Finite Group Databasebeta

← Group #307883

Character table — Group #307883

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11-1-1-11111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-111111111-1-1-11-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111111-111-1-1-1-111-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-111111-1-111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-1-1111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111-1-11-1-111-1-1-1-11
χ17222222222-2-22-222-2-222220000-222220000-2-2002200-2-200000000000000000-2000000000
χ18222222222-2-22-222-2-222220000-2-2-2-2-20000-2-200-2-20022000000000000000002000000000
χ19222222222-2-22-222-2-2-2-2-2-20000-2222200002200-2-200-2-2000000000000000002000000000
χ20222222222-2-22-222-2-2-2-2-2-20000-2-2-2-2-20000220022002200000000000000000-2000000000
χ2122222222-222-22-2-22-200002222-20000222200-2-2002200-2-2000000000000-2000000000000
χ2222222222-222-22-2-22-200002222-20000-2-2-2-200-2-200-2-200220000000000002000000000000
χ2322222222-222-22-2-22-20000-2-2-2-2-200002222002200-2-200-2-20000000000002000000000000
χ2422222222-222-22-2-22-20000-2-2-2-2-20000-2-2-2-2002200220022000000000000-2000000000000
χ25222-2-22-2-2222-2-22-2-2222-2-20000-2000000002-2000000000022-2-20000000002-20000000000
χ26222-2-22-2-2222-2-22-2-2222-2-20000-2000000002-20000000000-2-222000000000-220000000000
χ27222-2-22-2-2222-2-22-2-22-2-2220000-200000000-22000000000022-2-2000000000-220000000000
χ28222-2-22-2-2222-2-22-2-22-2-2220000-200000000-220000000000-2-2220000000002-20000000000
χ29222-2-22-2-22-2-2-222-22-222-2-22i2i−2i−2i200000000-222i−2i000000000000000000000000002i−2i00000
χ30222-2-22-2-22-2-2-222-22-222-2-2−2i−2i2i2i200000000-22−2i2i00000000000000000000000000−2i2i00000
χ31222-2-22-2-22-2-2-222-22-2-2-2222i2i−2i−2i2000000002-22i−2i00000000000000000000000000−2i2i00000
χ32222-2-22-2-22-2-2-222-22-2-2-222−2i−2i2i2i2000000002-2−2i2i000000000000000000000000002i−2i00000
χ33222-2-22-2-2-2-2-222-222200002i2i−2i−2i-20000000000−2i2i00000000000022-2-2000000002i−2i0000000
χ34222-2-22-2-2-2-2-222-222200002i2i−2i−2i-20000000000−2i2i000000000000-2-22200000000−2i2i0000000
χ35222-2-22-2-2-2-2-222-22220000−2i−2i2i2i-200000000002i−2i00000000000022-2-200000000−2i2i0000000
χ36222-2-22-2-2-2-2-222-22220000−2i−2i2i2i-200000000002i−2i000000000000-2-222000000002i−2i0000000
χ3722-22-2-2-22-200202-2002i−2i2i−2i000002i2i−2i−2ii2i2−i2−i200002-20000i2−i200002−22−222−2−20000000000i2−i20
χ3822-22-2-2-22-200202-2002i−2i2i−2i000002i2i−2i−2i−i2−i2i2i200002-20000−i2i20000−22−22−2−2220000000000−i2i20
χ3922-22-2-2-22-200202-2002i−2i2i−2i00000−2i−2i2i2ii2i2−i2−i20000-220000i2−i200002−22−2−2−2220000000000−i2i20
χ4022-22-2-2-22-200202-2002i−2i2i−2i00000−2i−2i2i2i−i2−i2i2i20000-220000−i2i20000−22−2222−2−20000000000i2−i20
χ4122-22-2-2-22-200202-200−2i2i−2i2i000002i2i−2i−2ii2i2−i2−i20000-220000i2−i20000−22−2222−2−20000000000−i2i20
χ4222-22-2-2-22-200202-200−2i2i−2i2i000002i2i−2i−2i−i2−i2i2i20000-220000−i2i200002−22−2−2−2220000000000i2−i20
χ4322-22-2-2-22-200202-200−2i2i−2i2i00000−2i−2i2i2ii2i2−i2−i200002-20000i2−i20000−22−22−2−2220000000000i2−i20
χ4422-22-2-2-22-200202-200−2i2i−2i2i00000−2i−2i2i2i−i2−i2i2i200002-20000−i2i200002−22−222−2−20000000000−i2i20
χ452-2-2-2-222202-20-2002000002-22-202−22−22-22-20000002-22−2002−22−200002−22−2000000002−2000
χ462-2-2-2-222202-20-2002000002-22-202−22−2-22-22000000-222−2002−22−20000−22−2200000000−22000
χ472-2-2-2-222202-20-2002000002-22-20−22−222-22-20000002-2−2200−22−220000−22−2200000000−22000
χ482-2-2-2-222202-20-2002000002-22-20−22−22-22-22000000-22−2200−22−2200002−22−2000000002−2000
χ492-2-2-2-222202-20-200200000-22-2202−22−22-22-2000000-222−200−22−2200002−22−200000000−22000
χ502-2-2-2-222202-20-200200000-22-2202−22−2-22-220000002-22−200−22−220000−22−22000000002−2000
χ512-2-2-2-222202-20-200200000-22-220−22−222-22-2000000-22−22002−22−20000−22−22000000002−2000
χ522-2-2-2-222202-20-200200000-22-220−22−22-22-220000002-2−22002−22−200002−22−200000000−22000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-44-4-4-4444-4-44-4-4000000004000000000000000000000000000000000000000000000
χ5544-44-4-4-44400-40-440000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ5644-44-4-4-44400-40-44000000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ5744-4-44-44-440040-4-40000000000000000000000000000000000022−22−222200000000000000000
χ5844-4-44-44-440040-4-400000000000000000000000000000000000−222222−2200000000000000000
χ5944-4-44-44-4-400-4044004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6044-4-44-44-4-400-404400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ614-44-44-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ624-44-44-4-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ634-44-44-4-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ644-44-44-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ654-4-4444-4-404-40400-400000000000000000000000000000022−22−2222000000000000000000000
χ664-4-4444-4-404-40400-4000000000000000000000000000000−222222−22000000000000000000000
χ674-4-4444-4-40-440-4004000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ684-4-4444-4-40-440-400400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ694-4-4-4-44440-440400-4000000000022−2222−22000000000000−2222000000000000000000000000000
χ704-4-4-4-44440-440400-40000000000−2222−222200000000000022−22000000000000000000000000000
χ718-888-8-88-8000000000000000000000000000000000000000000000000000000000000000

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