Finite Group Databasebeta

← Group #310071

Character table — Group #310071

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-111-111-1-11-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-111-1-1-1-11111111111-1-11-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-111-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-11111-1-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1111111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111111111-1-1111-1-11-1-1-1-11
χ17222222222-22-2-222-2-200002222-2222200000022-2-200000000-2-20000000000-20000000000
χ18222222222-22-2-222-2-200002222-2-2-2-2-2000000-2-2-2-20000000022000000000020000000000
χ19222222222-22-2-222-2-20000-2-2-2-2-22222000000-2-22200000000-2-2000000000020000000000
χ20222222222-22-2-222-2-20000-2-2-2-2-2-2-2-2-2000000222200000000220000000000-20000000000
χ2122222222-22-222-2-22-222220000-200002222-2-2000022-2-2000000000000000000000-200000
χ2222222222-22-222-2-22-222220000-20000-2-2-2-2-2-20000-2-222000000000000000000000200000
χ2322222222-22-222-2-22-2-2-2-2-20000-200002222220000-2-2-2-2000000000000000000000200000
χ2422222222-22-222-2-22-2-2-2-2-20000-20000-2-2-2-22200002222000000000000000000000-200000
χ25222-22-2-2-2-202002-20000002i2i−2i−2i022-2-2i2i2−i2−i2002i−2i0000i2−i200000022−2−2i2i2−i2−i200000000002−20
χ26222-22-2-2-2-202002-20000002i2i−2i−2i022-2-2−i2−i2i2i2002i−2i0000−i2i2000000−2−222−i2−i2i2i20000000000−220
χ27222-22-2-2-2-202002-20000002i2i−2i−2i0-2-222i2i2−i2−i200−2i2i0000i2−i200000022−2−2−i2−i2i2i20000000000−220
χ28222-22-2-2-2-202002-20000002i2i−2i−2i0-2-222−i2−i2i2i200−2i2i0000−i2i2000000−2−222i2i2−i2−i200000000002−20
χ29222-22-2-2-2-202002-2000000−2i−2i2i2i022-2-2i2i2−i2−i200−2i2i0000i2−i2000000−2−222i2i2−i2−i20000000000−220
χ30222-22-2-2-2-202002-2000000−2i−2i2i2i022-2-2−i2−i2i2i200−2i2i0000−i2i200000022−2−2−i2−i2i2i200000000002−20
χ31222-22-2-2-2-202002-2000000−2i−2i2i2i0-2-222i2i2−i2−i2002i−2i0000i2−i2000000−2−222−i2−i2i2i200000000002−20
χ32222-22-2-2-2-202002-2000000−2i−2i2i2i0-2-222−i2−i2i2i2002i−2i0000−i2i200000022−2−2i2i2−i2−i20000000000−220
χ3322-2-2-2-2220202-200-202i2i−2i−2i000002−22−22-22-20000002i−2i00i2i2−i2−i22−200002−22−200000000i2−i2000
χ3422-2-2-2-2220202-200-202i2i−2i−2i000002−22−2-22-22000000−2i2i00i2i2−i2−i22−20000−22−2200000000−i2i2000
χ3522-2-2-2-2220202-200-202i2i−2i−2i00000−22−222-22-20000002i−2i00−i2−i2i2i2−220000−22−2200000000−i2i2000
χ3622-2-2-2-2220202-200-202i2i−2i−2i00000−22−22-22-22000000−2i2i00−i2−i2i2i2−2200002−22−200000000i2−i2000
χ3722-2-2-2-2220202-200-20−2i−2i2i2i000002−22−22-22-2000000−2i2i00−i2−i2i2i22−200002−22−200000000−i2i2000
χ3822-2-2-2-2220202-200-20−2i−2i2i2i000002−22−2-22-220000002i−2i00−i2−i2i2i22−20000−22−2200000000i2−i2000
χ3922-2-2-2-2220202-200-20−2i−2i2i2i00000−22−222-22-2000000−2i2i00i2i2−i2−i2−220000−22−2200000000i2−i2000
χ4022-2-2-2-2220202-200-20−2i−2i2i2i00000−22−22-22-220000002i−2i00i2i2−i2−i2−2200002−22−200000000−i2i2000
χ412-222-2-22-222-2-2-22-22200002i−2i2i−2i-20000000000002i−2i00002-22-20000000000000002i−2i000000
χ422-222-2-22-222-2-2-22-22200002i−2i2i−2i-20000000000002i−2i0000-22-22000000000000000−2i2i000000
χ432-222-2-22-222-2-2-22-2220000−2i2i−2i2i-2000000000000−2i2i00002-22-2000000000000000−2i2i000000
χ442-222-2-22-222-2-2-22-2220000−2i2i−2i2i-2000000000000−2i2i0000-22-220000000000000002i−2i000000
χ452-222-2-22-22-2-2222-2-2-22i−2i2i−2i2i−2i2i−2i2000000002i−2i00−2i2i0000000000000000000002-200000000
χ462-222-2-22-22-2-2222-2-2-22i−2i2i−2i−2i2i−2i2i2000000002i−2i002i−2i000000000000000000000-2200000000
χ472-222-2-22-22-2-2222-2-2-2−2i2i−2i2i2i−2i2i−2i200000000−2i2i00−2i2i000000000000000000000-2200000000
χ482-222-2-22-22-2-2222-2-2-2−2i2i−2i2i−2i2i−2i2i200000000−2i2i002i−2i0000000000000000000002-200000000
χ492-222-2-22-2-2-2222-22-222i−2i2i−2i0000-200000000−2i2i000000000000002i−2i2i−2i00002-200000000000
χ502-222-2-22-2-2-2222-22-222i−2i2i−2i0000-200000000−2i2i00000000000000−2i2i−2i2i0000-2200000000000
χ512-222-2-22-2-2-2222-22-22−2i2i−2i2i0000-2000000002i−2i000000000000002i−2i2i−2i0000-2200000000000
χ522-222-2-22-2-2-2222-22-22−2i2i−2i2i0000-2000000002i−2i00000000000000−2i2i−2i2i00002-200000000000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-44-4-4-440-400-440000000000000002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ55444-44-4-4-440-400-44000000000000000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ5644-44-44-4-400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ5744-44-44-4-400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ5844-44-44-4-4000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ5944-44-44-4-4000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ6044-4-4-4-4440-40-44004000000000022−2222−22000000000000000000−2222000000000000000000000
χ6144-4-4-4-4440-40-440040000000000−2222−222200000000000000000022−22000000000000000000000
χ624-444-4-44-4-444-4-4-444-4000000004000000000000000000000000000000000000000000000
χ634-44-4-44-4440400-4-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ644-44-4-44-4440400-4-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ654-44-4-44-44-40-400440000004-4-440000000000000000000000000000000000000000000000
χ664-44-4-44-44-40-40044000000-444-40000000000000000000000000000000000000000000000
χ674-4-4-4444-4040-4400-400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ684-4-4-4444-4040-4400-40000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ694-4-4-4444-40-404-400404-4-4400000000000000000000000000000000000000000000000000
χ704-4-4-4444-40-404-40040-444-400000000000000000000000000000000000000000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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