Finite Group Databasebeta

← Group #7256

Character table — Group #7256

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size11112222224444444488888888888888888816161616
order124422244422448888444444448816161616161616168888
χ11111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11iiii−i−i−i−i11-1-1
χ61111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−i−i−iiiii-1-111
χ71111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11iiii−i−i−i−i-1-111
χ81111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11−i−i−i−iiiii11-1-1
χ911-1-11-1-111-11-11-1-1-111ii−i−iii−i−i1-111-1-111-1-1i−ii−i
χ1011-1-11-1-111-11-11-1-1-111ii−i−iii−i−i1-1-1-111-1-111−ii−ii
χ1111-1-11-1-111-11-11-1-1-111−i−iii−i−iii1-111-1-111-1-1−ii−ii
χ1211-1-11-1-111-11-11-1-1-111−i−iii−i−iii1-1-1-111-1-111i−ii−i
χ1311-1-11-1-111-1-11-1111-1-111-1-1-1-1111-1ii−i−i−i−iii−iii−i
χ1411-1-11-1-111-1-11-1111-1-111-1-1-1-1111-1−i−iiiii−i−ii−i−ii
χ1511-1-11-1-111-1-11-1111-1-1-1-11111-1-11-1ii−i−i−i−iiii−i−ii
χ1611-1-11-1-111-1-11-1111-1-1-1-11111-1-11-1−i−iiiii−i−i−iii−i
χ1722222222222222-2-2-2-200000000-2-2000000000000
χ182222222222-2-2-2-2222200000000-2-2000000000000
χ1922222-2-2-2-222-2-2200000000000000i2−i2i2−i2i2−i2i2−i20000
χ2022222-2-2-2-222-2-2200000000000000−i2i2−i2i2−i2i2−i2i20000
χ2122222-2-2-2-22-222-2000000000000002−22−2−22−220000
χ2222222-2-2-2-22-222-200000000000000−22−222−22−20000
χ232222-22-22-2-200002i−2i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ242222-22-22-2-200002i−2i2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ252222-22-22-2-20000−2i2i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ262222-22-22-2-20000−2i2i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ2722-2-2222-2-2-222-2-200000000000000i2−i2−i2i2i2−i2−i2i20000
χ2822-2-2222-2-2-222-2-200000000000000−i2i2i2−i2−i2i2i2−i20000
χ2922-2-2222-2-2-2-2-222000000000000002−2−22−222−20000
χ3022-2-2222-2-2-2-2-22200000000000000−222−22−2−220000
χ3122-2-22-2-222-22-22-222-2-200000000-22000000000000
χ3222-2-22-2-222-2-22-22-2-22200000000-22000000000000
χ3322-2-2-2-222-2200002i−2i−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000
χ3422-2-2-2-222-2200002i−2i−2i2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000
χ3522-2-2-2-222-220000−2i2i2i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000
χ3622-2-2-2-222-220000−2i2i2i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000
χ374444-4-44-44-4000000000000000000000000000000
χ3844-4-4-44-4-444000000000000000000000000000000
χ398-88i−8i000000000000000000000000000000000000
χ408-8−8i8i000000000000000000000000000000000000

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