Finite Group Databasebeta

← Group #7129

Character table — Group #7129

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size11112222224444444488888888888888888816161616
order1244222444444444444488888888888888884488
χ11111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ61111111111-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111
χ71111111111-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ81111111111-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ911-1-1-1-1111-1ii−i−iii−i−i1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ31-1i−i
χ1011-1-1-1-1111-1ii−i−iii−i−i1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3-11−ii
χ1111-1-1-1-1111-1ii−i−iii−i−i1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3-11−ii
χ1211-1-1-1-1111-1ii−i−iii−i−i1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ31-1i−i
χ1311-1-1-1-1111-1−i−iii−i−iii1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ1-1−ii
χ1411-1-1-1-1111-1−i−iii−i−iii1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ-11i−i
χ1511-1-1-1-1111-1−i−iii−i−iii1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζζ3ζ3−ζ3−ζ3ζζ−ζ−ζ-11i−i
χ1611-1-1-1-1111-1−i−iii−i−iii1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ−ζζζ1-1−ii
χ1722222222222-22-22-22-2-2-200000000000000000000
χ182222222222-22-22-22-22-2-200000000000000000000
χ1922222-2-22-2-202i0−2i0−2i02i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ2022222-2-22-2-202i0−2i0−2i02i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ2122222-2-22-2-20−2i02i02i0−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ2222222-2-22-2-20−2i02i02i0−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ232222-22-2-22-22i0−2i0−2i02i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ242222-22-2-22-22i0−2i0−2i02i00000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ252222-22-2-22-2−2i02i02i0−2i000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ262222-22-2-22-2−2i02i02i0−2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ2722-2-22-2-2-2222020-20-2000000000002−2−22−222−20000
χ2822-2-22-2-2-2222020-20-200000000000−222−22−2−220000
χ2922-2-22-2-2-222-20-2020200000000000i2−i2−i2i2i2−i2−i2i20000
χ3022-2-22-2-2-222-20-2020200000000000−i2i2i2−i2−i2i2i2−i20000
χ3122-2-2-22-22-2202020-20-2002−2−22−222−2000000000000
χ3222-2-2-22-22-2202020-20-200−222−22−2−22000000000000
χ3322-2-2-22-22-220-20-2020200i2−i2−i2i2i2−i2−i2i2000000000000
χ3422-2-2-22-22-220-20-2020200−i2i2i2−i2−i2i2i2−i2000000000000
χ3522-2-2-2-2222-22i−2i−2i2i2i−2i−2i2i-2200000000000000000000
χ3622-2-2-2-2222-2−2i2i2i−2i−2i2i2i−2i-2200000000000000000000
χ374444-4-44-4-44000000000000000000000000000000
χ3844-4-4444-4-4-4000000000000000000000000000000
χ398-88i−8i000000000000000000000000000000000000
χ408-8−8i8i000000000000000000000000000000000000

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