Finite Group Databasebeta

← Group #312913

Character table — Group #312913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-1111-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-1-1-1111-1
χ91111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111111-111-1-111-1-11-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-11111-11-1-111-1-111-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11-111-1-1-1-111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-11111-1-11-1
χ17222222222-22-22-22-22222-2-20000000022-2-2-2-20000-2-200002200000000000000000000
χ18222222222-22-22-22-22222-2-200000000-2-2-2-2220000220000-2-200000000000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-2000000002222-2-20000220000-2-200000000000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-200000000-2-222220000-2-200002200000000000000000000
χ2122222222-22-22-22-220000-2-22222-2-2-2-200000022220000000000000000-2-20000000000
χ2222222222-22-22-22-220000-2-22222-2-2-2-2000000-2-2-2-20000000000000000220000000000
χ2322222222-22-22-22-220000-2-2-2-2-2-2222200000022-2-20000000000000000-220000000000
χ2422222222-22-22-22-220000-2-2-2-2-2-22222000000-2-22200000000000000002-20000000000
χ252222-2-2-2-2-20-20202022-2-20022−2−222−2−200002i−2i00002i−2i22−2−200i2i2−i2−i2i2i2−i2−i2000000000000
χ262222-2-2-2-2-20-20202022-2-20022−2−222−2−20000−2i2i0000−2i2i22−2−200−i2−i2i2i2−i2−i2i2i2000000000000
χ272222-2-2-2-2-20-20202022-2-200−2−222−2−22200002i−2i00002i−2i−2−22200−i2−i2i2i2−i2−i2i2i2000000000000
χ282222-2-2-2-2-20-20202022-2-200−2−222−2−2220000−2i2i0000−2i2i−2−22200i2i2−i2−i2i2i2−i2−i2000000000000
χ292222-2-2-2-2-20-202020-2-2220022−2−222−2−200002i−2i0000−2i2i−2−22200i2i2−i2−i2−i2−i2i2i2000000000000
χ302222-2-2-2-2-20-202020-2-2220022−2−222−2−20000−2i2i00002i−2i−2−22200−i2−i2i2i2i2i2−i2−i2000000000000
χ312222-2-2-2-2-20-202020-2-22200−2−222−2−22200002i−2i0000−2i2i22−2−200−i2−i2i2i2i2i2−i2−i2000000000000
χ322222-2-2-2-2-20-202020-2-22200−2−222−2−2220000−2i2i00002i−2i22−2−200i2i2−i2−i2−i2−i2i2i2000000000000
χ3322-2-22-22-2-202020-202i−2i2i−2i00i2−i2i2−i2i2−i2i2−i22-200000000002−22−22i−2ii2−i2i2−i22−22−2000000000000
χ3422-2-22-22-2-202020-202i−2i2i−2i00i2−i2i2−i2i2−i2i2−i2-2200000000002−22−2−2i2i−i2i2−i2i2−22−22000000000000
χ3522-2-22-22-2-202020-202i−2i2i−2i00−i2i2−i2i2−i2i2−i2i22-20000000000−22−222i−2i−i2i2−i2i2−22−22000000000000
χ3622-2-22-22-2-202020-202i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2-220000000000−22−22−2i2ii2−i2i2−i22−22−2000000000000
χ3722-2-22-22-2-202020-20−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i22-20000000000−22−22−2i2ii2−i2i2−i2−22−22000000000000
χ3822-2-22-22-2-202020-20−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2-220000000000−22−222i−2i−i2i2−i2i22−22−2000000000000
χ3922-2-22-22-2-202020-20−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i22-200000000002−22−2−2i2i−i2i2−i2i22−22−2000000000000
χ4022-2-22-22-2-202020-20−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i2-2200000000002−22−22i−2ii2−i2i2−i2−22−22000000000000
χ4122-2-2-22-2222-2-222-2-22i−2i−2i2i-222i−2i−2i2i2i−2i−2i2i002i−2i000000002-2-220000000000000000000000
χ4222-2-2-22-2222-2-222-2-22i−2i−2i2i-22−2i2i2i−2i−2i2i2i−2i002i−2i00000000-222-20000000000000000000000
χ4322-2-2-22-2222-2-222-2-2−2i2i2i−2i-222i−2i−2i2i2i−2i−2i2i00−2i2i00000000-222-20000000000000000000000
χ4422-2-2-22-2222-2-222-2-2−2i2i2i−2i-22−2i2i2i−2i−2i2i2i−2i00−2i2i000000002-2-220000000000000000000000
χ4522-2-2-22-222-2-222-2-222i−2i−2i2i2-20000000000−2i2i000000000000002-2-22−2i2i2i−2i000000000000
χ4622-2-2-22-222-2-222-2-222i−2i−2i2i2-20000000000−2i2i00000000000000-222-22i−2i−2i2i000000000000
χ4722-2-2-22-222-2-222-2-22−2i2i2i−2i2-200000000002i−2i000000000000002-2-222i−2i−2i2i000000000000
χ4822-2-2-22-222-2-222-2-22−2i2i2i−2i2-200000000002i−2i00000000000000-222-2−2i2i2i−2i000000000000
χ4922-2-2-22-22-222-2-222-200002-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000002i−2i2-2000000
χ5022-2-2-22-22-222-2-222-200002-22i−2i−2i2i−2i2i2i−2i0000000000000000000000000000−2i2i-22000000
χ5122-2-2-22-22-222-2-222-200002-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000002i−2i-22000000
χ5222-2-2-22-22-222-2-222-200002-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000−2i2i2-2000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ544444-4-4-4-44040-40-400000002222−22−22−22−22222200000000000000000000000000000000000000
χ554444-4-4-4-44040-40-40000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5644-4-44-44-440-40-40400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ5744-4-44-44-440-40-4040000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ5844-4-4-44-44-4-444-4-4440000-440000000000000000000000000000000000000000000000
χ594-44-444-4-4040-40-40400000000000000000000000000000000000000000000002i2−2i20000
χ604-44-444-4-4040-40-4040000000000000000000000000000000000000000000000−2i22i20000
χ614-44-444-4-40-404040-400000000000000000000004i−4i0000000000000000000000000000
χ624-44-444-4-40-404040-40000000000000000000000−4i4i0000000000000000000000000000
χ634-4-44-444-404040-40-40000000000000000000000000000000000000000000000002i2−2i200
χ644-4-44-444-404040-40-4000000000000000000000000000000000000000000000000−2i22i200
χ654-4-44-444-40-40-40404000000000000000000004-4000000000000000000000000000000
χ664-4-44-444-40-40-4040400000000000000000000-44000000000000000000000000000000
χ678-88-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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