Finite Group Databasebeta

← Group #7132

Character table — Group #7132

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size1111111122224444444488888888888888888888888888
order1222222222224444444444444444448888888888888888
χ11111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911-1-11-1-1111-1-1ii−i−iii−i−i1-111-1-1ii−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ1011-1-11-1-1111-1-1ii−i−iii−i−i1-111-1-1ii−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ1111-1-11-1-1111-1-1ii−i−iii−i−i1-1-1-111−i−iiiζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ1211-1-11-1-1111-1-1ii−i−iii−i−i1-1-1-111−i−iii−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ1311-1-11-1-1111-1-1−i−iii−i−iii1-111-1-1−i−iiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ1411-1-11-1-1111-1-1−i−iii−i−iii1-111-1-1−i−iii−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ1511-1-11-1-1111-1-1−i−iii−i−iii1-1-1-111ii−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ1611-1-11-1-1111-1-1−i−iii−i−iii1-1-1-111ii−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ172222222222222-22-22-22-2-2-2000000000000000000000000
χ18222222222222-22-22-22-22-2-2000000000000000000000000
χ19222-2-22-2-22-22-202020-20-200000000002−22−22−22−200000000
χ20222-2-22-2-22-22-202020-20-20000000000−22−22−22−2200000000
χ21222-2-22-2-22-22-20-20-202020000000000i2−i2i2−i2−i2i2−i2i200000000
χ22222-2-22-2-22-22-20-20-202020000000000−i2i2−i2i2i2−i2i2−i200000000
χ23222-2-22-2-2-22-222i0−2i0−2i02i00000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ24222-2-22-2-2-22-222i0−2i0−2i02i0000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ25222-2-22-2-2-22-22−2i02i02i0−2i00000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ26222-2-22-2-2-22-22−2i02i02i0−2i0000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ2722-22-2-22-22-2-2202i0−2i0−2i02i00000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ2822-22-2-22-22-2-2202i0−2i0−2i02i0000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ2922-22-2-22-22-2-220−2i02i02i0−2i00000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ3022-22-2-22-22-2-220−2i02i02i0−2i0000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ3122-22-2-22-2-222-22020-20-200000000000000000002−2−22−222−2
χ3222-22-2-22-2-222-22020-20-20000000000000000000−222−22−2−22
χ3322-22-2-22-2-222-2-20-202020000000000000000000i2−i2−i2i2i2−i2−i2i2
χ3422-22-2-22-2-222-2-20-202020000000000000000000−i2i2i2−i2−i2i2i2−i2
χ3522-2-22-2-2222-2-22i−2i−2i2i2i−2i−2i2i-22000000000000000000000000
χ3622-2-22-2-2222-2-2−2i2i2i−2i−2i2i2i−2i-22000000000000000000000000
χ3744444444-4-4-4-40000000000000000000000000000000000
χ3844-4-44-4-44-4-4440000000000000000000000000000000000
χ394-444-4-4-440000000000000000002i−2i2i−2i0000000000000000
χ404-444-4-4-44000000000000000000−2i2i−2i2i0000000000000000
χ414-44-44-44-4000000000000002i−2i2i−2i00000000000000000000
χ424-44-44-44-400000000000000−2i2i−2i2i00000000000000000000
χ434-4-4444-4-4000000000000002i−2i−2i2i00000000000000000000
χ444-4-4444-4-400000000000000−2i2i2i−2i00000000000000000000
χ454-4-4-4-44440000000000000000002-2-220000000000000000
χ464-4-4-4-4444000000000000000000-222-20000000000000000

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