i2i200−2i2i0000000000−i2i2−2−222i2i2−i2−i200000000002−20
χ29222-2-2-2-2202-202-20000000−2i−2i2i2i022-2-2i2i2−i2−i200−2i2i0000000000i2−i2−2−222i2i2−i2−i20000000000−220
χ30222-2-2-2-2202-202-20000000−2i−2i2i2i022-2-2−i2−i2i2i200−2i2i0000000000−i2i222−2−2−i2−i2i2i200000000002−20
χ31222-2-2-2-2202-202-20000000−2i−2i2i2i0-2-222i2i2−i2−i2002i−2i0000000000i2−i2−2−222−i2−i2i2i200000000002−20
χ32222-2-2-2-2202-202-20000000−2i−2i2i2i0-2-222−i2−i2i2i2002i−2i0000000000−i2i222−2−2i2i2−i2−i20000000000−220
χ3322-22-22-2-2200-200-2222-2-2000000i2−i2i2−i22i−2i2i−2i00002i−2i00i2−i2i2i2−i2−i20000002−22−2000000002−2000
χ3422-22-22-2-2200-200-2222-2-2000000i2−i2i2−i2−2i2i−2i2i0000−2i2i00i2−i2i2i2−i2−i2000000−22−2200000000−22000
χ3522-22-22-2-2200-200-2222-2-2000000−i2i2−i2i22i−2i2i−2i00002i−2i00−i2i2−i2−i2i2i2000000−22−2200000000−22000
χ3622-22-22-2-2200-200-2222-2-2000000−i2i2−i2i2−2i2i−2i2i0000−2i2i00−i2i2−i2−i2i2i20000002−22−2000000002−2000
χ3722-22-22-2-2200-200-22-2-222000000i2−i2i2−i22i−2i2i−2i0000−2i2i00i2−i2−i2−i2i2i20000002−22−200000000−22000
χ3822-22-22-2-2200-200-22-2-222000000i2−i2i2−i2−2i2i−2i2i00002i−2i00i2−i2−i2−i2i2i2000000−22−22000000002−2000
χ3922-22-22-2-2200-200-22-2-222000000−i2i2−i2i22i−2i2i−2i0000−2i2i00−i2i2i2i2−i2−i2000000−22−22000000002−2000
χ4022-22-22-2-2200-200-22-2-222000000−i2i2−i2i2−2i2i−2i2i00002i−2i00−i2i2i2i2−i2−i20000002−22−200000000−22000
χ412-22-2-222-2222-2-2-22-22i−2i2i−2i-22-22-22000000002-200002i−2i00000000000000000002i−2i00000000
χ422-22-2-222-2222-2-2-22-22i−2i2i−2i-2-22-22200000000-2200002i−2i0000000000000000000−2i2i00000000
χ432-22-2-222-2222-2-2-22-2−2i2i−2i2i-22-22-22000000002-20000−2i2i0000000000000000000−2i2i00000000
χ442-22-2-222-2222-2-2-22-2−2i2i−2i2i-2-22-22200000000-220000−2i2i00000000000000000002i−2i00000000
χ452-22-2-222-22-2-2-2222-22i−2i2i−2i20000-200000000000000−2i2i000000002i−2i2i−2i000002-20000000000
χ462-22-2-222-22-2-2-2222-22i−2i2i−2i20000-200000000000000−2i2i00000000−2i2i−2i2i00000-220000000000
χ472-22-2-222-22-2-2-2222-2−2i2i−2i2i20000-2000000000000002i−2i000000002i−2i2i−2i00000-220000000000
χ482-22-2-222-22-2-2-2222-2−2i2i−2i2i20000-2000000000000002i−2i00000000−2i2i−2i2i000002-20000000000
χ492-22-2-222-2-2222-2-2-22000022-22-2-200000000-22000000002i−2i2i−2i0000000000000002i−2i000000
χ502-22-2-222-2-2222-2-2-22000022-22-2-200000000-2200000000−2i2i−2i2i000000000000000−2i2i000000
χ512-22-2-222-2-2222-2-2-2200002-22-22-2000000002-2000000002i−2i2i−2i000000000000000−2i2i000000
χ522-22-2-222-2-2222-2-2-2200002-22-22-2000000002-200000000−2i2i−2i2i0000000000000002i−2i000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-4-440-440-4400000000000000002i22i2−2i2−2i200000000000000−2i22i2000000000000000000000
χ55444-4-4-4-440-440-440000000000000000−2i2−2i22i22i2000000000000002i2−2i2000000000000000000000
χ5644-44-44-4-4-4004004-400000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ5744-44-44-4-4-4004004-40000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ5844-4-44-44-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ5944-4-44-44-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ6044-4-44-44-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ6144-4-44-44-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ624-4444-4-4-404-40-4400000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ634-4444-4-4-404-40-440000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ644-4444-4-4-40-4404-40000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ654-4444-4-4-40-4404-4000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ664-44-4-444-4-4-4-4444-440000-400004000000000000000000000000000000000000000000000
χ674-4-4-444-44400400-4-44i−4i−4i4i000000000000000000000000000000000000000000000000000
χ684-4-4-444-44400400-4-4−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ694-4-4-444-44-400-40044000000000000000000000000000022−22−222200000000000000000000000
χ704-4-4-444-44-400-400440000000000000000000000000000−222222−2200000000000000000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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