Finite Group Databasebeta

← Group #7621

Character table — Group #7621

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111111122222222222244444444888888888888888888888888
order1222222244444444444444444444222244448888888888888888
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-222-2-2-2-222-2-2000000000000000000000000
χ182222222222-2-2-2-2-2-2-2-222-2-222-2-222000000000000000000000000
χ1922222222-2-222222222-2-2-2-2-2-2-2-222000000000000000000000000
χ2022222222-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000
χ212222-2-2-2-2002i2i−2i−2i2i2i−2i−2i000000002-200000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ222222-2-2-2-2002i2i−2i−2i2i2i−2i−2i000000002-20000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ232222-2-2-2-2002i2i−2i−2i−2i−2i2i2i00000000-2200000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ242222-2-2-2-2002i2i−2i−2i−2i−2i2i2i00000000-220000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ252222-2-2-2-200−2i−2i2i2i2i2i−2i−2i00000000-2200000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ262222-2-2-2-200−2i−2i2i2i2i2i−2i−2i00000000-220000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ272222-2-2-2-200−2i−2i2i2i−2i−2i2i2i000000002-200000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ282222-2-2-2-200−2i−2i2i2i−2i−2i2i2i000000002-20000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ2922-2-222-2-22i−2i00002i−2i2i−2i2i−2i2-2000000002-2002i−2i0000000000000000
χ3022-2-222-2-22i−2i00002i−2i2i−2i2i−2i2-200000000-2200−2i2i0000000000000000
χ3122-2-222-2-22i−2i0000−2i2i−2i2i2i−2i-220000002-2002i−2i000000000000000000
χ3222-2-222-2-22i−2i0000−2i2i−2i2i2i−2i-22000000-2200−2i2i000000000000000000
χ3322-2-222-2-2−2i2i00002i−2i2i−2i−2i2i-220000002-200−2i2i000000000000000000
χ3422-2-222-2-2−2i2i00002i−2i2i−2i−2i2i-22000000-22002i−2i000000000000000000
χ3522-2-222-2-2−2i2i0000−2i2i−2i2i−2i2i2-2000000002-200−2i2i0000000000000000
χ3622-2-222-2-2−2i2i0000−2i2i−2i2i−2i2i2-200000000-22002i−2i0000000000000000
χ372-22-22-2-22222-22-20000-2-200002-20000000000i2−i2i2−i2i2−i2i2−i200000000
χ382-22-22-2-22222-22-20000-2-200002-20000000000−i2i2−i2i2−i2i2−i2i200000000
χ392-22-22-2-2222-22-220000-2-20000-220000000000i2−i2i2−i2−i2i2−i2i200000000
χ402-22-22-2-2222-22-220000-2-20000-220000000000−i2i2−i2i2i2−i2i2−i200000000
χ412-22-22-2-22-2-22-22-20000220000-2200000000002−2−222−2−2200000000
χ422-22-22-2-22-2-22-22-20000220000-220000000000−222−2−222−200000000
χ432-22-22-2-22-2-2-22-2200002200002-200000000002−2−22−222−200000000
χ442-22-22-2-22-2-2-22-2200002200002-20000000000−222−22−2−2200000000
χ4544-4-4-4-4440000004-4-440000000000000000000000000000000000
χ4644-4-4-4-444000000-444-40000000000000000000000000000000000
χ474-44-4-444-4004i−4i−4i4i00000000000000000000000000000000000000
χ484-44-4-444-400−4i4i4i−4i00000000000000000000000000000000000000
χ494-4-444-44-44i−4i00000000−4i4i00000000000000000000000000000000
χ504-4-444-44-4−4i4i000000004i−4i00000000000000000000000000000000
χ514-4-44-44-44000000000000004-40000000000000000000000000000
χ524-4-44-44-4400000000000000-440000000000000000000000000000

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