Finite Group Databasebeta

← Group #282784

Character table — Group #282784

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882222244488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111
χ5111111111111111111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-11111-1-11-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1111-1-111-1-1-1
χ911111111111111111-1-1-1-111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111-1-1-1111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-11-1-1111-1-1-1-11
χ1722222222222-2-2-2-22-222220000-200002222000022-2-2000000-2-20000000000-20000000000
χ1822222222222-2-2-2-22-222220000-20000-2-2-2-20000-2-2-2-200000022000000000020000000000
χ1922222222222-2-2-2-22-2-2-2-2-20000-2000022220000-2-222000000-2-2000000000020000000000
χ2022222222222-2-2-2-22-2-2-2-2-20000-20000-2-2-2-200002222000000220000000000-20000000000
χ2122222222-2-2-22222-2-200002222-222220000-2-2220000-2-20000000000000000000-20000000
χ2222222222-2-2-22222-2-200002222-2-2-2-2-20000-2-2-2-2000022000000000000000000020000000
χ2322222222-2-2-22222-2-20000-2-2-2-2-22222000022-2-20000-2-2000000000000000000020000000
χ2422222222-2-2-22222-2-20000-2-2-2-2-2-2-2-2-2000022220000220000000000000000000-20000000
χ25222-2-22-2-20002-22-200000022-2-202i2i−2i−2ii2i2−i2−i2002i−2i0000000000i2−i2i2i2−i2−i222−2−200000000002−20
χ26222-2-22-2-20002-22-200000022-2-202i2i−2i−2i−i2−i2i2i2002i−2i0000000000−i2i2−i2−i2i2i2−2−2220000000000−220
χ27222-2-22-2-20002-22-200000022-2-20−2i−2i2i2ii2i2−i2−i200−2i2i0000000000i2−i2i2i2−i2−i2−2−2220000000000−220
χ28222-2-22-2-20002-22-200000022-2-20−2i−2i2i2i−i2−i2i2i200−2i2i0000000000−i2i2−i2−i2i2i222−2−200000000002−20
χ29222-2-22-2-20002-22-2000000-2-22202i2i−2i−2ii2i2−i2−i200−2i2i0000000000i2−i2−i2−i2i2i222−2−20000000000−220
χ30222-2-22-2-20002-22-2000000-2-22202i2i−2i−2i−i2−i2i2i200−2i2i0000000000−i2i2i2i2−i2−i2−2−22200000000002−20
χ31222-2-22-2-20002-22-2000000-2-2220−2i−2i2i2ii2i2−i2−i2002i−2i0000000000i2−i2−i2−i2i2i2−2−22200000000002−20
χ32222-2-22-2-20002-22-2000000-2-2220−2i−2i2i2i−i2−i2i2i2002i−2i0000000000−i2i2i2i2−i2−i222−2−20000000000−220
χ3322-2-2-2-2222-220000-202i2i−2i−2i000002−22−22-22-200002i−2i002−2i2i2−i2−i20000002−22−200000000i2−i2000
χ3422-2-2-2-2222-220000-202i2i−2i−2i000002−22−2-22-220000−2i2i002−2i2i2−i2−i2000000−22−2200000000−i2i2000
χ3522-2-2-2-2222-220000-202i2i−2i−2i00000−22−222-22-200002i−2i00−22−i2−i2i2i2000000−22−2200000000−i2i2000
χ3622-2-2-2-2222-220000-202i2i−2i−2i00000−22−22-22-220000−2i2i00−22−i2−i2i2i20000002−22−200000000i2−i2000
χ3722-2-2-2-2222-220000-20−2i−2i2i2i000002−22−22-22-20000−2i2i002−2−i2−i2i2i20000002−22−200000000−i2i2000
χ3822-2-2-2-2222-220000-20−2i−2i2i2i000002−22−2-22-2200002i−2i002−2−i2−i2i2i2000000−22−2200000000i2−i2000
χ3922-2-2-2-2222-220000-20−2i−2i2i2i00000−22−222-22-20000−2i2i00−22i2i2−i2−i2000000−22−2200000000i2−i2000
χ4022-2-2-2-2222-220000-20−2i−2i2i2i00000−22−22-22-2200002i−2i00−22i2i2−i2−i20000002−22−200000000−i2i2000
χ412-2-22-222-222-222-2-2-2-22i−2i2i−2i00002000000000000002i−2i000000002i−2i2i−2i00000002-200000000
χ422-2-22-222-222-222-2-2-2-22i−2i2i−2i00002000000000000002i−2i00000000−2i2i−2i2i0000000-2200000000
χ432-2-22-222-222-222-2-2-2-2−2i2i−2i2i0000200000000000000−2i2i000000002i−2i2i−2i0000000-2200000000
χ442-2-22-222-222-222-2-2-2-2−2i2i−2i2i0000200000000000000−2i2i00000000−2i2i−2i2i00000002-200000000
χ452-2-22-222-222-2-2-222-222i−2i2i−2i2-22-2-2000000002-20000−2i2i00000000000000000000002i−2i00000
χ462-2-22-222-222-2-2-222-222i−2i2i−2i-22-22-200000000-220000−2i2i0000000000000000000000−2i2i00000
χ472-2-22-222-222-2-2-222-22−2i2i−2i2i2-22-2-2000000002-200002i−2i0000000000000000000000−2i2i00000
χ482-2-22-222-222-2-2-222-22−2i2i−2i2i-22-22-200000000-2200002i−2i00000000000000000000002i−2i00000
χ492-2-22-222-2-2-22-2-2222-200002-22-2200000000-22000000002-22-200000000002-200000000000
χ502-2-22-222-2-2-22-2-2222-200002-22-2200000000-2200000000-22-220000000000-2200000000000
χ512-2-22-222-2-2-22-2-2222-20000-22-222000000002-2000000002-22-20000000000-2200000000000
χ522-2-22-222-2-2-22-2-2222-20000-22-222000000002-200000000-22-2200000000002-200000000000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-44-4-4000-44-440000000000000002i22i2−2i2−2i200000000000000−2i22i2000000000000000000000
χ55444-4-44-4-4000-44-44000000000000000−2i2−2i22i22i2000000000000002i2−2i2000000000000000000000
χ5644-444-4-4-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ5744-444-4-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ5844-444-4-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ5944-444-4-4-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ6044-4-4-4-444-44-400004000000000022−2222−22000000000000−2222000000000000000000000000000
χ6144-4-4-4-444-44-4000040000000000−2222−222200000000000022−22000000000000000000000000000
χ624-44-44-44-44-4-40000404-4-4400000000000000000000000000000000000000000000000000
χ634-44-44-44-44-4-4000040-444-400000000000000000000000000000000000000000000000000
χ644-44-44-44-4-4440000-400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ654-44-44-44-4-4440000-40000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ664-4-44-444-4-4-4444-4-44400000000-4000000000000000000000000000000000000000000000
χ674-4-4-444-440004-4-440000000000000000000000000000000000022−22−222200000000000000000
χ684-4-4-444-440004-4-4400000000000000000000000000000000000−222222−2200000000000000000
χ694-4-4-444-44000-444-40000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-444-44000-444-4000000-444-40000000000000000000000000000000000000000000000
χ718-888-8-8-88000000000000000000000000000000000000000000000000000000000000000

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