Finite Group Databasebeta

← Group #279872

Character table — Group #279872

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882224444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-1111-111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-11111111111-1-1-11-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111111-1-1-11111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-111-1-1-1-1-111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-111-11111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-111111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1111111111-1-1111-1-1-1-1-1-11
χ172222222222-2-22-2-22-200002222-200002222000022-2-2000000-2-200000000-2000000000000
χ182222222222-2-22-2-22-200002222-20000-2-2-2-20000-2-2-2-200000022000000002000000000000
χ192222222222-2-22-2-22-20000-2-2-2-2-2000022220000-2-222000000-2-2000000002000000000000
χ202222222222-2-22-2-22-20000-2-2-2-2-20000-2-2-2-2000022220000002200000000-2000000000000
χ2122222222-2-222-222-2-222220000-22222000022-2-20000-2-200000000000000000-2000000000
χ2222222222-2-222-222-2-222220000-2-2-2-2-20000-2-2-2-2000022000000000000000002000000000
χ2322222222-2-222-222-2-2-2-2-2-20000-222220000-2-2220000-2-2000000000000000002000000000
χ2422222222-2-222-222-2-2-2-2-2-20000-2-2-2-2-20000222200002200000000000000000-2000000000
χ25222-2-2-22-22-200-20020000022-2-20i2i2−i2−i22i2i−2i−2i00002i−2i00i2−i2i2i2−i2−i200000022−2−200000000002−20
χ26222-2-2-22-22-200-20020000022-2-20i2i2−i2−i2−2i−2i2i2i0000−2i2i00i2−i2i2i2−i2−i2000000−2−2220000000000−220
χ27222-2-2-22-22-200-20020000022-2-20−i2−i2i2i22i2i−2i−2i00002i−2i00−i2i2−i2−i2i2i2000000−2−2220000000000−220
χ28222-2-2-22-22-200-20020000022-2-20−i2−i2i2i2−2i−2i2i2i0000−2i2i00−i2i2−i2−i2i2i200000022−2−200000000002−20
χ29222-2-2-22-22-200-200200000-2-2220i2i2−i2−i22i2i−2i−2i0000−2i2i00i2−i2−i2−i2i2i200000022−2−20000000000−220
χ30222-2-2-22-22-200-200200000-2-2220i2i2−i2−i2−2i−2i2i2i00002i−2i00i2−i2−i2−i2i2i2000000−2−22200000000002−20
χ31222-2-2-22-22-200-200200000-2-2220−i2−i2i2i22i2i−2i−2i0000−2i2i00−i2i2i2i2−i2−i2000000−2−22200000000002−20
χ32222-2-2-22-22-200-200200000-2-2220−i2−i2i2i2−2i−2i2i2i00002i−2i00−i2i2i2i2−i2−i200000022−2−20000000000−220
χ3322-2-222-2-2002-202-20022-2-2000002-22-2i2−i2i2−i22-2000000000000i2−i2i2i2−i2−i2i2−i2i2−i200000000i2−i2000
χ3422-2-222-2-2002-202-20022-2-2000002-22-2−i2i2−i2i22-2000000000000−i2i2−i2−i2i2i2−i2i2−i2i200000000−i2i2000
χ3522-2-222-2-2002-202-20022-2-200000-22-22i2−i2i2−i2-22000000000000i2−i2i2i2−i2−i2−i2i2−i2i200000000−i2i2000
χ3622-2-222-2-2002-202-20022-2-200000-22-22−i2i2−i2i2-22000000000000−i2i2−i2−i2i2i2i2−i2i2−i200000000i2−i2000
χ3722-2-222-2-2002-202-200-2-222000002-22-2i2−i2i2−i2-22000000000000i2−i2−i2−i2i2i2i2−i2i2−i200000000−i2i2000
χ3822-2-222-2-2002-202-200-2-222000002-22-2−i2i2−i2i2-22000000000000−i2i2i2i2−i2−i2−i2i2−i2i200000000i2−i2000
χ3922-2-222-2-2002-202-200-2-22200000-22-22i2−i2i2−i22-2000000000000i2−i2−i2−i2i2i2−i2i2−i2i200000000i2−i2000
χ4022-2-222-2-2002-202-200-2-22200000-22-22−i2i2−i2i22-2000000000000−i2i2i2i2−i2−i2i2−i2i2−i200000000−i2i2000
χ412-222-22-2-22-2222-2-2-2-22-22-22i−2i2i−2i200000000002-2002i−2i000000000000000000002i−2i0000000
χ422-222-22-2-22-2222-2-2-2-22-22-2−2i2i−2i2i200000000002-200−2i2i00000000000000000000−2i2i0000000
χ432-222-22-2-22-2222-2-2-2-2-22-222i−2i2i−2i20000000000-22002i−2i00000000000000000000−2i2i0000000
χ442-222-22-2-22-2222-2-2-2-2-22-22−2i2i−2i2i20000000000-2200−2i2i000000000000000000002i−2i0000000
χ452-222-22-2-22-2-2-2222-2200002i−2i2i−2i-200000000000000−2i2i000000002i−2i2i−2i000002-20000000000
χ462-222-22-2-22-2-2-2222-2200002i−2i2i−2i-200000000000000−2i2i00000000−2i2i−2i2i00000-220000000000
χ472-222-22-2-22-2-2-2222-220000−2i2i−2i2i-2000000000000002i−2i000000002i−2i2i−2i00000-220000000000
χ482-222-22-2-22-2-2-2222-220000−2i2i−2i2i-2000000000000002i−2i00000000−2i2i−2i2i000002-20000000000
χ492-222-22-2-2-2222-2-2-2222-22-20000-20000000000-220000002i−2i2i−2i00000000000000002i−2i00000
χ502-222-22-2-2-2222-2-2-2222-22-20000-20000000000-22000000−2i2i−2i2i0000000000000000−2i2i00000
χ512-222-22-2-2-2222-2-2-222-22-220000-200000000002-20000002i−2i2i−2i0000000000000000−2i2i00000
χ522-222-22-2-2-2222-2-2-222-22-220000-200000000002-2000000−2i2i−2i2i00000000000000002i−2i00000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4400400-400000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ55444-4-4-44-4-4400400-40000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ5644-44-4-4-440000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ5744-44-4-4-440000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ5844-44-4-4-44000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ5944-44-4-4-44000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ6044-4-444-4-400-440-440000000000000002i2−2i22i2−2i200000000000000−2i22i2000000000000000000000
χ6144-4-444-4-400-440-44000000000000000−2i22i2−2i22i2000000000000002i2−2i2000000000000000000000
χ624-444-44-4-4-44-4-4-4444-4000000004000000000000000000000000000000000000000000000
χ634-44-44-4-444400-400-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ644-44-44-4-444400-400-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ654-44-44-4-44-4-4004004000000000000000000000000000022−22−222200000000000000000000000
χ664-44-44-4-44-4-40040040000000000000000000000000000−222222−2200000000000000000000000
χ674-4-4-4-4444004-40-44004-4-4400000000000000000000000000000000000000000000000000
χ684-4-4-4-4444004-40-4400-444-400000000000000000000000000000000000000000000000000
χ694-4-4-4-444400-4404-40000000000000000000000000000000000022−22−222200000000000000000
χ704-4-4-4-444400-4404-400000000000000000000000000000000000−222222−2200000000000000000
χ718-8-888-88-8000000000000000000000000000000000000000000000000000000000000000

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