Finite Group Databasebeta

← Group #282767

Character table — Group #282767

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11-1-111-1111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111-1-1111-1-1-1-1-1-11
χ17222222222-2-222-2-222222-20000-222220000002200-2-2-2-20000000000000000000-20000000
χ18222222222-2-222-2-222222-20000-2-2-2-2-2000000-2-200-2-222000000000000000000020000000
χ19222222222-2-222-2-22-2-2-2-2-20000-22222000000-2-20022-2-2000000000000000000020000000
χ20222222222-2-222-2-22-2-2-2-2-20000-2-2-2-2-2000000220022220000000000000000000-20000000
χ2122222222-222-2-222-20000-22222-200002222-2-200220000-2-2000000000000-2000000000000
χ2222222222-222-2-222-20000-22222-20000-2-2-2-2-2-200-2-20000220000000000002000000000000
χ2322222222-222-2-222-20000-2-2-2-2-2-2000022222200-2-20000-2-20000000000002000000000000
χ2422222222-222-2-222-20000-2-2-2-2-2-20000-2-2-2-2220022000022000000000000-2000000000000
χ2522-22-2-2-2202-2002-20000002i2i−2i−2i0i2i2−i2−i222-2-200002i−2i00i2−i200000022−2−2i2i2−i2−i200000000002−20
χ2622-22-2-2-2202-2002-20000002i2i−2i−2i0i2i2−i2−i2-2-2220000−2i2i00i2−i200000022−2−2−i2−i2i2i20000000000−220
χ2722-22-2-2-2202-2002-20000002i2i−2i−2i0−i2−i2i2i222-2-200002i−2i00−i2i2000000−2−222−i2−i2i2i20000000000−220
χ2822-22-2-2-2202-2002-20000002i2i−2i−2i0−i2−i2i2i2-2-2220000−2i2i00−i2i2000000−2−222i2i2−i2−i200000000002−20
χ2922-22-2-2-2202-2002-2000000−2i−2i2i2i0i2i2−i2−i222-2-20000−2i2i00i2−i2000000−2−222i2i2−i2−i20000000000−220
χ3022-22-2-2-2202-2002-2000000−2i−2i2i2i0i2i2−i2−i2-2-22200002i−2i00i2−i2000000−2−222−i2−i2i2i200000000002−20
χ3122-22-2-2-2202-2002-2000000−2i−2i2i2i0−i2−i2i2i222-2-20000−2i2i00−i2i200000022−2−2−i2−i2i2i200000000002−20
χ3222-22-2-2-2202-2002-2000000−2i−2i2i2i0−i2−i2i2i2-2-22200002i−2i00−i2i200000022−2−2i2i2−i2−i20000000000−220
χ332-22-2-22-22222-2-2-2-2222-2-222i−2i2i−2i-2000000002i−2i00002-200000000000000000002i−2i00000000
χ342-22-2-22-22222-2-2-2-2222-2-22−2i2i−2i2i-200000000−2i2i00002-20000000000000000000−2i2i00000000
χ352-22-2-22-22222-2-2-2-22-2-22222i−2i2i−2i-2000000002i−2i0000-220000000000000000000−2i2i00000000
χ362-22-2-22-22222-2-2-2-22-2-2222−2i2i−2i2i-200000000−2i2i0000-2200000000000000000002i−2i00000000
χ372-22-2-22-222-2-2-2-222222-2-2-20000200000000000000-22000000002-22-200000000002-200000
χ382-22-2-22-222-2-2-2-222222-2-2-20000200000000000000-2200000000-22-220000000000-2200000
χ392-22-2-22-222-2-2-2-2222-2-222-200002000000000000002-2000000002-22-20000000000-2200000
χ402-22-2-22-222-2-2-2-2222-2-222-200002000000000000002-200000000-22-2200000000002-200000
χ412-22-2-22-22-22222-2-2-20000-22i−2i2i−2i200000000−2i2i00000000002i2i−2i−2i0000000002-20000000000
χ422-22-2-22-22-22222-2-2-20000-22i−2i2i−2i200000000−2i2i0000000000−2i−2i2i2i000000000-220000000000
χ432-22-2-22-22-22222-2-2-20000-2−2i2i−2i2i2000000002i−2i00000000002i2i−2i−2i000000000-220000000000
χ442-22-2-22-22-22222-2-2-20000-2−2i2i−2i2i2000000002i−2i0000000000−2i−2i2i2i0000000002-20000000000
χ452-2-22-222-22002-200-22-22-20000002i−2i2i−2i2−22−2002i−2i0000002−22−22−20000i2−i2i2−i200000000i2−i2000
χ462-2-22-222-22002-200-22-22-20000002i−2i2i−2i−22−22002i−2i000000−22−22−220000−i2i2−i2i200000000−i2i2000
χ472-2-22-222-22002-200-22-22-2000000−2i2i−2i2i2−22−200−2i2i0000002−22−22−20000−i2i2−i2i200000000−i2i2000
χ482-2-22-222-22002-200-22-22-2000000−2i2i−2i2i−22−2200−2i2i000000−22−22−220000i2−i2i2−i200000000i2−i2000
χ492-2-22-222-22002-200-2-22-220000002i−2i2i−2i2−22−200−2i2i0000002−2−22−220000i2−i2i2−i200000000−i2i2000
χ502-2-22-222-22002-200-2-22-220000002i−2i2i−2i−22−2200−2i2i000000−222−22−20000−i2i2−i2i200000000i2−i2000
χ512-2-22-222-22002-200-2-22-22000000−2i2i−2i2i2−22−2002i−2i0000002−2−22−220000−i2i2−i2i200000000i2−i2000
χ522-2-22-222-22002-200-2-22-22000000−2i2i−2i2i−22−22002i−2i000000−222−22−20000i2−i2i2−i200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ5444-44-4-4-440-4400-44000000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ5544-44-4-4-440-4400-4400000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ5644-4-444-4-4400-4400-44-4-44000000000000000000000000000000000000000000000000000
χ5744-4-444-4-4400-4400-4-444-4000000000000000000000000000000000000000000000000000
χ5844-4-444-4-4-4004-40040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5944-4-444-4-4-4004-4004000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ604-4444-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ614-4444-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ624-4444-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ634-4444-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ644-44-4-44-44-4-4-44444-4000040000-4000000000000000000000000000000000000000000000
χ654-4-44-444-4-400-440040000000000000022−2222−220000000000−22220000000000000000000000000
χ664-4-44-444-4-400-4400400000000000000−2222−2222000000000022−220000000000000000000000000
χ674-4-4-44-44404-400-440000004-4-440000000000000000000000000000000000000000000000
χ684-4-4-44-44404-400-44000000-444-40000000000000000000000000000000000000000000000
χ694-4-4-44-4440-44004-40000000000000000000000000000000000022−22−222200000000000000000
χ704-4-4-44-4440-44004-400000000000000000000000000000000000−222222−2200000000000000000
χ71888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000

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