Finite Group Databasebeta

← Group #7108

Character table — Group #7108

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112222222222222244444444888888888888888816161616
order12222244448888888844448888161616161616161616161616161616164444
χ11111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ61111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111
χ71111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ81111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ91-1-11-1111-1-1iiii−i−i−i−i11-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζi−i1-1
χ101-1-11-1111-1-1iiii−i−i−i−i11-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ii-11
χ111-1-11-1111-1-1iiii−i−i−i−i11-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ii-11
χ121-1-11-1111-1-1iiii−i−i−i−i11-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζi−i1-1
χ131-1-11-1111-1-1−i−i−i−iiiii11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ii1-1
χ141-1-11-1111-1-1−i−i−i−iiiii11-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3i−i-11
χ151-1-11-1111-1-1−i−i−i−iiiii11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3i−i-11
χ161-1-11-1111-1-1−i−i−i−iiiii11-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ii1-1
χ17222222222222-2-222-2-2-2-2-2-22-22-200000000000000000000
χ182222222222-2-222-2-222-2-2-2-2-22-2200000000000000000000
χ192222-2-22-22-20022002200000-20-22−22−22−22−2000000000000
χ202222-2-22-22-20022002200000-20-2−22−22−22−22000000000000
χ212222-2-22-22-200-2-200-2-200000202i2−i2i2−i2−i2i2−i2i2000000000000
χ222222-2-22-22-200-2-200-2-200000202−i2i2−i2i2i2−i2i2−i2000000000000
χ232222-2-2-22-22220022000000-20-20000000002−22−22−22−20000
χ242222-2-2-22-22220022000000-20-2000000000−22−22−22−220000
χ252222-2-2-22-22-2-200-2-2000000202000000000i2−i2i2−i2−i2i2−i2i20000
χ262222-2-2-22-22-2-200-2-2000000202000000000−i2i2−i2i2i2−i2i2−i20000
χ272-2-222-22-2-22002i2i00−2i−2i00000−2i02i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ282-2-222-22-2-22002i2i00−2i−2i00000−2i02i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ292-2-222-22-2-2200−2i−2i002i2i000002i0−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ302-2-222-22-2-2200−2i−2i002i2i000002i0−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ312-2-222-2-222-22i2i00−2i−2i000000−2i02i0000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ322-2-222-2-222-22i2i00−2i−2i000000−2i02i000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ332-2-222-2-222-2−2i−2i002i2i0000002i0−2i0000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ342-2-222-2-222-2−2i−2i002i2i0000002i0−2i000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ352-2-22-2222-2-22i2i−2i−2i−2i−2i2i2i-2-2222i−2i−2i2i00000000000000000000
χ362-2-22-2222-2-2−2i−2i2i2i2i2i−2i−2i-2-222−2i2i2i−2i00000000000000000000
χ37444444-4-4-4-4000000000000000000000000000000000000
χ3844-4-400000022−2222−2222−2222−222-22-2000000000000000000000000
χ3944-4-400000022−22−222222−22−2222-22-22000000000000000000000000
χ4044-4-4000000−222222−22−222222−22-22-22000000000000000000000000
χ4144-4-4000000−2222−2222−2222−22222-22-2000000000000000000000000
χ424-44-40000002i2−2i22i2−2i2−2i22i2−2i22i22-2-22000000000000000000000000
χ434-44-40000002i2−2i2−2i22i2−2i22i22i2−2i2-222-2000000000000000000000000
χ444-44-4000000−2i22i22i2−2i22i2−2i2−2i22i2-222-2000000000000000000000000
χ454-44-4000000−2i22i2−2i22i22i2−2i22i2−2i22-2-22000000000000000000000000
χ464-4-44-44-4-444000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.