Finite Group Databasebeta

← Group #309541

Character table — Group #309541

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-11111-1-1-1-111111111-1-1-11-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1111111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111-1-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-222-2-22-20000-22222-200002222-2-200002200-2-2000000000000-2000000000000
χ18222222222-222-2-22-20000-22222-20000-2-2-2-2-2-20000-2-200220000000000002000000000000
χ19222222222-222-2-22-20000-2-2-2-2-2-200002222220000-2-200-2-20000000000002000000000000
χ20222222222-222-2-22-20000-2-2-2-2-2-20000-2-2-2-2220000220022000000000000-2000000000000
χ2122222222-22-2-222-222222-20000-2222200000022-2-200-2-200000000000000000-2000000000
χ2222222222-22-2-222-222222-20000-2-2-2-2-2000000-2-2-2-20022000000000000000002000000000
χ2322222222-22-2-222-22-2-2-2-2-20000-22222000000-2-22200-2-2000000000000000002000000000
χ2422222222-22-2-222-22-2-2-2-2-20000-2-2-2-2-20000002222002200000000000000000-2000000000
χ2522-2-222-2-20-2002-2022i2i−2i−2i00000022-2-222−2−2002i−2i0000002−20000i2i2−i2−i222−2−200000000i2−i2000
χ2622-2-222-2-20-2002-2022i2i−2i−2i00000022-2-2−2−222002i−2i000000−220000−i2−i2i2i2−2−22200000000−i2i2000
χ2722-2-222-2-20-2002-2022i2i−2i−2i000000-2-22222−2−200−2i2i0000002−20000i2i2−i2−i2−2−22200000000−i2i2000
χ2822-2-222-2-20-2002-2022i2i−2i−2i000000-2-222−2−22200−2i2i000000−220000−i2−i2i2i222−2−200000000i2−i2000
χ2922-2-222-2-20-2002-202−2i−2i2i2i00000022-2-222−2−200−2i2i0000002−20000−i2−i2i2i222−2−200000000−i2i2000
χ3022-2-222-2-20-2002-202−2i−2i2i2i00000022-2-2−2−22200−2i2i000000−220000i2i2−i2−i2−2−22200000000i2−i2000
χ3122-2-222-2-20-2002-202−2i−2i2i2i000000-2-22222−2−2002i−2i0000002−20000−i2−i2i2i2−2−22200000000i2−i2000
χ3222-2-222-2-20-2002-202−2i−2i2i2i000000-2-222−2−222002i−2i000000−220000i2i2−i2−i222−2−200000000−i2i2000
χ3322-2-2-2-222202-200-20000002i2i−2i−2i02−22−22-22-20000002i−2i2−200i2i2−i2−i200002−22−20000000000i2−i20
χ3422-2-2-2-222202-200-20000002i2i−2i−2i02−22−2-22-22000000−2i2i2−200i2i2−i2−i20000−22−220000000000−i2i20
χ3522-2-2-2-222202-200-20000002i2i−2i−2i0−22−222-22-20000002i−2i−2200−i2−i2i2i20000−22−220000000000−i2i20
χ3622-2-2-2-222202-200-20000002i2i−2i−2i0−22−22-22-22000000−2i2i−2200−i2−i2i2i200002−22−20000000000i2−i20
χ3722-2-2-2-222202-200-2000000−2i−2i2i2i02−22−22-22-2000000−2i2i2−200−i2−i2i2i200002−22−20000000000−i2i20
χ3822-2-2-2-222202-200-2000000−2i−2i2i2i02−22−2-22-220000002i−2i2−200−i2−i2i2i20000−22−220000000000i2−i20
χ3922-2-2-2-222202-200-2000000−2i−2i2i2i0−22−222-22-2000000−2i2i−2200i2i2−i2−i20000−22−220000000000i2−i20
χ4022-2-2-2-222202-200-2000000−2i−2i2i2i0−22−22-22-220000002i−2i−2200i2i2−i2−i200002−22−20000000000−i2i20
χ412-2-22-222-222-2-2-2-2222i−2i2i−2i22i−2i2i−2i-2000000002i−2i002i−2i00000000000000000002-20000000000
χ422-2-22-222-222-2-2-2-2222i−2i2i−2i2−2i2i−2i2i-200000000−2i2i002i−2i0000000000000000000-220000000000
χ432-2-22-222-222-2-2-2-222−2i2i−2i2i22i−2i2i−2i-2000000002i−2i00−2i2i0000000000000000000-220000000000
χ442-2-22-222-222-2-2-2-222−2i2i−2i2i2−2i2i−2i2i-200000000−2i2i00−2i2i00000000000000000002-20000000000
χ452-2-22-222-22-2-2-2222-20000-22i−2i2i−2i200000000−2i2i000000000000002-22-200000000002i−2i00000
χ462-2-22-222-22-2-2-2222-20000-22i−2i2i−2i200000000−2i2i00000000000000-22-220000000000−2i2i00000
χ472-2-22-222-22-2-2-2222-20000-2−2i2i−2i2i2000000002i−2i000000000000002-22-20000000000−2i2i00000
χ482-2-22-222-22-2-2-2222-20000-2−2i2i−2i2i2000000002i−2i00000000000000-22-2200000000002i−2i00000
χ492-2-22-222-2-2222-2-2-222i−2i2i−2i-200002000000000000−2i2i0000002-22-20000000000002i−2i0000000
χ502-2-22-222-2-2222-2-2-222i−2i2i−2i-200002000000000000−2i2i000000-22-22000000000000−2i2i0000000
χ512-2-22-222-2-2222-2-2-22−2i2i−2i2i-2000020000000000002i−2i0000002-22-2000000000000−2i2i0000000
χ522-2-22-222-2-2222-2-2-22−2i2i−2i2i-2000020000000000002i−2i000000-22-220000000000002i−2i0000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ544444-4-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ554444-4-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ564444-4-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ574444-4-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ5844-4-444-4-40400-440-4000000000000002222−22−220000000000−22220000000000000000000000000
χ5944-4-444-4-40400-440-400000000000000−22−222222000000000022−220000000000000000000000000
χ6044-4-4-4-444-40-440040000000000022−2222−22000000000000−2222000000000000000000000000000
χ6144-4-4-4-444-40-4400400000000000−2222−222200000000000022−22000000000000000000000000000
χ624-44-44-44-440-4400-40000004-4-440000000000000000000000000000000000000000000000
χ634-44-44-44-440-4400-4000000-444-40000000000000000000000000000000000000000000000
χ644-44-44-44-4-404-400400000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ654-44-44-44-4-404-40040000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ664-44-4-44-4404004-40-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ674-44-4-44-4404004-40-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ684-44-4-44-440-400-44044-4-44000000000000000000000000000000000000000000000000000
χ694-44-4-44-440-400-4404-444-4000000000000000000000000000000000000000000000000000
χ704-4-44-444-4-4-44444-4-4000040000-4000000000000000000000000000000000000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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