Finite Group Databasebeta

← Group #7730

Character table — Group #7730

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11111111222222224444444444888888888888888816161616
order1222222244444444224444444488888888888888882444
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
χ51111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911111111-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i1-11-1
χ1011111111-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii-11-11
χ1111111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i-11-11
χ1211111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−iii−i−iii−i−iii−i−iii1-11-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i-111-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii-111-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ172222222222-2-2-2-2222222-2-2-2-2-2-200000000000000000000
χ182222222222-2-2-2-222-2-2-2-222-2-22200000000000000000000
χ1922222222-2-22222-2-222-2-222-2-2-2-200000000000000000000
χ2022222222-2-22222-2-2-2-222-2-2-2-22200000000000000000000
χ21222-2-2-2-222i−2i2i2i−2i−2i2i−2i0000002-20000002ζ−2ζ2ζ3−2ζ3000000000000
χ22222-2-2-2-222i−2i2i2i−2i−2i2i−2i0000002-2000000−2ζ2ζ−2ζ32ζ3000000000000
χ23222-2-2-2-222i−2i−2i−2i2i2i2i−2i000000-22002ζ3−2ζ32ζ−2ζ0000000000000000
χ24222-2-2-2-222i−2i−2i−2i2i2i2i−2i000000-2200−2ζ32ζ3−2ζ2ζ0000000000000000
χ25222-2-2-2-22−2i2i2i2i−2i−2i−2i2i000000-22002ζ−2ζ2ζ3−2ζ30000000000000000
χ26222-2-2-2-22−2i2i2i2i−2i−2i−2i2i000000-2200−2ζ2ζ−2ζ32ζ30000000000000000
χ27222-2-2-2-22−2i2i−2i−2i2i2i−2i2i0000002-20000002ζ3−2ζ32ζ−2ζ000000000000
χ28222-2-2-2-22−2i2i−2i−2i2i2i−2i2i0000002-2000000−2ζ32ζ3−2ζ2ζ000000000000
χ2922-222-2-2-2002-22-200002i−2i00002i−2i000000002−22−2i2−i2i2−i20000
χ3022-222-2-2-2002-22-200002i−2i00002i−2i00000000−22−22−i2i2−i2i20000
χ3122-222-2-2-2002-22-20000−2i2i0000−2i2i000000002−22−2−i2i2−i2i20000
χ3222-222-2-2-2002-22-20000−2i2i0000−2i2i00000000−22−22i2−i2i2−i20000
χ3322-222-2-2-200-22-2200002i−2i0000−2i2i00000000i2−i2−i2i22−2−220000
χ3422-222-2-2-200-22-2200002i−2i0000−2i2i00000000−i2i2i2−i2−222−20000
χ3522-222-2-2-200-22-220000−2i2i00002i−2i00000000i2−i2−i2i2−222−20000
χ3622-222-2-2-200-22-220000−2i2i00002i−2i00000000−i2i2i2−i22−2−220000
χ3744-4-4-444-4004i−4i−4i4i00000000000000000000000000000000
χ3844-4-4-444-400−4i4i4i−4i00000000000000000000000000000000
χ394-444-44-4-4440000-4-4000000000000000000000000000000
χ404-444-44-4-4-4-4000044000000000000000000000000000000
χ414-44-44-44-44i−4i0000−4i4i000000000000000000000000000000
χ424-44-44-44-4−4i4i00004i−4i000000000000000000000000000000
χ434-4-44-4-444000000004-40000000000000000000000000000
χ444-4-44-4-44400000000-440000000000000000000000000000
χ454-4-4-444-440000000000004-4000000000000000000000000
χ464-4-4-444-44000000000000-44000000000000000000000000

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