Finite Group Databasebeta

← Group #20868

Character table — Group #20868

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111111122222222444444444444444444888811111111222222224444444444444444448888
order1222222244444444222244444488888888444422222222444444442222444444888888884444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ41111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911-1-11-11-11-1ii−i−i1-111-1-1i−iii−i−i11-1-1ii−i−i1-1i−i11-1-11-11-11-1ii−i−i1-111-1-1i−iii−i−i11-1-1ii−i−i1-1i−i
χ1011-1-11-11-11-1ii−i−i1-111-1-1i−iii−i−i-1-111−i−iii-11−ii11-1-11-11-11-1ii−i−i1-111-1-1i−iii−i−i-1-111−i−iii-11−ii
χ1111-1-11-11-11-1ii−i−i1-1-1-111i−i−i−iii11-1-1ii−i−i-11−ii11-1-11-11-11-1ii−i−i1-1-1-111i−i−i−iii11-1-1ii−i−i-11−ii
χ1211-1-11-11-11-1ii−i−i1-1-1-111i−i−i−iii-1-111−i−iii1-1i−i11-1-11-11-11-1ii−i−i1-1-1-111i−i−i−iii-1-111−i−iii1-1i−i
χ1311-1-11-11-11-1−i−iii1-111-1-1−ii−i−iii11-1-1−i−iii1-1−ii11-1-11-11-11-1−i−iii1-111-1-1−ii−i−iii11-1-1−i−iii1-1−ii
χ1411-1-11-11-11-1−i−iii1-111-1-1−ii−i−iii-1-111ii−i−i-11i−i11-1-11-11-11-1−i−iii1-111-1-1−ii−i−iii-1-111ii−i−i-11i−i
χ1511-1-11-11-11-1−i−iii1-1-1-111−iiii−i−i11-1-1−i−iii-11i−i11-1-11-11-11-1−i−iii1-1-1-111−iiii−i−i11-1-1−i−iii-11i−i
χ1611-1-11-11-11-1−i−iii1-1-1-111−iiii−i−i-1-111ii−i−i1-1−ii11-1-11-11-11-1−i−iii1-1-1-111−iiii−i−i-1-111ii−i−i1-1−ii
χ1722222222-2-22222-2-20000-2-2000000000000000022222222-2-22222-2-20000-2-20000000000000000
χ1822222222-2-2-2-2-2-2-2-2000022000000000000000022222222-2-2-2-2-2-2-2-20000220000000000000000
χ1922-2-22-22-2-222i2i−2i−2i-220000−2i2i000000000000000022-2-22-22-2-222i2i−2i−2i-220000−2i2i0000000000000000
χ2022-2-22-22-2-22−2i−2i2i2i-2200002i−2i000000000000000022-2-22-22-2-22−2i−2i2i2i-2200002i−2i0000000000000000
χ212-2222-2-2-2220000-2-22-22-20000000000000000002-2222-2-2-2220000-2-22-22-2000000000000000000
χ222-2222-2-2-2220000-2-2-22-220000000000000000002-2222-2-2-2220000-2-2-22-22000000000000000000
χ232-2222-2-2-2-2-20000220000002i−2i2i−2i0000000000002-2222-2-2-2-2-20000220000002i−2i2i−2i000000000000
χ242-2222-2-2-2-2-2000022000000−2i2i−2i2i0000000000002-2222-2-2-2-2-2000022000000−2i2i−2i2i000000000000
χ252-22-2-222-2002i−2i2i−2i0000000000002−22−2i2−i2i2−i200002-22-2-222-2002i−2i2i−2i0000000000002−22−2i2−i2i2−i20000
χ262-22-2-222-2002i−2i2i−2i000000000000−22−22−i2i2−i2i200002-22-2-222-2002i−2i2i−2i000000000000−22−22−i2i2−i2i20000
χ272-22-2-222-200−2i2i−2i2i0000000000002−22−2−i2i2−i2i200002-22-2-222-200−2i2i−2i2i0000000000002−22−2−i2i2−i2i20000
χ282-22-2-222-200−2i2i−2i2i000000000000−22−22i2−i2i2−i200002-22-2-222-200−2i2i−2i2i000000000000−22−22i2−i2i2−i20000
χ292-2-22-2-222002-2-220000000000002−2−222−2−2200002-2-22-2-222002-2-220000000000002−2−222−2−220000
χ302-2-22-2-222002-2-22000000000000−222−2−222−200002-2-22-2-222002-2-22000000000000−222−2−222−20000
χ312-2-22-2-22200-222-20000000000002−2−22−222−200002-2-22-2-22200-222-20000000000002−2−22−222−20000
χ322-2-22-2-22200-222-2000000000000−222−22−2−2200002-2-22-2-22200-222-2000000000000−222−22−2−220000
χ332-2-2-222-222-20000-222-2-220000000000000000002-2-2-222-222-20000-222-2-22000000000000000000
χ342-2-2-222-222-20000-22-222-20000000000000000002-2-2-222-222-20000-22-222-2000000000000000000
χ352-2-2-222-22-2200002-20000002-2-220000000000002-2-2-222-22-2200002-20000002-2-22000000000000
χ362-2-2-222-22-2200002-2000000-222-20000000000002-2-2-222-22-2200002-2000000-222-2000000000000
χ37444-4-4-4-44000000000000000000000000000000444-4-4-4-44000000000000000000000000000000
χ3844-44-44-4-400000000000000000000000000000044-44-44-4-4000000000000000000000000000000
χ3911111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4011111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ411111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ421111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1
χ431111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ441111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ451111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ461111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ4711-1-11-11-11-1ii−i−i1-111-1-1i−iii−i−i11-1-1ii−i−i1-1i−i-1-111-11-11-11−i−iii-11-1-111−ii−i−iii-1-111−i−iii-11−ii
χ4811-1-11-11-11-1ii−i−i1-111-1-1i−iii−i−i-1-111−i−iii-11−ii-1-111-11-11-11−i−iii-11-1-111−ii−i−iii11-1-1ii−i−i1-1i−i
χ4911-1-11-11-11-1ii−i−i1-1-1-111i−i−i−iii11-1-1ii−i−i-11−ii-1-111-11-11-11−i−iii-1111-1-1−iiii−i−i-1-111−i−iii1-1i−i
χ5011-1-11-11-11-1ii−i−i1-1-1-111i−i−i−iii-1-111−i−iii1-1i−i-1-111-11-11-11−i−iii-1111-1-1−iiii−i−i11-1-1ii−i−i-11−ii
χ5111-1-11-11-11-1−i−iii1-111-1-1−ii−i−iii11-1-1−i−iii1-1−ii-1-111-11-11-11ii−i−i-11-1-111i−iii−i−i-1-111ii−i−i-11i−i
χ5211-1-11-11-11-1−i−iii1-111-1-1−ii−i−iii-1-111ii−i−i-11i−i-1-111-11-11-11ii−i−i-11-1-111i−iii−i−i11-1-1−i−iii1-1−ii
χ5311-1-11-11-11-1−i−iii1-1-1-111−iiii−i−i11-1-1−i−iii-11i−i-1-111-11-11-11ii−i−i-1111-1-1i−i−i−iii-1-111ii−i−i1-1−ii
χ5411-1-11-11-11-1−i−iii1-1-1-111−iiii−i−i-1-111ii−i−i1-1−ii-1-111-11-11-11ii−i−i-1111-1-1i−i−i−iii11-1-1−i−iii-11i−i
χ5522222222-2-22222-2-20000-2-20000000000000000-2-2-2-2-2-2-2-222-2-2-2-2220000220000000000000000
χ5622222222-2-2-2-2-2-2-2-20000220000000000000000-2-2-2-2-2-2-2-2222222220000-2-20000000000000000
χ5722-2-22-22-2-222i2i−2i−2i-220000−2i2i0000000000000000-2-222-22-222-2−2i−2i2i2i2-200002i−2i0000000000000000
χ5822-2-22-22-2-22−2i−2i2i2i-2200002i−2i0000000000000000-2-222-22-222-22i2i−2i−2i2-20000−2i2i0000000000000000
χ592-2222-2-2-2220000-2-22-22-2000000000000000000-22-2-2-2222-2-2000022-22-22000000000000000000
χ602-2222-2-2-2220000-2-2-22-22000000000000000000-22-2-2-2222-2-20000222-22-2000000000000000000
χ612-2222-2-2-2-2-20000220000002i−2i2i−2i000000000000-22-2-2-2222220000-2-2000000−2i2i−2i2i000000000000
χ622-2222-2-2-2-2-2000022000000−2i2i−2i2i000000000000-22-2-2-2222220000-2-20000002i−2i2i−2i000000000000
χ632-22-2-222-2002i−2i2i−2i0000000000002−22−2i2−i2i2−i20000-22-222-2-2200−2i2i−2i2i000000000000−22−22−i2i2−i2i20000
χ642-22-2-222-2002i−2i2i−2i000000000000−22−22−i2i2−i2i20000-22-222-2-2200−2i2i−2i2i0000000000002−22−2i2−i2i2−i20000
χ652-22-2-222-200−2i2i−2i2i0000000000002−22−2−i2i2−i2i20000-22-222-2-22002i−2i2i−2i000000000000−22−22i2−i2i2−i20000
χ662-22-2-222-200−2i2i−2i2i000000000000−22−22i2−i2i2−i20000-22-222-2-22002i−2i2i−2i0000000000002−22−2−i2i2−i2i20000
χ672-2-22-2-222002-2-220000000000002−2−222−2−220000-222-222-2-200-222-2000000000000−222−2−222−20000
χ682-2-22-2-222002-2-22000000000000−222−2−222−20000-222-222-2-200-222-20000000000002−2−222−2−220000
χ692-2-22-2-22200-222-20000000000002−2−22−222−20000-222-222-2-2002-2-22000000000000−222−22−2−220000
χ702-2-22-2-22200-222-2000000000000−222−22−2−220000-222-222-2-2002-2-220000000000002−2−22−222−20000
χ712-2-2-222-222-20000-222-2-22000000000000000000-2222-2-22-2-2200002-2-222-2000000000000000000
χ722-2-2-222-222-20000-22-222-2000000000000000000-2222-2-22-2-2200002-22-2-22000000000000000000
χ732-2-2-222-22-2200002-20000002-2-22000000000000-2222-2-22-22-20000-22000000-222-2000000000000
χ742-2-2-222-22-2200002-2000000-222-2000000000000-2222-2-22-22-20000-220000002-2-22000000000000
χ75444-4-4-4-44000000000000000000000000000000-4-4-44444-4000000000000000000000000000000
χ7644-44-44-4-4000000000000000000000000000000-4-44-44-444000000000000000000000000000000

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