Finite Group Databasebeta

← Group #312120

Character table — Group #312120

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-111111111-1-1-11-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-1111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-11-1-11111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-111111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-11111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111-1-1-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11
χ17222222222-22-22-22-2-222220000-200002222-2-20000220000000000-2-20000000-2000000000
χ18222222222-22-22-22-2-222220000-20000-2-2-2-2-2-20000-2-200000000002200000002000000000
χ19222222222-22-22-22-2-2-2-2-2-20000-200002222220000-2-20000000000-2-200000002000000000
χ20222222222-22-22-22-2-2-2-2-2-20000-20000-2-2-2-2220000220000000000220000000-2000000000
χ2122222222-22-22-22-22-200002222-22222000000-2-2220000000000-2-2000000-2000000000000
χ2222222222-22-22-22-22-200002222-2-2-2-2-2000000-2-2-2-20000000000220000002000000000000
χ2322222222-22-22-22-22-20000-2-2-2-2-2222200000022-2-20000000000-2-20000002000000000000
χ2422222222-22-22-22-22-20000-2-2-2-2-2-2-2-2-20000002222000000000022000000-2000000000000
χ2522-2-2-22-222-2-222-2-22-200002i2i−2i−2i200000000002i−2i00002i2i−2i−2i00000000000000002-20000000
χ2622-2-2-22-222-2-222-2-22-200002i2i−2i−2i200000000002i−2i0000−2i−2i2i2i0000000000000000-220000000
χ2722-2-2-22-222-2-222-2-22-20000−2i−2i2i2i20000000000−2i2i00002i2i−2i−2i0000000000000000-220000000
χ2822-2-2-22-222-2-222-2-22-20000−2i−2i2i2i20000000000−2i2i0000−2i−2i2i2i00000000000000002-20000000
χ2922-2-2-22-22-222-2-222-2-22i2i−2i−2i00002000000002i−2i00000000002i2i−2i−2i000000000000002-200000
χ3022-2-2-22-22-222-2-222-2-22i2i−2i−2i00002000000002i−2i0000000000−2i−2i2i2i00000000000000-2200000
χ3122-2-2-22-22-222-2-222-2-2−2i−2i2i2i0000200000000−2i2i00000000002i2i−2i−2i00000000000000-2200000
χ3222-2-2-22-22-222-2-222-2-2−2i−2i2i2i0000200000000−2i2i0000000000−2i−2i2i2i000000000000002-200000
χ3322-2-2-22-22-2-222-2-22222i2i−2i−2i2i2i−2i−2i-200000000−2i2i−2i2i0000000000000000000002-20000000000
χ3422-2-2-22-22-2-222-2-22222i2i−2i−2i−2i−2i2i2i-200000000−2i2i2i−2i000000000000000000000-220000000000
χ3522-2-2-22-22-2-222-2-2222−2i−2i2i2i2i2i−2i−2i-2000000002i−2i−2i2i000000000000000000000-220000000000
χ3622-2-2-22-22-2-222-2-2222−2i−2i2i2i−2i−2i2i2i-2000000002i−2i2i−2i0000000000000000000002-20000000000
χ372-222-2-2-22020-20-202000002i−2i2i−2i02i2i−2i−2ii2i2−i2−i200002-20000002−22−200i2−i222−2−20000000000i2−i20
χ382-222-2-2-22020-20-202000002i−2i2i−2i02i2i−2i−2i−i2−i2i2i200002-2000000−22−2200−i2i2−2−2220000000000−i2i20
χ392-222-2-2-22020-20-202000002i−2i2i−2i0−2i−2i2i2ii2i2−i2−i20000-220000002−22−200i2−i2−2−2220000000000−i2i20
χ402-222-2-2-22020-20-202000002i−2i2i−2i0−2i−2i2i2i−i2−i2i2i20000-22000000−22−2200−i2i222−2−20000000000i2−i20
χ412-222-2-2-22020-20-20200000−2i2i−2i2i02i2i−2i−2ii2i2−i2−i20000-22000000−22−2200i2−i222−2−20000000000−i2i20
χ422-222-2-2-22020-20-20200000−2i2i−2i2i02i2i−2i−2i−i2−i2i2i20000-220000002−22−200−i2i2−2−2220000000000i2−i20
χ432-222-2-2-22020-20-20200000−2i2i−2i2i0−2i−2i2i2ii2i2−i2−i200002-2000000−22−2200i2−i2−2−2220000000000i2−i20
χ442-222-2-2-22020-20-20200000−2i2i−2i2i0−2i−2i2i2i−i2−i2i2i200002-20000002−22−200−i2i222−2−20000000000−i2i20
χ452-22-2-222-220-20-202002-22-200000i2−i2i2−i22i−2i2i−2i0000002i−2ii2−i2i2−i20000i2−i2002−22−2000000002−2000
χ462-22-2-222-220-20-202002-22-200000i2−i2i2−i2−2i2i−2i2i000000−2i2ii2−i2i2−i20000i2−i200−22−2200000000−22000
χ472-22-2-222-220-20-202002-22-200000−i2i2−i2i22i−2i2i−2i0000002i−2i−i2i2−i2i20000−i2i200−22−2200000000−22000
χ482-22-2-222-220-20-202002-22-200000−i2i2−i2i2−2i2i−2i2i000000−2i2i−i2i2−i2i20000−i2i2002−22−2000000002−2000
χ492-22-2-222-220-20-20200-22-2200000i2−i2i2−i22i−2i2i−2i000000−2i2i−i2i2−i2i20000i2−i2002−22−200000000−22000
χ502-22-2-222-220-20-20200-22-2200000i2−i2i2−i2−2i2i−2i2i0000002i−2i−i2i2−i2i20000i2−i200−22−22000000002−2000
χ512-22-2-222-220-20-20200-22-2200000−i2i2−i2i22i−2i2i−2i000000−2i2ii2−i2i2−i20000−i2i200−22−22000000002−2000
χ522-22-2-222-220-20-20200-22-2200000−i2i2−i2i2−2i2i−2i2i0000002i−2ii2−i2i2−i20000−i2i2002−22−200000000−22000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-44-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ55444-44-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ56444-44-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ57444-44-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ5844-4-4-44-4444-4-444-4-4400000000-4000000000000000000000000000000000000000000000
χ594-444-4-4-440-404040-4000000000000002i22i2−2i2−2i2000000000000000000−2i22i200000000000000000
χ604-444-4-4-440-404040-400000000000000−2i2−2i22i22i20000000000000000002i2−2i200000000000000000
χ614-44-4-444-4-404040-4000000000002i2−2i22i2−2i200000000000000000000−2i22i20000000000000000000
χ624-44-4-444-4-404040-400000000000−2i22i2−2i22i2000000000000000000002i2−2i20000000000000000000
χ634-4-4444-4-44040-40-400000000000000000000000000022−22−22220000000000000000000000000
χ644-4-4444-4-44040-40-4000000000000000000000000000−222222−220000000000000000000000000
χ654-4-4444-4-4-40-40404004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ664-4-4444-4-4-40-4040400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ674-4-4-44-44404040-40-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ684-4-4-44-44404040-40-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ694-4-4-44-4440-40-40404000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-44-4440-40-4040400000-444-40000000000000000000000000000000000000000000000
χ7188-88-8-88-8000000000000000000000000000000000000000000000000000000000000000

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