Finite Group Databasebeta

← Group #229380

Character table — Group #229380

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888844444444444488888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-11111-1-111-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ171-11-1-111-1-111-1-1-111iiii−i−i−i−iii−i−iii−i−i1-1ii−i−i11-1-111-1-1iiii−i−i−i−ii−i11-1-1i−ii−ii−i11-1-111-1-1i−i1-11-1i−ii−i1-1
χ181-11-1-111-1-111-1-1-111iiii−i−i−i−iii−i−iii−i−i1-1ii−i−i11-1-111-1-1iiii−i−i−i−i−ii-1-111i−ii−i−ii11-1-111-1-1−ii-11-11−ii−ii-11
χ191-11-1-111-1-111-1-1-111iiii−i−i−i−iii−i−i−i−iii1-1ii−i−i-1-111-1-111−i−i−i−iiiiii−i11-1-1i−i−iii−i11-1-1-1-111i−i1-1-11−ii−ii-11
χ201-11-1-111-1-111-1-1-111iiii−i−i−i−iii−i−i−i−iii1-1ii−i−i-1-111-1-111−i−i−i−iiiii−ii-1-111i−i−ii−ii11-1-1-1-111−ii-111-1i−ii−i1-1
χ211-11-1-111-1-111-1-1-111iiii−i−i−i−i−i−iiiii−i−i1-1ii−i−i-1-111-1-111−i−i−i−iiiiii−i11-1-1−iii−ii−i-1-11111-1-1−ii-111-1i−i−ii-11
χ221-11-1-111-1-111-1-1-111iiii−i−i−i−i−i−iiiii−i−i1-1ii−i−i-1-111-1-111−i−i−i−iiiii−ii-1-111−iii−i−ii-1-11111-1-1i−i1-1-11−iii−i1-1
χ231-11-1-111-1-111-1-1-111iiii−i−i−i−i−i−iii−i−iii1-1ii−i−i11-1-111-1-1iiii−i−i−i−ii−i11-1-1−ii−iii−i-1-111-1-111−ii-11-11−iii−i1-1
χ241-11-1-111-1-111-1-1-111iiii−i−i−i−i−i−iii−i−iii1-1ii−i−i11-1-111-1-1iiii−i−i−i−i−ii-1-111−ii−ii−ii-1-111-1-111i−i1-11-1i−i−ii-11
χ251-11-1-111-1-111-1-1-111−i−i−i−iiiiiii−i−iii−i−i1-1−i−iii11-1-111-1-1−i−i−i−iiiiii−i-1-111i−ii−ii−i-1-111-1-111−ii1-11-1−iii−i-11
χ261-11-1-111-1-111-1-1-111−i−i−i−iiiiiii−i−iii−i−i1-1−i−iii11-1-111-1-1−i−i−i−iiiii−ii11-1-1i−ii−i−ii-1-111-1-111i−i-11-11i−i−ii1-1
χ271-11-1-111-1-111-1-1-111−i−i−i−iiiiiii−i−i−i−iii1-1−i−iii-1-111-1-111iiii−i−i−i−ii−i-1-111i−i−iii−i-1-11111-1-1−ii1-1-11i−i−ii1-1
χ281-11-1-111-1-111-1-1-111−i−i−i−iiiiiii−i−i−i−iii1-1−i−iii-1-111-1-111iiii−i−i−i−i−ii11-1-1i−i−ii−ii-1-11111-1-1i−i-111-1−iii−i-11
χ291-11-1-111-1-111-1-1-111−i−i−i−iiiii−i−iiiii−i−i1-1−i−iii-1-111-1-111iiii−i−i−i−ii−i-1-111−iii−ii−i11-1-1-1-111i−i-111-1−ii−ii1-1
χ301-11-1-111-1-111-1-1-111−i−i−i−iiiii−i−iiiii−i−i1-1−i−iii-1-111-1-111iiii−i−i−i−i−ii11-1-1−iii−i−ii11-1-1-1-111−ii1-1-11i−ii−i-11
χ311-11-1-111-1-111-1-1-111−i−i−i−iiiii−i−iii−i−iii1-1−i−iii11-1-111-1-1−i−i−i−iiiiii−i-1-111−ii−iii−i11-1-111-1-1i−i-11-11i−ii−i-11
χ321-11-1-111-1-111-1-1-111−i−i−i−iiiii−i−iii−i−iii1-1−i−iii11-1-111-1-1−i−i−i−iiiii−ii11-1-1−ii−ii−ii11-1-111-1-1−ii1-11-1−ii−ii1-1
χ33222222222-22-2-222-20000000022222222-2-200002222-2-2-2-200000000000000-2-2-2-20000000000000000000000
χ34222222222-22-2-222-2000000002222-2-2-2-2-2-20000-2-2-2-2222200000000000000-2-2220000000000000000000000
χ35222222222-22-2-222-200000000-2-2-2-22222-2-20000-2-2-2-222220000000000000022-2-20000000000000000000000
χ36222222222-22-2-222-200000000-2-2-2-2-2-2-2-2-2-200002222-2-2-2-20000000000000022220000000000000000000000
χ3722222222-22-222-2-222222222200000000-2-2-2-2-2-20000000000000000222-22-20000-2-200000000000000000000
χ3822222222-22-222-2-222222222200000000-2-2-2-2-2-20000000000000000-2-2-22-2200002200000000000000000000
χ3922222222-22-222-2-22-2-2-2-2-2-2-2-200000000-2-22222000000000000000022-22-220000-2-200000000000000000000
χ4022222222-22-222-2-22-2-2-2-2-2-2-2-200000000-2-222220000000000000000-2-22-22-200002200000000000000000000
χ412222-2-2-2-220200-2-2022−2−222−2−22-22-22-22-2002−22−22-22-2000022−2−222−2−20000000000002−22−22−22−2000000000000
χ422222-2-2-2-220200-2-2022−2−222−2−22-22-2-22-22002−22−2-22-220000−2−222−2−2220000000000002−22−2−22−22000000000000
χ432222-2-2-2-220200-2-2022−2−222−2−2-22-222-22-2002−22−2-22-220000−2−222−2−222000000000000−22−222−22−2000000000000
χ442222-2-2-2-220200-2-2022−2−222−2−2-22-22-22-22002−22−22-22-2000022−2−222−2−2000000000000−22−22−22−22000000000000
χ452222-2-2-2-220200-2-20−2−222−2−2222-22-22-22-200−22−222-22-20000−2−222−2−222000000000000−22−22−22−22000000000000
χ462222-2-2-2-220200-2-20−2−222−2−2222-22-2-22-2200−22−22-22-22000022−2−222−2−2000000000000−22−222−22−2000000000000
χ472222-2-2-2-220200-2-20−2−222−2−222-22-222-22-200−22−22-22-22000022−2−222−2−20000000000002−22−2−22−22000000000000
χ482222-2-2-2-220200-2-20−2−222−2−222-22-22-22-2200−22−222-22-20000−2−222−2−2220000000000002−22−22−22−2000000000000
χ492-22-22-2-22-202002-20i2i2−i2−i2−i2−i2i2i22i−2i−2i2i2i−2i−2i2i00i2−i2−i2i22-2-220000i2i2−i2−i2−i2−i2i2i20000000000002−2−222−2−22000000000000
χ502-22-22-2-22-202002-20i2i2−i2−i2−i2−i2i2i22i−2i−2i2i−2i2i2i−2i00i2−i2−i2i2-222-20000−i2−i2i2i2i2i2−i2−i20000000000002−2−22−222−2000000000000
χ512-22-22-2-22-202002-20i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i2i−2i−2i2i00i2−i2−i2i2-222-20000−i2−i2i2i2i2i2−i2−i2000000000000−222−22−2−22000000000000
χ522-22-22-2-22-202002-20i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i−2i2i2i−2i00i2−i2−i2i22-2-220000i2i2−i2−i2−i2−i2i2i2000000000000−222−2−222−2000000000000
χ532-22-22-2-22-202002-20−i2−i2i2i2i2i2−i2−i22i−2i−2i2i2i−2i−2i2i00−i2i2i2−i22-2-220000−i2−i2i2i2i2i2−i2−i2000000000000−222−2−222−2000000000000
χ542-22-22-2-22-202002-20−i2−i2i2i2i2i2−i2−i22i−2i−2i2i−2i2i2i−2i00−i2i2i2−i2-222-20000i2i2−i2−i2−i2−i2i2i2000000000000−222−22−2−22000000000000
χ552-22-22-2-22-202002-20−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i2i−2i−2i2i00−i2i2i2−i2-222-20000i2i2−i2−i2−i2−i2i2i20000000000002−2−22−222−2000000000000
χ562-22-22-2-22-202002-20−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i−2i2i2i−2i00−i2i2i2−i22-2-220000−i2−i2i2i2i2i2−i2−i20000000000002−2−222−2−22000000000000
χ572-22-2-222-222-2-2-22-222i2i2i2i−2i−2i−2i−2i00000000-22−2i−2i2i2i00000000000000002i−2i2-2-220000−2i2i00000000000000000000
χ582-22-2-222-222-2-2-22-222i2i2i2i−2i−2i−2i−2i00000000-22−2i−2i2i2i0000000000000000−2i2i-222-200002i−2i00000000000000000000
χ592-22-2-222-222-2-2-22-22−2i−2i−2i−2i2i2i2i2i00000000-222i2i−2i−2i00000000000000002i−2i-222-20000−2i2i00000000000000000000
χ602-22-2-222-222-2-2-22-22−2i−2i−2i−2i2i2i2i2i00000000-222i2i−2i−2i0000000000000000−2i2i2-2-2200002i−2i00000000000000000000
χ612-22-2-222-2-2-2222-22-2000000002i2i−2i−2i2i2i−2i−2i-22000022-2-2-2-22200000000000000−2i2i−2i2i0000000000000000000000
χ622-22-2-222-2-2-2222-22-2000000002i2i−2i−2i−2i−2i2i2i-220000-2-22222-2-200000000000000−2i2i2i−2i0000000000000000000000
χ632-22-2-222-2-2-2222-22-200000000−2i−2i2i2i2i2i−2i−2i-220000-2-22222-2-2000000000000002i−2i−2i2i0000000000000000000000
χ642-22-2-222-2-2-2222-22-200000000−2i−2i2i2i−2i−2i2i2i-22000022-2-2-2-222000000000000002i−2i2i−2i0000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ664444-4-4-4-4-40-4004402222−22−222222−22−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ674444-4-4-4-4-40-400440−22−222222−22−222222000000000022−2222−22000000000000000000000000000000000000000000000000
χ6844-4-444-4-40404-400-400000000000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ6944-4-444-4-40404-400-4000000000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000
χ7044-4-444-4-40-40-440044i−4i4i−4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ7144-4-444-4-40-40-44004−4i4i−4i4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7244-4-4-4-444000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000002i2−2i22i2−2i22-2-222-2-2200000000000000000000000000000000
χ7344-4-4-4-444000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000−2i22i2−2i22i2-222-2-222-200000000000000000000000000000000
χ7444-4-4-4-44400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000002i2−2i22i2−2i2-222-2-222-200000000000000000000000000000000
χ7544-4-4-4-44400000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000−2i22i2−2i22i22-2-222-2-2200000000000000000000000000000000
χ764-44-44-4-4440-400-4402i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ774-44-44-4-4440-400-440−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ784-44-4-444-44-4-4444-4-400000000000000004-40000000000000000000000000000000000000000000000000000
χ794-4-444-44-40000000022−22−2222−222222−220000000000000000002i2−2i2−2i22i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ804-4-444-44-40000000022−22−2222−222222−22000000000000000000−2i22i22i2−2i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ814-4-444-44-400000000−222222−2222−22−22220000000000000000002i2−2i2−2i22i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ824-4-444-44-400000000−222222−2222−22−2222000000000000000000−2i22i22i2−2i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ834-4-44-44-44040-4400-40000000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ844-4-44-44-44040-4400-4000000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ854-4-44-44-440-404-40044-44-4-44-4400000000000000000000000000000000000000000000000000000000000000
χ864-4-44-44-440-404-4004-44-444-44-400000000000000000000000000000000000000000000000000000000000000

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