Finite Group Databasebeta

← Group #7041

Character table — Group #7041

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111111122222222222244444444888888888888888888888888
order1222222244444444444444444444888888888888888888888888
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
χ51111111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ61111111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ71111111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii
χ81111111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i
χ911111111-1-111-1-1-1-1-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1011111111-1-111-1-1-1-1-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ1111111111-1-111-1-1-1-1-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ1211111111-1-111-1-1-1-1-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ1311111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ1511111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1611111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ17222222222222-2-2-2-22222-2-2-2-2-2-222000000000000000000000000
χ182222222222-2-2222222-2-2-2-2-2-222-2-2000000000000000000000000
χ1922222222-2-2222222-2-222-2-222-2-2-2-2000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ212222-2-2-2-2002i−2i22-2-2002i−2i002i−2i0000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ222222-2-2-2-2002i−2i22-2-2002i−2i002i−2i000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ232222-2-2-2-2002i−2i-2-222002i−2i00−2i2i0000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ242222-2-2-2-2002i−2i-2-222002i−2i00−2i2i000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ252222-2-2-2-200−2i2i22-2-200−2i2i00−2i2i0000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ262222-2-2-2-200−2i2i22-2-200−2i2i00−2i2i000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ272222-2-2-2-200−2i2i-2-22200−2i2i002i−2i0000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ282222-2-2-2-200−2i2i-2-22200−2i2i002i−2i000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ2922-2-222-2-222220000-2-2-2-20000002-22−22−22−22−20000000000000000
χ3022-2-222-2-222220000-2-2-2-20000002-2−22−22−22−220000000000000000
χ3122-2-222-2-222-2-20000-2-222000000-22i2−i2i2−i2−i2i2−i2i20000000000000000
χ3222-2-222-2-222-2-20000-2-222000000-22−i2i2−i2i2i2−i2i2−i20000000000000000
χ3322-2-222-2-2-2-222000022-2-2000000-22i2−i2−i2i2i2−i2−i2i20000000000000000
χ3422-2-222-2-2-2-222000022-2-2000000-22−i2i2i2−i2−i2i2i2−i20000000000000000
χ3522-2-222-2-2-2-2-2-2000022220000002-22−2−22−222−20000000000000000
χ3622-2-222-2-2-2-2-2-2000022220000002-2−222−22−2−220000000000000000
χ372-22-22-22-22i−2i002i−2i2i−2i2i−2i0000002-20000000000000000002−2i2−i22−2i2−i2
χ382-22-22-22-22i−2i002i−2i2i−2i2i−2i0000002-2000000000000000000−22−i2i2−22−i2i2
χ392-22-22-22-22i−2i00−2i2i−2i2i2i−2i000000-22000000000000000000i2−i2−22−i2i22−2
χ402-22-22-22-22i−2i00−2i2i−2i2i2i−2i000000-22000000000000000000−i2i22−2i2−i2−22
χ412-22-22-22-2−2i2i002i−2i2i−2i−2i2i000000-22000000000000000000i2−i22−2−i2i2−22
χ422-22-22-22-2−2i2i002i−2i2i−2i−2i2i000000-22000000000000000000−i2i2−22i2−i22−2
χ432-22-22-22-2−2i2i00−2i2i−2i2i−2i2i0000002-20000000000000000002−2−i2i22−2−i2i2
χ442-22-22-22-2−2i2i00−2i2i−2i2i−2i2i0000002-2000000000000000000−22i2−i2−22i2−i2
χ4544-4-4-4-444004i−4i000000−4i4i00000000000000000000000000000000
χ4644-4-4-4-44400−4i4i0000004i−4i00000000000000000000000000000000
χ474-44-4-44-4400004i−4i−4i4i000000000000000000000000000000000000
χ484-44-4-44-440000−4i4i4i−4i000000000000000000000000000000000000
χ494-4-444-4-444i−4i000000−4i4i0000000000000000000000000000000000
χ504-4-444-4-44−4i4i0000004i−4i0000000000000000000000000000000000
χ514-4-44-444-40000000000004i−4i000000000000000000000000000000
χ524-4-44-444-4000000000000−4i4i000000000000000000000000000000

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