Finite Group Databasebeta

← Group #9352

Character table — Group #9352

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size1111222222444444444444888888888888161616161616
order1222444444244444448888248888888888448888
χ11111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1
χ4111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111-1-11-1-111111-1-111-1-1-1-11111-1-1-1-111
χ6111111111111-1-11-1-111111-1-111-1-1-1-1-1-1-1-11111-1-1
χ7111111111111-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ8111111111111-1-11-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ911111-1-11-1-11111-1-1-1-1ii−i−i1-1i−iii−i−iii−i−i1-1i−i1-1
χ1011111-1-11-1-11111-1-1-1-1ii−i−i1-1i−iii−i−i−i−iii-11−ii-11
χ1111111-1-11-1-11111-1-1-1-1−i−iii1-1−ii−i−iiiii−i−i-11i−i-11
χ1211111-1-11-1-11111-1-1-1-1−i−iii1-1−ii−i−iii−i−iii1-1−ii1-1
χ1311111-1-11-1-111-1-1-111-1ii−i−i-11i−i−i−iiiii−i−i-11−ii1-1
χ1411111-1-11-1-111-1-1-111-1ii−i−i-11i−i−i−iii−i−iii1-1i−i-11
χ1511111-1-11-1-111-1-1-111-1−i−iii-11−iiii−i−iii−i−i1-1−ii-11
χ1611111-1-11-1-111-1-1-111-1−i−iii-11−iiii−i−i−i−iii-11i−i1-1
χ1722222222-2-2-2-222-2-2-220000-220000000000000000
χ1822222222-2-2-2-2-2-2-222200002-20000000000000000
χ1922222-2-2222-2-222222-20000-2-20000000000000000
χ2022222-2-2222-2-2-2-22-2-2-20000220000000000000000
χ212222-222-222-2200-200-2222200-2-200000000000000
χ222222-222-222-2200-200-2-2-2-2-2002200000000000000
χ232222-222-2-2-22-200200-2000000002i−2i2i−2i0000000000
χ242222-222-2-2-22-200200-200000000−2i2i−2i2i0000000000
χ252222-2-2-2-2222-200-2002000000002-2-220000000000
χ262222-2-2-2-2222-200-200200000000-222-20000000000
χ272222-2-2-2-2-2-2-220020022i2i−2i−2i00−2i2i00000000000000
χ282222-2-2-2-2-2-2-22002002−2i−2i2i2i002i−2i00000000000000
χ2944-4-4400-400004-400000000000000000000000000
χ3044-4-4400-40000-4400000000000000000000000000
χ3144-4-4-400400000004i−4i00000000000000000000000
χ3244-4-4-40040000000−4i4i00000000000000000000000
χ334-44-400004i−4i000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ344-44-400004i−4i00000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ354-44-40000−4i4i000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ364-44-40000−4i4i00000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ374-4-4404i−4i000000000002+2i−2−2i2−2i−2+2i000000000000000000
χ384-4-4404i−4i00000000000−2−2i2+2i−2+2i2−2i000000000000000000
χ394-4-440−4i4i000000000002−2i−2+2i2+2i−2−2i000000000000000000
χ404-4-440−4i4i00000000000−2+2i2−2i−2−2i2+2i000000000000000000

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