Finite Group Databasebeta

← Group #134539

Character table — Group #134539

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222222222444444448888888844444444888888888888161616161616161616161616161616164444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ6111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ7111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ8111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ1011111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ1211111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-20000000022-2-2-2-2-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ192222222222222222-2-2-2-20000000022-2-2-2-2-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-22222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-200000000-2-222-2-222000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2522222222-2-2-2-22222-2-2-2-200000000-2-222-2-222000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2622222222-2-2-2-2-2-2-2-222222222222222-2-2-2-222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2922-2-22-22-200002i2i−2i−2i2-22-22i2i−2i−2i2i2i−2i−2i00002i−2i000000000022-2-20000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ3022-2-22-22-200002i2i−2i−2i2-22-22i2i−2i−2i2i2i−2i−2i00002i−2i000000000022-2-2000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ3122-2-22-22-200002i2i−2i−2i2-22-2−2i−2i2i2i−2i−2i2i2i00002i−2i0000000000-2-2220000000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ3222-2-22-22-200002i2i−2i−2i2-22-2−2i−2i2i2i−2i−2i2i2i00002i−2i0000000000-2-222000000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ3322-2-22-22-20000−2i−2i2i2i2-22-22i2i−2i−2i2i2i−2i−2i0000−2i2i0000000000-2-2220000000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ3422-2-22-22-20000−2i−2i2i2i2-22-22i2i−2i−2i2i2i−2i−2i0000−2i2i0000000000-2-222000000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ3522-2-22-22-20000−2i−2i2i2i2-22-2−2i−2i2i2i−2i−2i2i2i0000−2i2i000000000022-2-20000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ3622-2-22-22-20000−2i−2i2i2i2-22-2−2i−2i2i2i−2i−2i2i2i0000−2i2i000000000022-2-2000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ372-22-22-2-222-22-22i−2i2i−2i00002−22−22−22−22i−2i00000022−2−2i2i2−i2−i2i2−i2i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ382-22-22-2-222-22-22i−2i2i−2i00002−22−22−22−22i−2i00000022−2−2i2i2−i2−i2i2−i2i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ392-22-22-2-222-22-22i−2i2i−2i0000−22−22−22−222i−2i000000−2−222−i2−i2i2i2−i2i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ402-22-22-2-222-22-22i−2i2i−2i0000−22−22−22−222i−2i000000−2−222−i2−i2i2i2−i2i2−i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ412-22-22-2-222-22-2−2i2i−2i2i00002−22−22−22−2−2i2i00000022−2−2−i2−i2i2i2−i2i2−i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ422-22-22-2-222-22-2−2i2i−2i2i00002−22−22−22−2−2i2i00000022−2−2−i2−i2i2i2−i2i2−i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ432-22-22-2-222-22-2−2i2i−2i2i0000−22−22−22−22−2i2i000000−2−222i2i2−i2−i2i2−i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ442-22-22-2-222-22-2−2i2i−2i2i0000−22−22−22−22−2i2i000000−2−222i2i2−i2−i2i2−i2i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ452-22-22-2-22-22-222i−2i2i−2i00002−22−22−22−2−2i2i000000−2−222−i2−i2i2i2i2−i2i2−i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ462-22-22-2-22-22-222i−2i2i−2i00002−22−22−22−2−2i2i000000−2−222−i2−i2i2i2i2−i2i2−i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ472-22-22-2-22-22-222i−2i2i−2i0000−22−22−22−22−2i2i00000022−2−2i2i2−i2−i2−i2i2−i2i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ482-22-22-2-22-22-222i−2i2i−2i0000−22−22−22−22−2i2i00000022−2−2i2i2−i2−i2−i2i2−i2i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ492-22-22-2-22-22-22−2i2i−2i2i00002−22−22−22−22i−2i000000−2−222i2i2−i2−i2−i2i2−i2i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ502-22-22-2-22-22-22−2i2i−2i2i00002−22−22−22−22i−2i000000−2−222i2i2−i2−i2−i2i2−i2i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ512-22-22-2-22-22-22−2i2i−2i2i0000−22−22−22−222i−2i00000022−2−2−i2−i2i2i2i2−i2i2−i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ522-22-22-2-22-22-22−2i2i−2i2i0000−22−22−22−222i−2i00000022−2−2−i2−i2i2i2i2−i2i2−i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ532-22-2-222-222-2-200002-2-222222-2-2-2-2002-200002-22-2000000000000000000000000002-2002-200000000
χ542-22-2-222-222-2-200002-2-222222-2-2-2-2002-200002-22-200000000000000000000000000-2200-2200000000
χ552-22-2-222-222-2-200002-2-22-2-2-2-22222002-20000-22-220000000000000000000000002i−2i002i−2i0000000000
χ562-22-2-222-222-2-200002-2-22-2-2-2-22222002-20000-22-22000000000000000000000000−2i2i00−2i2i0000000000
χ572-22-2-222-2-2-22200002-2-222222-2-2-2-200-220000-22-220000000000000000000000002i−2i00−2i2i0000000000
χ582-22-2-222-2-2-22200002-2-222222-2-2-2-200-220000-22-22000000000000000000000000−2i2i002i−2i0000000000
χ592-22-2-222-2-2-22200002-2-22-2-2-2-2222200-2200002-22-2000000000000000000000000002-200-2200000000
χ602-22-2-222-2-2-22200002-2-22-2-2-2-2222200-2200002-22-200000000000000000000000000-22002-200000000
χ614444-4-4-4-44-4-440000000022−2222−22−2222−22220000000022−22−22220000000000000000000000000000000000000000
χ624444-4-4-4-44-4-4400000000−2222−222222−2222−2200000000−222222−220000000000000000000000000000000000000000
χ634444-4-4-4-4-444-40000000022−2222−22−2222−222200000000−222222−220000000000000000000000000000000000000000
χ644444-4-4-4-4-444-400000000−2222−222222−2222−220000000022−22−22220000000000000000000000000000000000000000
χ6544-4-44-44-400004i4i−4i−4i-44-44000000000000−4i4i0000000000000000000000000000000000000000000000
χ6644-4-44-44-40000−4i−4i4i4i-44-440000000000004i−4i0000000000000000000000000000000000000000000000
χ6744-4-4-44-440000000000002i2−2i2−2i22i2−2i22i22i2−2i20000004-400002i2−2i22i2−2i2000000000000000000000000000000000000
χ6844-4-4-44-440000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000-440000−2i22i2−2i22i2000000000000000000000000000000000000
χ6944-4-4-44-44000000000000−2i22i22i2−2i22i2−2i2−2i22i20000004-40000−2i22i2−2i22i2000000000000000000000000000000000000
χ7044-4-4-44-44000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000-4400002i2−2i22i2−2i2000000000000000000000000000000000000
χ714-44-4-444-444-4-40000-444-40000000000-44000000000000000000000000000000000000000000000000
χ724-44-4-444-4-4-4440000-444-400000000004-4000000000000000000000000000000000000000000000000
χ734-4-4444-4-400004-4-4400002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ744-4-4444-4-400004-4-440000−2i22i22i2−2i2−2i22i22i2−2i200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ754-4-4444-4-40000-444-400002i2−2i2−2i22i22i2−2i2−2i22i200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ764-4-4444-4-40000-444-40000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ774-4-44-4-4440000000044-4-44i4i−4i−4i−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ784-4-44-4-4440000000044-4-4−4i−4i4i4i4i4i−4i−4i0000000000000000000000000000000000000000000000000000
χ794-4-44-4-44400000000-4-444000000000000000000004-4-44000000000000000000000000000000000000
χ804-4-44-4-44400000000-4-44400000000000000000000-444-4000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.