Finite Group Databasebeta

← Group #7037

Character table — Group #7037

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111111122222222222244444444888888888888888888888888
order1222222222224444444444444444444444448888888888888888
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
χ5111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-1-1-111-1-1-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ1311111111-1-1-1-1-1-11111-1-111-1-1-1-111ii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i
χ1411111111-1-1-1-1-1-11111-1-111-1-1-1-111ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii
χ1511111111-1-1-1-1-1-11111-1-111-1-1-1-111−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii
χ1611111111-1-1-1-1-1-11111-1-111-1-1-1-111−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i
χ1722222222222222-2-2-2-222-2-2-2-2-2-222000000000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-222-2-2000000000000000000000000
χ1922222222-2-2-2-222222222-2-222-2-2-2-2000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ21222-2-22-2-200002i−2i22-2-22i−2i002i−2i00001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000000000
χ22222-2-22-2-200002i−2i22-2-22i−2i002i−2i0000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000000000
χ23222-2-22-2-200002i−2i-2-2222i−2i00−2i2i00001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000000000000000
χ24222-2-22-2-200002i−2i-2-2222i−2i00−2i2i0000−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000000000000000
χ25222-2-22-2-20000−2i2i22-2-2−2i2i00−2i2i00001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000000000
χ26222-2-22-2-20000−2i2i22-2-2−2i2i00−2i2i0000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000000000
χ27222-2-22-2-20000−2i2i-2-222−2i2i002i−2i00001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000000000000
χ28222-2-22-2-20000−2i2i-2-222−2i2i002i−2i0000−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000000000000
χ2922-22-2-22-222-2-2220000-2-20000002-2000000002−22−22−22−200000000
χ3022-22-2-22-222-2-2220000-2-20000002-200000000−22−22−22−2200000000
χ3122-22-2-22-222-2-2-2-2000022000000-2200000000i2−i2i2−i2−i2i2−i2i200000000
χ3222-22-2-22-222-2-2-2-2000022000000-2200000000−i2i2−i2i2i2−i2i2−i200000000
χ3322-22-2-22-2-2-222220000-2-2000000-2200000000i2−i2−i2i2i2−i2−i2i200000000
χ3422-22-2-22-2-2-222220000-2-2000000-2200000000−i2i2i2−i2−i2i2i2−i200000000
χ3522-22-2-22-2-2-222-2-20000220000002-2000000002−2−22−222−200000000
χ3622-22-2-22-2-2-222-2-20000220000002-200000000−222−22−2−2200000000
χ372-22-22-22-22-22-2002i−2i2i−2i0000002i−2i0000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ382-22-22-22-22-22-2002i−2i2i−2i0000002i−2i000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ392-22-22-22-22-22-200−2i2i−2i2i000000−2i2i0000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ402-22-22-22-22-22-200−2i2i−2i2i000000−2i2i000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ412-22-22-22-2-22-22002i−2i2i−2i000000−2i2i0000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ422-22-22-22-2-22-22002i−2i2i−2i000000−2i2i000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ432-22-22-22-2-22-2200−2i2i−2i2i0000002i−2i0000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ442-22-22-22-2-22-2200−2i2i−2i2i0000002i−2i000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ4544-4-44-4-4400004i−4i0000−4i4i00000000000000000000000000000000
χ4644-4-44-4-440000−4i4i00004i−4i00000000000000000000000000000000
χ474-444-4-4-440000004i−4i−4i4i0000000000000000000000000000000000
χ484-444-4-4-44000000−4i4i4i−4i0000000000000000000000000000000000
χ494-4-4444-4-40000000000004i−4i000000000000000000000000000000
χ504-4-4444-4-4000000000000−4i4i000000000000000000000000000000
χ514-4-4-4-44444-4-440000000000000000000000000000000000000000
χ524-4-4-4-4444-444-40000000000000000000000000000000000000000

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