Finite Group Databasebeta

← Group #7633

Character table — Group #7633

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111111122222222222244444444888888888888888888888888
order1222222244444444444422444444224444448888888888888888
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
χ51111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-222-2-2-2-2-2-222000000000000000000000000
χ182222222222-2-2-2-2-2-2-2-22222-2-222-2-2000000000000000000000000
χ1922222222-2-222222222-2-222-2-2-2-2-2-2000000000000000000000000
χ2022222222-2-2-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000
χ21222-2-2-2-222i−2i22-2-200002i−2i0000002i−2i000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ22222-2-2-2-222i−2i22-2-200002i−2i0000002i−2i00000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ23222-2-2-2-222i−2i-2-22200002i−2i000000−2i2i000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ24222-2-2-2-222i−2i-2-22200002i−2i000000−2i2i00000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ25222-2-2-2-22−2i2i22-2-20000−2i2i000000−2i2i000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ26222-2-2-2-22−2i2i22-2-20000−2i2i000000−2i2i00000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ27222-2-2-2-22−2i2i-2-2220000−2i2i0000002i−2i000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ28222-2-2-2-22−2i2i-2-2220000−2i2i0000002i−2i00000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ2922-222-2-2-2002i−2i2i−2i2i2i−2i−2i002-200000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ3022-222-2-2-2002i−2i2i−2i2i2i−2i−2i002-20000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ3122-222-2-2-2002i−2i2i−2i−2i−2i2i2i00-2200000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ3222-222-2-2-2002i−2i2i−2i−2i−2i2i2i00-220000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ3322-222-2-2-200−2i2i−2i2i2i2i−2i−2i00-2200000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ3422-222-2-2-200−2i2i−2i2i2i2i−2i−2i00-220000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ3522-222-2-2-200−2i2i−2i2i−2i−2i2i2i002-200000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ3622-222-2-2-200−2i2i−2i2i−2i−2i2i2i002-20000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ372-222-22-2-22i−2i00002i−2i2i−2i−2i2i002-2000000002-22i−2i0000000000000000
χ382-222-22-2-22i−2i00002i−2i2i−2i−2i2i002-200000000-22−2i2i0000000000000000
χ392-222-22-2-22i−2i0000−2i2i−2i2i−2i2i00-2200002-22i−2i00000000000000000000
χ402-222-22-2-22i−2i0000−2i2i−2i2i−2i2i00-220000-22−2i2i00000000000000000000
χ412-222-22-2-2−2i2i00002i−2i2i−2i2i−2i00-2200002-2−2i2i00000000000000000000
χ422-222-22-2-2−2i2i00002i−2i2i−2i2i−2i00-220000-222i−2i00000000000000000000
χ432-222-22-2-2−2i2i0000−2i2i−2i2i2i−2i002-2000000002-2−2i2i0000000000000000
χ442-222-22-2-2−2i2i0000−2i2i−2i2i2i−2i002-200000000-222i−2i0000000000000000
χ4544-4-4-444-4004i−4i−4i4i00000000000000000000000000000000000000
χ4644-4-4-444-400−4i4i4i−4i00000000000000000000000000000000000000
χ474-44-44-44-44400000000-4-400000000000000000000000000000000
χ484-44-44-44-4-4-4000000004400000000000000000000000000000000
χ494-4-44-4-4440000004-4-440000000000000000000000000000000000
χ504-4-44-4-444000000-444-40000000000000000000000000000000000
χ514-4-4-444-4400000000000000004-400000000000000000000000000
χ524-4-4-444-440000000000000000-4400000000000000000000000000

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