Finite Group Databasebeta

← Group #309558

Character table — Group #309558

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1111-11111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-1-1-111111111-1-1-1-111111111-1-11-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-111-1-1-111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-111111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1111-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111111-1-11-1-1-1-1-1-11
χ1722222222222-2-2-2-22-222220000-222220000-2-2220000-2-20000000000000000000-20000000
χ1822222222222-2-2-2-22-222220000-2-2-2-2-20000-2-2-2-2000022000000000000000000020000000
χ1922222222222-2-2-2-22-2-2-2-2-20000-22222000022-2-20000-2-2000000000000000000020000000
χ2022222222222-2-2-2-22-2-2-2-2-20000-2-2-2-2-2000022220000220000000000000000000-20000000
χ2122222222-2-2-22222-2-200002222-200002222000022-2-200-2-200000000000000-20000000000
χ2222222222-2-2-22222-2-200002222-20000-2-2-2-20000-2-2-2-200220000000000000020000000000
χ2322222222-2-2-22222-2-20000-2-2-2-2-2000022220000-2-22200-2-20000000000000020000000000
χ2422222222-2-2-22222-2-20000-2-2-2-2-20000-2-2-2-200002222002200000000000000-20000000000
χ25222-22-2-2-2-22-20000202i2i−2i−2i000002i2i−2i−2i22−2−2002-20000002−2i2i2−i2−i20000i2i2−i2−i2000000002−2000
χ26222-22-2-2-2-22-20000202i2i−2i−2i000002i2i−2i−2i−2−222002-2000000−22−i2−i2i2i20000−i2−i2i2i200000000−22000
χ27222-22-2-2-2-22-20000202i2i−2i−2i00000−2i−2i2i2i22−2−200-220000002−2i2i2−i2−i20000−i2−i2i2i200000000−22000
χ28222-22-2-2-2-22-20000202i2i−2i−2i00000−2i−2i2i2i−2−22200-22000000−22−i2−i2i2i20000i2i2−i2−i2000000002−2000
χ29222-22-2-2-2-22-2000020−2i−2i2i2i000002i2i−2i−2i22−2−200-220000002−2−i2−i2i2i20000i2i2−i2−i200000000−22000
χ30222-22-2-2-2-22-2000020−2i−2i2i2i000002i2i−2i−2i−2−22200-22000000−22i2i2−i2−i20000−i2−i2i2i2000000002−2000
χ31222-22-2-2-2-22-2000020−2i−2i2i2i00000−2i−2i2i2i22−2−2002-20000002−2−i2−i2i2i20000−i2−i2i2i2000000002−2000
χ32222-22-2-2-2-22-2000020−2i−2i2i2i00000−2i−2i2i2i−2−222002-2000000−22i2i2−i2−i20000i2i2−i2−i200000000−22000
χ3322-22-2-2-220002-22-200000022-2-20i2−i2i2−i22i−2i2i−2i00002i−2i00i2−i2000000i2i2−i2−i22−22−200000000002−20
χ3422-22-2-2-220002-22-200000022-2-20i2−i2i2−i2−2i2i−2i2i0000−2i2i00i2−i2000000i2i2−i2−i2−22−220000000000−220
χ3522-22-2-2-220002-22-200000022-2-20−i2i2−i2i22i−2i2i−2i00002i−2i00−i2i2000000−i2−i2i2i2−22−220000000000−220
χ3622-22-2-2-220002-22-200000022-2-20−i2i2−i2i2−2i2i−2i2i0000−2i2i00−i2i2000000−i2−i2i2i22−22−200000000002−20
χ3722-22-2-2-220002-22-2000000-2-2220i2−i2i2−i22i−2i2i−2i0000−2i2i00i2−i2000000−i2−i2i2i22−22−20000000000−220
χ3822-22-2-2-220002-22-2000000-2-2220i2−i2i2−i2−2i2i−2i2i00002i−2i00i2−i2000000−i2−i2i2i2−22−2200000000002−20
χ3922-22-2-2-220002-22-2000000-2-2220−i2i2−i2i22i−2i2i−2i0000−2i2i00−i2i2000000i2i2−i2−i2−22−2200000000002−20
χ4022-22-2-2-220002-22-2000000-2-2220−i2i2−i2i2−2i2i−2i2i00002i−2i00−i2i2000000i2i2−i2−i22−22−20000000000−220
χ412-222-22-2-22-2-222-2-22-22i−2i2i−2i00002000000002i−2i000000000000002-22-200000000002i−2i00000
χ422-222-22-2-22-2-222-2-22-22i−2i2i−2i00002000000002i−2i00000000000000-22-220000000000−2i2i00000
χ432-222-22-2-22-2-222-2-22-2−2i2i−2i2i0000200000000−2i2i000000000000002-22-20000000000−2i2i00000
χ442-222-22-2-22-2-222-2-22-2−2i2i−2i2i0000200000000−2i2i00000000000000-22-2200000000002i−2i00000
χ452-222-22-2-22-2-2-2-222222i−2i2i−2i2i−2i2i−2i-200000000−2i2i00002i−2i00000000000000002-200000000000
χ462-222-22-2-22-2-2-2-222222i−2i2i−2i−2i2i−2i2i-200000000−2i2i0000−2i2i0000000000000000-2200000000000
χ472-222-22-2-22-2-2-2-22222−2i2i−2i2i2i−2i2i−2i-2000000002i−2i00002i−2i0000000000000000-2200000000000
χ482-222-22-2-22-2-2-2-22222−2i2i−2i2i−2i2i−2i2i-2000000002i−2i0000−2i2i00000000000000002-200000000000
χ492-222-22-2-2-222-2-222-2-200002i−2i2i−2i200000000000000−2i2i00002-22-2000000000002i−2i00000000
χ502-222-22-2-2-222-2-222-2-200002i−2i2i−2i200000000000000−2i2i0000-22-2200000000000−2i2i00000000
χ512-222-22-2-2-222-2-222-2-20000−2i2i−2i2i2000000000000002i−2i00002-22-200000000000−2i2i00000000
χ522-222-22-2-2-222-2-222-2-20000−2i2i−2i2i2000000000000002i−2i0000-22-22000000000002i−2i00000000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-44-4-4-44-440000-4000000000000002222−22−220000000000−22220000000000000000000000000
χ55444-44-4-4-44-440000-400000000000000−22−222222000000000022−220000000000000000000000000
χ5644-44-4-4-44000-44-44000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ5744-44-4-4-44000-44-4400000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ5844-4-4-444-400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ5944-4-4-444-400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ6044-4-4-444-4000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ6144-4-4-444-4000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ624-444-44-4-4-44444-4-4-4400000000-4000000000000000000000000000000000000000000000
χ634-44-4-4-44444-40000-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ644-44-4-4-44444-40000-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ654-44-4-4-444-4-440000404-4-4400000000000000000000000000000000000000000000000000
χ664-44-4-4-444-4-44000040-444-400000000000000000000000000000000000000000000000000
χ674-4-444-44-40004-4-44000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ684-4-444-44-40004-4-4400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ694-4-444-44-4000-444-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ704-4-444-44-4000-444-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ718-8-8-888-88000000000000000000000000000000000000000000000000000000000000000

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