Finite Group Databasebeta

← Group #310219

Character table — Group #310219

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-11-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-111-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111111-1-111-1-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-11-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-111111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-11111-1-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111111-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-111-1-111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111111111-1-1111-1-11-1-1-1-11
χ17222222222-22-2-222-22222-20000-22222000022-2-20000000000-2-2000000000000000-200000
χ18222222222-22-2-222-22222-20000-2-2-2-2-20000-2-2-2-2000000000022000000000000000200000
χ19222222222-22-2-222-2-2-2-2-2-20000-222220000-2-2220000000000-2-2000000000000000200000
χ20222222222-22-2-222-2-2-2-2-2-20000-2-2-2-2-200002222000000000022000000000000000-200000
χ2122222222-22-222-2-220000-22222-2000022220000-2-222-2-20000000000000000-20000000000
χ2222222222-22-222-2-220000-22222-20000-2-2-2-20000-2-2-2-222000000000000000020000000000
χ2322222222-22-222-2-220000-2-2-2-2-2-200002222000022-2-2-2-2000000000000000020000000000
χ2422222222-22-222-2-220000-2-2-2-2-2-20000-2-2-2-200002222220000000000000000-20000000000
χ2522-22-2-22-220-200-2202i2i−2i−2i0000002i2i−2i−2ii2i2−i2−i22-2000000i2−i200000022−2−222−2−20000000000i2−i20
χ2622-22-2-22-220-200-2202i2i−2i−2i0000002i2i−2i−2i−i2−i2i2i22-2000000−i2i2000000−2−222−2−2220000000000−i2i20
χ2722-22-2-22-220-200-2202i2i−2i−2i000000−2i−2i2i2ii2i2−i2−i2-22000000i2−i200000022−2−2−2−2220000000000−i2i20
χ2822-22-2-22-220-200-2202i2i−2i−2i000000−2i−2i2i2i−i2−i2i2i2-22000000−i2i2000000−2−22222−2−20000000000i2−i20
χ2922-22-2-22-220-200-220−2i−2i2i2i0000002i2i−2i−2ii2i2−i2−i2-22000000i2−i2000000−2−22222−2−20000000000−i2i20
χ3022-22-2-22-220-200-220−2i−2i2i2i0000002i2i−2i−2i−i2−i2i2i2-22000000−i2i200000022−2−2−2−2220000000000i2−i20
χ3122-22-2-22-220-200-220−2i−2i2i2i000000−2i−2i2i2ii2i2−i2−i22-2000000i2−i2000000−2−222−2−2220000000000i2−i20
χ3222-22-2-22-220-200-220−2i−2i2i2i000000−2i−2i2i2i−i2−i2i2i22-2000000−i2i200000022−2−222−2−20000000000−i2i20
χ3322-2-2-22-2222-2-2-22-222i−2i2i−2i20000-200000000002i−2i00000022-2-20000000000000002i−2i000000
χ3422-2-2-22-2222-2-2-22-222i−2i2i−2i20000-200000000002i−2i000000-2-222000000000000000−2i2i000000
χ3522-2-2-22-2222-2-2-22-22−2i2i−2i2i20000-20000000000−2i2i00000022-2-2000000000000000−2i2i000000
χ3622-2-2-22-2222-2-2-22-22−2i2i−2i2i20000-20000000000−2i2i000000-2-2220000000000000002i−2i000000
χ3722-2-2-22-222-2-2222-2-22i−2i2i−2i-22i2i−2i−2i20000000000−2i2i2i−2i0000000000000000000002-200000000
χ3822-2-2-22-222-2-2222-2-22i−2i2i−2i-2−2i−2i2i2i20000000000−2i2i−2i2i000000000000000000000-2200000000
χ3922-2-2-22-222-2-2222-2-2−2i2i−2i2i-22i2i−2i−2i200000000002i−2i2i−2i000000000000000000000-2200000000
χ4022-2-2-22-222-2-2222-2-2−2i2i−2i2i-2−2i−2i2i2i200000000002i−2i−2i2i0000000000000000000002-200000000
χ4122-2-2-22-22-2-2222-22-2000022i2i−2i−2i-2000000000000−2i2i00000000002i−2i2i−2i00002-200000000000
χ4222-2-2-22-22-2-2222-22-2000022i2i−2i−2i-2000000000000−2i2i0000000000−2i2i−2i2i0000-2200000000000
χ4322-2-2-22-22-2-2222-22-200002−2i−2i2i2i-20000000000002i−2i00000000002i−2i2i−2i0000-2200000000000
χ4422-2-2-22-22-2-2222-22-200002−2i−2i2i2i-20000000000002i−2i0000000000−2i2i−2i2i00002-200000000000
χ452-2-222-2-220202-200-2000002i−2i2i−2i02−22−22i−2i2i−2i0000002-200i2−i2i2−i22−20000i2−i2i2−i2000000002−2000
χ462-2-222-2-220202-200-2000002i−2i2i−2i02−22−2−2i2i−2i2i000000-2200i2−i2i2−i22−20000−i2i2−i2i200000000−22000
χ472-2-222-2-220202-200-2000002i−2i2i−2i0−22−222i−2i2i−2i0000002-200−i2i2−i2i2−220000−i2i2−i2i200000000−22000
χ482-2-222-2-220202-200-2000002i−2i2i−2i0−22−22−2i2i−2i2i000000-2200−i2i2−i2i2−220000i2−i2i2−i2000000002−2000
χ492-2-222-2-220202-200-200000−2i2i−2i2i02−22−22i−2i2i−2i000000-2200−i2i2−i2i22−20000i2−i2i2−i200000000−22000
χ502-2-222-2-220202-200-200000−2i2i−2i2i02−22−2−2i2i−2i2i0000002-200−i2i2−i2i22−20000−i2i2−i2i2000000002−2000
χ512-2-222-2-220202-200-200000−2i2i−2i2i0−22−222i−2i2i−2i000000-2200i2−i2i2−i2−220000−i2i2−i2i2000000002−2000
χ522-2-222-2-220202-200-200000−2i2i−2i2i0−22−22−2i2i−2i2i0000002-200i2−i2i2−i2−220000i2−i2i2−i200000000−22000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-44-4-4-440400-4-404-4-44000000000000000000000000000000000000000000000000000
χ55444-44-4-4-440400-4-40-444-4000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-40-40044000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ57444-44-4-4-4-40-4004400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ5844-44-4-44-4-404004-40000000000000002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ5944-44-4-44-4-404004-4000000000000000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ6044-4-4-44-44-444-4-4-4440000-400004000000000000000000000000000000000000000000000
χ614-444-44-4-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ624-444-44-4-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ634-444-44-4-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ644-444-44-4-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ654-44-4-4-444040-4400-400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ664-44-4-4-444040-4400-40000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ674-44-4-4-4440-404-4004000004-4-440000000000000000000000000000000000000000000000
χ684-44-4-4-4440-404-400400000-444-40000000000000000000000000000000000000000000000
χ694-4-444-4-440-40-44004000000000022−2222−22000000000000000000−2222000000000000000000000
χ704-4-444-4-440-40-440040000000000−2222−222200000000000000000022−22000000000000000000000
χ718-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000

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