Finite Group Databasebeta

← Group #9568

Character table — Group #9568

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222222244444444888888884444444444888888888888888888884444
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91-1-111-11-111-1-1-111-1iiii−i−i−i−iii−i−i1-1ii−i−iii−i−i1111-1-1-1-1ii−i−i11-1-11-1i−i
χ101-1-111-11-111-1-1-111-1iiii−i−i−i−iii−i−i1-1ii−i−iii−i−i1111-1-1-1-1−i−iii-1-111-11−ii
χ111-1-111-11-111-1-1-111-1iiii−i−i−i−i−i−iii1-1−i−iiiii−i−i-1-1-1-11111ii−i−i11-1-1-11−ii
χ121-1-111-11-111-1-1-111-1iiii−i−i−i−i−i−iii1-1−i−iiiii−i−i-1-1-1-11111−i−iii-1-1111-1i−i
χ131-1-111-11-111-1-1-111-1−i−i−i−iiiiiii−i−i1-1ii−i−i−i−iii-1-1-1-11111ii−i−i-1-1111-1−ii
χ141-1-111-11-111-1-1-111-1−i−i−i−iiiiiii−i−i1-1ii−i−i−i−iii-1-1-1-11111−i−iii11-1-1-11i−i
χ151-1-111-11-111-1-1-111-1−i−i−i−iiiii−i−iii1-1−i−iii−i−iii1111-1-1-1-1ii−i−i-1-111-11i−i
χ161-1-111-11-111-1-1-111-1−i−i−i−iiiii−i−iii1-1−i−iii−i−iii1111-1-1-1-1−i−iii11-1-11-1−ii
χ17222222222-22-2-22-22000000002222-2-2-2-2-2-2000000000000000000000000
χ18222222222-22-2-22-2200000000-2-2-2-2-2-22222000000000000000000000000
χ1922222222-22-222-22-2222222220000-2-20000-2-2-2-200000000000000000000
χ2022222222-22-222-22-2-2-2-2-2-2-2-2-20000-2-20000222200000000000000000000
χ2122222222-2-2-2-2-2-2-2-200000000000022000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2222222222-2-2-2-2-2-2-2-20000000000002200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ232222-2-2-2-20202-20-2022-2-222-2-200000000000000000000002−22−22−22−20000
χ242222-2-2-2-20202-20-2022-2-222-2-20000000000000000000000−22−22−22−220000
χ252222-2-2-2-20202-20-20-2-222-2-22200000000000000000000002−22−2−22−220000
χ262222-2-2-2-20202-20-20-2-222-2-2220000000000000000000000−22−222−22−20000
χ2722-2-222-2-220200-20-22−22−22−22−22-22-20000002−22−22−22−22−22−2000000000000
χ2822-2-222-2-220200-20-22−22−22−22−2-22-220000002−22−2−22−22−22−22000000000000
χ2922-2-222-2-220200-20-2−22−22−22−222-22-2000000−22−22−22−22−22−22000000000000
χ3022-2-222-2-220200-20-2−22−22−22−22-22-22000000−22−222−22−22−22−2000000000000
χ3122-2-222-2-2-20-2002022−22−22−22−20000002i−2i2i−2i−22−22i2−i2−i2i2i2−i2−i2i2000000000000
χ3222-2-222-2-2-20-2002022−22−22−22−2000000−2i2i−2i2i−22−22−i2i2i2−i2−i2i2i2−i2000000000000
χ3322-2-222-2-2-20-200202−22−22−22−220000002i−2i2i−2i2−22−2−i2i2i2−i2−i2i2i2−i2000000000000
χ3422-2-222-2-2-20-200202−22−22−22−22000000−2i2i−2i2i2−22−2i2−i2−i2i2i2−i2−i2i2000000000000
χ352-22-22-2-2220-200-202i2−i2i2−i2−i2i2−i2i22i−2i−2i2i000000i2−i2−i2i22−22−2−22−22000000000000
χ362-22-22-2-2220-200-202i2−i2i2−i2−i2i2−i2i2−2i2i2i−2i000000i2−i2−i2i2−22−222−22−2000000000000
χ372-22-22-2-2220-200-202−i2i2−i2i2i2−i2i2−i22i−2i−2i2i000000−i2i2i2−i2−22−222−22−2000000000000
χ382-22-22-2-2220-200-202−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i000000−i2i2i2−i22−22−2−22−22000000000000
χ392-22-22-2-22-2020020-2i2−i2i2−i2−i2i2−i2i20000002-2-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ402-22-22-2-22-2020020-2i2−i2i2−i2−i2i2−i2i2000000-222-2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ412-22-22-2-22-2020020-2−i2i2−i2i2i2−i2i2−i20000002-2-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ422-22-22-2-22-2020020-2−i2i2−i2i2i2−i2i2−i2000000-222-2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ432-2-222-22-22-2-2222-2-2000000002i2i−2i−2i-22−2i−2i2i2i000000000000000000000000
χ442-2-222-22-22-2-2222-2-200000000−2i−2i2i2i-222i2i−2i−2i000000000000000000000000
χ452-2-222-22-2-222-2-2-2222i2i2i2i−2i−2i−2i−2i0000-220000−2i−2i2i2i00000000000000000000
χ462-2-222-22-2-222-2-2-222−2i−2i−2i−2i2i2i2i2i0000-2200002i2i−2i−2i00000000000000000000
χ472-2-222-22-2-2-2222-2-220000000000002-2000000002i2i−2i−2i−2i−2i2i2i000000000000
χ482-2-222-22-2-2-2222-2-220000000000002-200000000−2i−2i2i2i2i2i−2i−2i000000000000
χ492-2-22-22-22020-220-202i2i−2i−2i−2i−2i2i2i0000000000000000000000i2−i2−i2i22−2−220000
χ502-2-22-22-22020-220-202i2i−2i−2i−2i−2i2i2i0000000000000000000000−i2i2i2−i2−222−20000
χ512-2-22-22-22020-220-20−2i−2i2i2i2i2i−2i−2i0000000000000000000000i2−i2−i2i2−222−20000
χ522-2-22-22-22020-220-20−2i−2i2i2i2i2i−2i−2i0000000000000000000000−i2i2i2−i22−2−220000
χ534444-4-4-4-40-40-44040000000000000000000000000000000000000000000
χ5444-4-4-4-4440000000022−22−222222−22−22220000000000000000000000000000000000
χ5544-4-4-4-44400000000−222222−22−222222−220000000000000000000000000000000000
χ564-44-4-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ574-44-4-444-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ584-4-44-44-440-404-4040000000000000000000000000000000000000000000

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