Finite Group Databasebeta

← Group #312927

Character table — Group #312927

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888224444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-111-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1111-1-1111-1
χ91111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ111111111111111111-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-11111-1-11-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1111111-11-1-1-1-111-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-11-111-1-111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-111-11-1-111-1-11-1
χ17222222222-22-22-22-20000-2-22222-2-2-2-2002200-2-200000000000000000000-2200000000
χ18222222222-22-22-22-20000-2-22222-2-2-2-200-2-20022000000000000000000002-200000000
χ19222222222-22-22-22-20000-2-2-2-2-2-222220022002200000000000000000000-2-200000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2222200-2-200-2-2000000000000000000002200000000
χ2122222222-22-22-22-222222-2-2000000002200-2-200-2-2-2-200002200000000000000000000
χ2222222222-22-22-22-222222-2-200000000-2-2002200-2-2220000-2-200000000000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000000002200-2-20022220000-2-200000000000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200000000-2-200220022-2-200002200000000000000000000
χ25222-22-2-2-2020-20-20222-2-200i2i2−i2−i2i2i2−i2−i22-20000000000i2i2−i2−i22-2i2i2−i2−i2i2i2−i2−i2000000000000
χ26222-22-2-2-2020-20-20222-2-200i2i2−i2−i2i2i2−i2−i2-220000000000i2i2−i2−i2-22−i2−i2i2i2−i2−i2i2i2000000000000
χ27222-22-2-2-2020-20-20222-2-200−i2−i2i2i2−i2−i2i2i22-20000000000−i2−i2i2i22-2−i2−i2i2i2−i2−i2i2i2000000000000
χ28222-22-2-2-2020-20-20222-2-200−i2−i2i2i2−i2−i2i2i2-220000000000−i2−i2i2i2-22i2i2−i2−i2i2i2−i2−i2000000000000
χ29222-22-2-2-2020-20-202-2-22200i2i2−i2−i2i2i2−i2−i22-20000000000−i2−i2i2i2-22i2i2−i2−i2−i2−i2i2i2000000000000
χ30222-22-2-2-2020-20-202-2-22200i2i2−i2−i2i2i2−i2−i2-220000000000−i2−i2i2i22-2−i2−i2i2i2i2i2−i2−i2000000000000
χ31222-22-2-2-2020-20-202-2-22200−i2−i2i2i2−i2−i2i2i22-20000000000i2i2−i2−i2-22−i2−i2i2i2i2i2−i2−i2000000000000
χ32222-22-2-2-2020-20-202-2-22200−i2−i2i2i2−i2−i2i2i2-220000000000i2i2−i2−i22-2i2i2−i2−i2−i2−i2i2i2000000000000
χ332-222-2-22-222-2-222-2-22i−2i2i−2i-222i−2i2i−2i2i−2i2i−2i000000002i−2i002-22-20000000000000000000000
χ342-222-2-22-222-2-222-2-22i−2i2i−2i-22−2i2i−2i2i−2i2i−2i2i000000002i−2i00-22-220000000000000000000000
χ352-222-2-22-222-2-222-2-2−2i2i−2i2i-222i−2i2i−2i2i−2i2i−2i00000000−2i2i00-22-220000000000000000000000
χ362-222-2-22-222-2-222-2-2−2i2i−2i2i-22−2i2i−2i2i−2i2i−2i2i00000000−2i2i002-22-20000000000000000000000
χ372-222-2-22-22-2-222-2-2200002-22i−2i2i−2i−2i2i−2i2i000000000000000000000000002-2002i−2i000000
χ382-222-2-22-22-2-222-2-2200002-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000-2200−2i2i000000
χ392-222-2-22-22-2-222-2-2200002-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000002-200−2i2i000000
χ402-222-2-22-22-2-222-2-2200002-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000-22002i−2i000000
χ412-222-2-22-2-222-2-222-22i−2i2i−2i2-20000000000000000−2i2i000000002-22-22i−2i2i−2i000000000000
χ422-222-2-22-2-222-2-222-22i−2i2i−2i2-20000000000000000−2i2i00000000-22-22−2i2i−2i2i000000000000
χ432-222-2-22-2-222-2-222-2−2i2i−2i2i2-200000000000000002i−2i000000002-22-2−2i2i−2i2i000000000000
χ442-222-2-22-2-222-2-222-2−2i2i−2i2i2-200000000000000002i−2i00000000-22-222i−2i2i−2i000000000000
χ452-22-2-22-2202020-20-22i−2i−2i2i002−2−222−2−2200002i−2i00002-2−i2i2i2−i200i2−i2−i2i2−222−2000000000000
χ462-22-2-22-2202020-20-22i−2i−2i2i002−2−222−2−220000−2i2i0000-22−i2i2i2−i200−i2i2i2−i22−2−22000000000000
χ472-22-2-22-2202020-20-22i−2i−2i2i00−222−2−222−200002i−2i00002-2i2−i2−i2i200−i2i2i2−i22−2−22000000000000
χ482-22-2-22-2202020-20-22i−2i−2i2i00−222−2−222−20000−2i2i0000-22i2−i2−i2i200i2−i2−i2i2−222−2000000000000
χ492-22-2-22-2202020-20-2−2i2i2i−2i002−2−222−2−2200002i−2i0000-22i2−i2−i2i200i2−i2−i2i22−2−22000000000000
χ502-22-2-22-2202020-20-2−2i2i2i−2i002−2−222−2−220000−2i2i00002-2i2−i2−i2i200−i2i2i2−i2−222−2000000000000
χ512-22-2-22-2202020-20-2−2i2i2i−2i00−222−2−222−200002i−2i0000-22−i2i2i2−i200−i2i2i2−i2−222−2000000000000
χ522-22-2-22-2202020-20-2−2i2i2i−2i00−222−2−222−20000−2i2i00002-2−i2i2i2−i200i2−i2−i2i22−2−22000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-44-4-4-40-404040-40000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ55444-44-4-4-40-404040-4000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ5644-44-44-4-440-40-404000000000000000004i−4i0000000000000000000000000000000000
χ5744-44-44-4-440-40-40400000000000000000−4i4i0000000000000000000000000000000000
χ5844-44-44-4-4-404040-400000000000000000000000000000000000000000000000002i2−2i200
χ5944-44-44-4-4-404040-40000000000000000000000000000000000000000000000000−2i22i200
χ604-444-4-44-4-4-444-4-4440000-440000000000000000000000000000000000000000000000
χ614-44-4-44-440-40-4040400000022−22−2222−222222−2200000000000000000000000000000000000000
χ624-44-4-44-440-40-40404000000−222222−2222−22−222200000000000000000000000000000000000000
χ634-4-444-4-444040-40-40000000000000000000004i−4i000000000000000000000000000000
χ644-4-444-4-444040-40-4000000000000000000000−4i4i000000000000000000000000000000
χ654-4-444-4-44-40-404040000000000000000000000000000000000000000000000022−220000
χ664-4-444-4-44-40-4040400000000000000000000000000000000000000000000000−22220000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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