Finite Group Databasebeta

← Group #326253

Character table — Group #326253

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888822224444444488888888888888888844884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11-11
χ611111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1
χ711111111111111111111111111-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-11-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-111-1
χ17222222222-22-22-22-2-2-22222-2-2-2-200000022000000-2-2000000000000000000-22000000
χ18222222222-22-22-22-2-2-22222-2-2-2-2000000-2-2000000220000000000000000002-2000000
χ19222222222-22-22-22-2-2-2-2-2-2-2222200000022000000-2-20000000000000000002-2000000
χ20222222222-22-22-22-2-2-2-2-2-2-22222000000-2-200000022000000000000000000-22000000
χ2122222222-22-22-22-22-2-20000000022222200-2-2-2-22200-2-2000000000000000000000000
χ2222222222-22-22-22-22-2-2000000002222-2-2002222-2-200-2-2000000000000000000000000
χ2322222222-22-22-22-22-2-200000000-2-2-2-22200-2-222-2-20022000000000000000000000000
χ2422222222-22-22-22-22-2-200000000-2-2-2-2-2-20022-2-2220022000000000000000000000000
χ2522-2-2-22-22020-20-20200i2i2−i2−i2i2i2−i2−i222-2-200002i−2i2i−2i00000022−2−222−2−20000i2i2−i2−i200000000
χ2622-2-2-22-22020-20-20200i2i2−i2−i2i2i2−i2−i222-2-20000−2i2i−2i2i000000−2−222−2−2220000i2i2−i2−i200000000
χ2722-2-2-22-22020-20-20200i2i2−i2−i2i2i2−i2−i2-2-22200002i−2i−2i2i000000−2−22222−2−20000−i2−i2i2i200000000
χ2822-2-2-22-22020-20-20200i2i2−i2−i2i2i2−i2−i2-2-2220000−2i2i2i−2i00000022−2−2−2−2220000−i2−i2i2i200000000
χ2922-2-2-22-22020-20-20200−i2−i2i2i2−i2−i2i2i222-2-200002i−2i2i−2i000000−2−222−2−2220000−i2−i2i2i200000000
χ3022-2-2-22-22020-20-20200−i2−i2i2i2−i2−i2i2i222-2-20000−2i2i−2i2i00000022−2−222−2−20000−i2−i2i2i200000000
χ3122-2-2-22-22020-20-20200−i2−i2i2i2−i2−i2i2i2-2-22200002i−2i−2i2i00000022−2−2−2−2220000i2i2−i2−i200000000
χ3222-2-2-22-22020-20-20200−i2−i2i2i2−i2−i2i2i2-2-2220000−2i2i2i−2i000000−2−22222−2−20000i2i2−i2−i200000000
χ332-22-22-2-2222-2-222-2-2-222i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000002i−2i0000000000002-22-200000000
χ342-22-22-2-2222-2-222-2-2-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000−2i2i000000000000-22-2200000000
χ352-22-22-2-2222-2-222-2-2-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000000000002i−2i000000000000-22-2200000000
χ362-22-22-2-2222-2-222-2-2-22−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000−2i2i0000000000002-22-200000000
χ372-22-22-2-222-2-222-2-222-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000022-2-20000002i−2i0000
χ382-22-22-2-222-2-222-2-222-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000-2-222000000−2i2i0000
χ392-22-22-2-222-2-222-2-222-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000022-2-2000000−2i2i0000
χ402-22-22-2-222-2-222-2-222-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000-2-2220000002i−2i0000
χ412-22-22-2-22-222-2-222-22-2000000002i−2i2i−2i000000000000−2i2i2i−2i2i−2i2-22-20000000000000000
χ422-22-22-2-22-222-2-222-22-2000000002i−2i2i−2i000000000000−2i2i−2i2i−2i2i-22-220000000000000000
χ432-22-22-2-22-222-2-222-22-200000000−2i2i−2i2i0000000000002i−2i2i−2i2i−2i-22-220000000000000000
χ442-22-22-2-22-222-2-222-22-200000000−2i2i−2i2i0000000000002i−2i−2i2i−2i2i2-22-20000000000000000
χ452-2-22-2-22202020-20-2002−2−222−2−222i−2i−2i2i2-20000002i−2i0000i2−i2−i2i22−2−220000−i2i2i2−i200000000
χ462-2-22-2-22202020-20-2002−2−222−2−222i−2i−2i2i-22000000−2i2i0000−i2i2i2−i2−222−20000−i2i2i2−i200000000
χ472-2-22-2-22202020-20-2002−2−222−2−22−2i2i2i−2i2-2000000−2i2i0000−i2i2i2−i22−2−220000i2−i2−i2i200000000
χ482-2-22-2-22202020-20-2002−2−222−2−22−2i2i2i−2i-220000002i−2i0000i2−i2−i2i2−222−20000i2−i2−i2i200000000
χ492-2-22-2-22202020-20-200−222−2−222−22i−2i−2i2i2-20000002i−2i0000−i2i2i2−i2−222−20000i2−i2−i2i200000000
χ502-2-22-2-22202020-20-200−222−2−222−22i−2i−2i2i-22000000−2i2i0000i2−i2−i2i22−2−220000i2−i2−i2i200000000
χ512-2-22-2-22202020-20-200−222−2−222−2−2i2i2i−2i2-2000000−2i2i0000i2−i2−i2i2−222−20000−i2i2i2−i200000000
χ522-2-22-2-22202020-20-200−222−2−222−2−2i2i2i−2i-220000002i−2i0000−i2i2i2−i22−2−220000−i2i2i2−i200000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ54444-4-4-44-44040-40-4000000000000000004-40000000000000000000000000000000000
χ55444-4-4-44-44040-40-400000000000000000-440000000000000000000000000000000000
χ56444-4-4-44-4-40-4040400000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ57444-4-4-44-4-40-404040000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ5844-4-4-44-440-404040-4002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ5944-4-4-44-440-404040-400−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ604-444-44-4-440-40-40400000000000000000000000004i−4i00000000000000000000000000
χ614-444-44-4-440-40-4040000000000000000000000000−4i4i00000000000000000000000000
χ624-444-44-4-4-404040-400000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ634-444-44-4-4-404040-40000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ644-44-44-4-44-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ654-4-44-4-4440-40-404040022−22−2222−222222−22000000000000000000000000000000000000000000
χ664-4-44-4-4440-40-4040400−222222−2222−22−2222000000000000000000000000000000000000000000
χ6788-888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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