Finite Group Databasebeta

← Group #306455

Character table — Group #306455

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-111111111-1-1-1-11111-11-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-111-1-111-1-111-1
χ911111111111111111-1-1-1-1111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1111-1-11111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-111111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111111111-1-111-1-1-1-1-1-11
χ17222222222-22-22-22-2-200002222-222220000-2-2000022000000-2-200000000-2000000000000
χ18222222222-22-22-22-2-200002222-2-2-2-2-20000-2-20000-2-200000022000000002000000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-222220000220000-2-2000000-2-2000000002000000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-2-2-20000220000220000002200000000-2000000000000
χ2122222222-22-22-22-22-222220000-20000222200-2-22200-2-2000000000000000-200000000000
χ2222222222-22-22-22-22-222220000-20000-2-2-2-200-2-2-2-20022000000000000000200000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-2000022220022-2-200-2-2000000000000000200000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-20000-2-2-2-20022220022000000000000000-200000000000
χ2522-2-2-222-22-2-222-2-22-22i2i−2i−2i0000200000000002i−2i00000000000022-2-20000002i−2i000000000
χ2622-2-2-222-22-2-222-2-22-22i2i−2i−2i0000200000000002i−2i000000000000-2-222000000−2i2i000000000
χ2722-2-2-222-22-2-222-2-22-2−2i−2i2i2i000020000000000−2i2i00000000000022-2-2000000−2i2i000000000
χ2822-2-2-222-22-2-222-2-22-2−2i−2i2i2i000020000000000−2i2i000000000000-2-2220000002i−2i000000000
χ2922-2-2-222-2-222-2-222-2-2000022-2-22000000002-2000000002i2i−2i−2i00000000000000002i−2i00000
χ3022-2-2-222-2-222-2-222-2-2000022-2-22000000002-200000000−2i−2i2i2i0000000000000000−2i2i00000
χ3122-2-2-222-2-222-2-222-2-20000-2-222200000000-22000000002i2i−2i−2i0000000000000000−2i2i00000
χ3222-2-2-222-2-222-2-222-2-20000-2-222200000000-2200000000−2i−2i2i2i00000000000000002i−2i00000
χ3322-2-2-222-2-2-222-2-22222i2i−2i−2i22-2-2-200000000-22−2i2i0000000000000000000000002i−2i0000000
χ3422-2-2-222-2-2-222-2-22222i2i−2i−2i-2-222-2000000002-2−2i2i000000000000000000000000−2i2i0000000
χ3522-2-2-222-2-2-222-2-2222−2i−2i2i2i22-2-2-200000000-222i−2i000000000000000000000000−2i2i0000000
χ3622-2-2-222-2-2-222-2-2222−2i−2i2i2i-2-222-2000000002-22i−2i0000000000000000000000002i−2i0000000
χ372-22-2-22-2202020-20-202-22-20000022−2−22i2i−2i−2i00002i−2i00002−22−22−20000i2i2−i2−i20000000000i2−i20
χ382-22-2-22-2202020-20-202-22-20000022−2−2−2i−2i2i2i0000−2i2i00002−22−22−20000−i2−i2i2i20000000000−i2i20
χ392-22-2-22-2202020-20-202-22-200000−2−2222i2i−2i−2i00002i−2i0000−22−22−220000−i2−i2i2i20000000000−i2i20
χ402-22-2-22-2202020-20-202-22-200000−2−222−2i−2i2i2i0000−2i2i0000−22−22−220000i2i2−i2−i20000000000i2−i20
χ412-22-2-22-2202020-20-20-22-220000022−2−22i2i−2i−2i0000−2i2i0000−22−222−20000i2i2−i2−i20000000000−i2i20
χ422-22-2-22-2202020-20-20-22-220000022−2−2−2i−2i2i2i00002i−2i0000−22−222−20000−i2−i2i2i20000000000i2−i20
χ432-22-2-22-2202020-20-20-22-2200000−2−2222i2i−2i−2i0000−2i2i00002−22−2−220000−i2−i2i2i20000000000i2−i20
χ442-22-2-22-2202020-20-20-22-2200000−2−222−2i−2i2i2i00002i−2i00002−22−2−220000i2i2−i2−i20000000000−i2i20
χ452-2-22-2-2222020-20-20000002i−2i2i−2i02-22-22−22−20000002i−2i2−2000000i2−i2i2−i22−22−200000000i2−i2000
χ462-2-22-2-2222020-20-20000002i−2i2i−2i02-22-2−22−220000002i−2i−22000000−i2i2−i2i2−22−2200000000−i2i2000
χ472-2-22-2-2222020-20-20000002i−2i2i−2i0-22-222−22−2000000−2i2i2−2000000i2−i2i2−i2−22−2200000000−i2i2000
χ482-2-22-2-2222020-20-20000002i−2i2i−2i0-22-22−22−22000000−2i2i−22000000−i2i2−i2i22−22−200000000i2−i2000
χ492-2-22-2-2222020-20-2000000−2i2i−2i2i02-22-22−22−2000000−2i2i2−2000000−i2i2−i2i22−22−200000000−i2i2000
χ502-2-22-2-2222020-20-2000000−2i2i−2i2i02-22-2−22−22000000−2i2i−22000000i2−i2i2−i2−22−2200000000i2−i2000
χ512-2-22-2-2222020-20-2000000−2i2i−2i2i0-22-222−22−20000002i−2i2−2000000−i2i2−i2i2−22−2200000000i2−i2000
χ522-2-22-2-2222020-20-2000000−2i2i−2i2i0-22-22−22−220000002i−2i−22000000i2−i2i2−i22−22−200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ5444-4-44-4-4400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ5544-4-44-4-4400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ5644-4-44-4-44000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ5744-4-44-4-44000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ5844-4-4-444-444-4-444-4-4400000000-4000000000000000000000000000000000000000000000
χ594-44-44-44-440-40-404000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ604-44-44-44-440-40-40400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ614-44-44-44-4-404040-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ624-44-44-44-4-404040-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ634-44-4-44-440-40-4040400000000002222−22−22000000000000000000−2222000000000000000000000
χ644-44-4-44-440-40-404040000000000−22−22222200000000000000000022−22000000000000000000000
χ654-4-4444-4-4040-40-40400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ664-4-4444-4-4040-40-4040000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ674-4-4444-4-40-404040-404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ684-4-4444-4-40-404040-40−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ694-4-44-4-444-40-4040400000000000000022−2222−2200000000−2222000000000000000000000000000
χ704-4-44-4-444-40-40404000000000000000−2222−22220000000022−22000000000000000000000000000
χ718888-8-8-8-8000000000000000000000000000000000000000000000000000000000000000

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