Finite Group Databasebeta

← Group #308077

Character table — Group #308077

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-11-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1111111-1-11-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-11111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111111111-1-11111-1-1-1-1-1-11
χ17222222222-2-2222-2-22222-20000-22222000022-2-20000-2-20000000000000000000-20000000
χ18222222222-2-2222-2-22222-20000-2-2-2-2-20000-2-2-2-2000022000000000000000000020000000
χ19222222222-2-2222-2-2-2-2-2-2-20000-222220000-2-2220000-2-2000000000000000000020000000
χ20222222222-2-2222-2-2-2-2-2-2-20000-2-2-2-2-2000022220000220000000000000000000-20000000
χ2122222222-222-2-2-2220000-22222-2000022220000-2-222000000-2-2000000000000-200000000
χ2222222222-222-2-2-2220000-22222-20000-2-2-2-20000-2-2-2-200000022000000000000200000000
χ2322222222-222-2-2-2220000-2-2-2-2-2-200002222000022-2-2000000-2-2000000000000200000000
χ2422222222-222-2-2-2220000-2-2-2-2-2-20000-2-2-2-20000222200000022000000000000-200000000
χ2522-22-22-2-2222-22-2-2-222-2-220000-200000000002-200000022-2-200000000002-200000000000
χ2622-22-22-2-2222-22-2-2-222-2-220000-200000000002-2000000-2-2220000000000-2200000000000
χ2722-22-22-2-2222-22-2-2-2-2-22220000-20000000000-2200000022-2-20000000000-2200000000000
χ2822-22-22-2-2222-22-2-2-2-2-22220000-20000000000-22000000-2-22200000000002-200000000000
χ2922-22-22-2-22-2-2-22-22222-2-2-22i2i−2i−2i20000000000-222i−2i000000000000000000002i−2i000000000
χ3022-22-22-2-22-2-2-22-22222-2-2-2−2i−2i2i2i20000000000-22−2i2i00000000000000000000−2i2i000000000
χ3122-22-22-2-22-2-2-22-222-2-222-22i2i−2i−2i200000000002-22i−2i00000000000000000000−2i2i000000000
χ3222-22-22-2-22-2-2-22-222-2-222-2−2i−2i2i2i200000000002-2−2i2i000000000000000000002i−2i000000000
χ3322-22-22-2-2-2-2-22-2222000022i2i−2i−2i-2000000000000−2i2i000000000022-2-200000000002i−2i00000
χ3422-22-22-2-2-2-2-22-2222000022i2i−2i−2i-2000000000000−2i2i0000000000-2-2220000000000−2i2i00000
χ3522-22-22-2-2-2-2-22-222200002−2i−2i2i2i-20000000000002i−2i000000000022-2-20000000000−2i2i00000
χ3622-22-22-2-2-2-2-22-222200002−2i−2i2i2i-20000000000002i−2i0000000000-2-22200000000002i−2i00000
χ3722-2-2-2-2222002-2-2002-22-20000002i2i−2i−2i22−2−22i−2i0000000000002−22−22−2i2i2−i2−i200000000i2−i2000
χ3822-2-2-2-2222002-2-2002-22-20000002i2i−2i−2i−2−2222i−2i000000000000−22−22−22−i2−i2i2i200000000−i2i2000
χ3922-2-2-2-2222002-2-2002-22-2000000−2i−2i2i2i22−2−2−2i2i0000000000002−22−22−2−i2−i2i2i200000000−i2i2000
χ4022-2-2-2-2222002-2-2002-22-2000000−2i−2i2i2i−2−222−2i2i000000000000−22−22−22i2i2−i2−i200000000i2−i2000
χ4122-2-2-2-2222002-2-200-22-220000002i2i−2i−2i22−2−2−2i2i0000000000002−2−22−22i2i2−i2−i200000000−i2i2000
χ4222-2-2-2-2222002-2-200-22-220000002i2i−2i−2i−2−222−2i2i000000000000−222−22−2−i2−i2i2i200000000i2−i2000
χ4322-2-2-2-2222002-2-200-22-22000000−2i−2i2i2i22−2−22i−2i0000000000002−2−22−22−i2−i2i2i200000000i2−i2000
χ4422-2-2-2-2222002-2-200-22-22000000−2i−2i2i2i−2−2222i−2i000000000000−222−22−2i2i2−i2−i200000000−i2i2000
χ452-2-222-22-202-20002-2000002-22-20i2−i2i2−i22i−2i2i−2i0000002i−2ii2−i2i2−i2i2−i20000002−22−200000000002−20
χ462-2-222-22-202-20002-2000002-22-20i2−i2i2−i2−2i2i−2i2i000000−2i2ii2−i2i2−i2i2−i2000000−22−220000000000−220
χ472-2-222-22-202-20002-2000002-22-20−i2i2−i2i22i−2i2i−2i0000002i−2i−i2i2−i2i2−i2i2000000−22−220000000000−220
χ482-2-222-22-202-20002-2000002-22-20−i2i2−i2i2−2i2i−2i2i000000−2i2i−i2i2−i2i2−i2i20000002−22−200000000002−20
χ492-2-222-22-202-20002-200000-22-220i2−i2i2−i22i−2i2i−2i000000−2i2ii2−i2−i2i2−i2i20000002−22−20000000000−220
χ502-2-222-22-202-20002-200000-22-220i2−i2i2−i2−2i2i−2i2i0000002i−2ii2−i2−i2i2−i2i2000000−22−2200000000002−20
χ512-2-222-22-202-20002-200000-22-220−i2i2−i2i22i−2i2i−2i000000−2i2i−i2i2i2−i2i2−i2000000−22−2200000000002−20
χ522-2-222-22-202-20002-200000-22-220−i2i2−i2i2−2i2i−2i2i0000002i−2i−i2i2i2−i2i2−i20000002−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-44-4-4-4400-4-44004-4-44000000000000000000000000000000000000000000000000000
χ55444-44-4-4-4400-4-4400-444-4000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-40044-400000000000000000000000000000000000022−22−222200000000000000000
χ57444-44-4-4-4-40044-4000000000000000000000000000000000000−222222−2200000000000000000
χ5844-44-44-4-4-4444-44-4-40000-400004000000000000000000000000000000000000000000000
χ5944-4-4-4-444-400-44400000000000000002222−22−2200000000000000−2222000000000000000000000
χ6044-4-4-4-444-400-4440000000000000000−22−2222220000000000000022−22000000000000000000000
χ614-444-4-4-4404-4000-4400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ624-444-4-4-4404-4000-440000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ634-444-4-4-440-440004-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ644-444-4-4-440-440004-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ654-44-4-444-400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ664-44-4-444-400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ674-44-4-444-4000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ684-44-4-444-4000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ694-4-444-44-40-44000-4400000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ704-4-444-44-40-44000-440000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ718-8-8-888-88000000000000000000000000000000000000000000000000000000000000000

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