Finite Group Databasebeta

← Group #22923

Character table — Group #22923

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1111111122222222222222222222222244444444444444444444444444888888888888
order1222222244444444444444448888888822444444444444888888888888224444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ4111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ51111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1
χ61111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ71111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1
χ81111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111
χ9111111111-1-1-1-11111-1-1-1-111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ10111111111-1-1-1-11111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ11111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111
χ12111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-111-1-1
χ13111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1
χ14111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ15111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ16111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111
χ171-111-1-11-1-111-1-1ii−i−iii−i−i11-1iiii−i−i−i−i1-1i−ii−i11-1-1ii−i−i11-1-111-1-1ii−i−i1-11-1i−ii−i1-1i−i
χ181-111-1-11-1-111-1-1ii−i−iii−i−i11-1iiii−i−i−i−i1-1i−ii−i-1-111−i−iii11-1-111-1-1ii−i−i-11-11−ii−ii-11−ii
χ191-111-1-11-1-111-1-1ii−i−iii−i−i11-1−i−i−i−iiiii1-1i−ii−i11-1-1−i−iii-1-111-1-111−i−iii-111-1i−i−ii-11i−i
χ201-111-1-11-1-111-1-1ii−i−iii−i−i11-1−i−i−i−iiiii1-1i−ii−i-1-111ii−i−i-1-111-1-111−i−iii1-1-11−iii−i1-1−ii
χ211-111-1-11-1-111-1-1−i−iii−i−iii11-1iiii−i−i−i−i1-1−ii−ii11-1-1ii−i−i-1-111-1-111ii−i−i-111-1−iii−i-11−ii
χ221-111-1-11-1-111-1-1−i−iii−i−iii11-1iiii−i−i−i−i1-1−ii−ii-1-111−i−iii-1-111-1-111ii−i−i1-1-11i−i−ii1-1i−i
χ231-111-1-11-1-111-1-1−i−iii−i−iii11-1−i−i−i−iiiii1-1−ii−ii11-1-1−i−iii11-1-111-1-1−i−iii1-11-1−ii−ii1-1−ii
χ241-111-1-11-1-111-1-1−i−iii−i−iii11-1−i−i−i−iiiii1-1−ii−ii-1-111ii−i−i11-1-111-1-1−i−iii-11-11i−ii−i-11i−i
χ251-111-1-11-1-1-1-111ii−i−i−i−iii11-1iiii−i−i−i−i-11i−i−ii11-1-1ii−i−i11-1-1-1-111−i−iii-11-11−ii−ii1-1i−i
χ261-111-1-11-1-1-1-111ii−i−i−i−iii11-1iiii−i−i−i−i-11i−i−ii-1-111−i−iii11-1-1-1-111−i−iii1-11-1i−ii−i-11−ii
χ271-111-1-11-1-1-1-111ii−i−i−i−iii11-1−i−i−i−iiiii-11i−i−ii11-1-1−i−iii-1-11111-1-1ii−i−i1-1-11−iii−i-11i−i
χ281-111-1-11-1-1-1-111ii−i−i−i−iii11-1−i−i−i−iiiii-11i−i−ii-1-111ii−i−i-1-11111-1-1ii−i−i-111-1i−i−ii1-1−ii
χ291-111-1-11-1-1-1-111−i−iiiii−i−i11-1iiii−i−i−i−i-11−iii−i11-1-1ii−i−i-1-11111-1-1−i−iii1-1-11i−i−ii-11−ii
χ301-111-1-11-1-1-1-111−i−iiiii−i−i11-1iiii−i−i−i−i-11−iii−i-1-111−i−iii-1-11111-1-1−i−iii-111-1−iii−i1-1i−i
χ311-111-1-11-1-1-1-111−i−iiiii−i−i11-1−i−i−i−iiiii-11−iii−i11-1-1−i−iii11-1-1-1-111ii−i−i-11-11i−ii−i1-1−ii
χ321-111-1-11-1-1-1-111−i−iiiii−i−i11-1−i−i−i−iiiii-11−iii−i-1-111ii−i−i11-1-1-1-111ii−i−i1-11-1−ii−ii-11i−i
χ3322222222-2222222222222-2-2-200000000-2-2-2-2-2-200000000000000000000000000000000
χ3422222222-22222-2-2-2-2-2-2-2-2-2-2-200000000-2-2222200000000000000000000000000000000
χ3522222222-2-2-2-2-22222-2-2-2-2-2-2-20000000022-2-22200000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2-22222-2-2-2000000002222-2-200000000000000000000000000000000
χ37222-22-2-2-2-20000000000002-2222-2-222-2-20000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ38222-22-2-2-2-20000000000002-2222-2-222-2-2000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ39222-22-2-2-2-20000000000002-22-2-222-2-2220000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ40222-22-2-2-2-20000000000002-22-2-222-2-222000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4122-22-2-2-2202i−2i2i−2i2i−2i2i−2i2-22-2000i2−i2i2−i2i2−i2i2−i2000000000000002−22−2i2−i2i2−i22−22−2000000000000
χ4222-22-2-2-2202i−2i2i−2i2i−2i2i−2i2-22-2000−i2i2−i2i2−i2i2−i2i200000000000000−22−22−i2i2−i2i2−22−22000000000000
χ4322-22-2-2-2202i−2i2i−2i−2i2i−2i2i-22-22000i2−i2i2−i2i2−i2i2−i200000000000000−22−22−i2i2−i2i22−22−2000000000000
χ4422-22-2-2-2202i−2i2i−2i−2i2i−2i2i-22-22000−i2i2−i2i2−i2i2−i2i2000000000000002−22−2i2−i2i2−i2−22−22000000000000
χ4522-22-2-2-220−2i2i−2i2i2i−2i2i−2i-22-22000i2−i2i2−i2i2−i2i2−i2000000000000002−22−2−i2i2−i2i2−22−22000000000000
χ4622-22-2-2-220−2i2i−2i2i2i−2i2i−2i-22-22000−i2i2−i2i2−i2i2−i2i200000000000000−22−22i2−i2i2−i22−22−2000000000000
χ4722-22-2-2-220−2i2i−2i2i−2i2i−2i2i2-22-2000i2−i2i2−i2i2−i2i2−i200000000000000−22−22i2−i2i2−i2−22−22000000000000
χ4822-22-2-2-220−2i2i−2i2i−2i2i−2i2i2-22-2000−i2i2−i2i2−i2i2−i2i2000000000000002−22−2−i2i2−i2i22−22−2000000000000
χ492-222-2-22-2222-2-22i2i−2i−2i2i2i−2i−2i-2-2200000000-22−2i2i−2i2i00000000000000000000000000000000
χ502-222-2-22-2222-2-2−2i−2i2i2i−2i−2i2i2i-2-2200000000-222i−2i2i−2i00000000000000000000000000000000
χ512-222-2-22-22-2-2222i2i−2i−2i−2i−2i2i2i-2-22000000002-2−2i2i2i−2i00000000000000000000000000000000
χ522-222-2-22-22-2-222−2i−2i2i2i2i2i−2i−2i-2-22000000002-22i−2i−2i2i00000000000000000000000000000000
χ532-22-2-22-2220000000000002-2-22i2i−2i−2i−2i−2i2i2i0000002i−2i−2i2i-222-2000000000000000000000000
χ542-22-2-22-2220000000000002-2-22i2i−2i−2i−2i−2i2i2i000000−2i2i2i−2i2-2-22000000000000000000000000
χ552-22-2-22-2220000000000002-2-2−2i−2i2i2i2i2i−2i−2i0000002i−2i−2i2i2-2-22000000000000000000000000
χ562-22-2-22-2220000000000002-2-2−2i−2i2i2i2i2i−2i−2i000000−2i2i2i−2i-222-2000000000000000000000000
χ572-2-2222-2-202i−2i−2i2i2-2-22−2i2i2i−2i0002−22−2−22−22000000000000002−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ582-2-2222-2-202i−2i−2i2i2-2-22−2i2i2i−2i000−22−222−22−200000000000000−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ592-2-2222-2-202i−2i−2i2i-222-22i−2i−2i2i0002−22−2−22−2200000000000000−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ602-2-2222-2-202i−2i−2i2i-222-22i−2i−2i2i000−22−222−22−2000000000000002−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ612-2-2222-2-20−2i2i2i−2i2-2-222i−2i−2i2i0002−22−2−22−22000000000000002−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ622-2-2222-2-20−2i2i2i−2i2-2-222i−2i−2i2i000−22−222−22−200000000000000−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ632-2-2222-2-20−2i2i2i−2i-222-2−2i2i2i−2i0002−22−2−22−2200000000000000−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ642-2-2222-2-20−2i2i2i−2i-222-2−2i2i2i−2i000−22−222−22−2000000000000002−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ65444-44-4-4-44000000000000-44-40000000000000000000000000000000000000000000000
χ6644-4-4-444-400000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ6744-4-4-444-40000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ684-44-4-44-44-4000000000000-4440000000000000000000000000000000000000000000000
χ694-4-4-44-444000000000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ704-4-4-44-4440000000000000000−222222−2222−22−222200000000000000000000000000000000000000

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