Finite Group Databasebeta

← Group #119968

Character table — Group #119968

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444422224444444444448888888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-111-1-1-1-111-111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1
χ1011111111-1-1-1-111-1-1-1-111-1-1-1-111-111-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii-1-111
χ1111111111-1-1-1-111-1-1-1-111-1-1-1-111-111-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i-1-111
χ1211111111-1-1-1-111-1-1-1-111-1-1-1-111-111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii11-1-1
χ1311111111-1-1-1-111-1-1-1-111-1-1-1-111-111-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iii-1-111
χ1411111111-1-1-1-111-1-1-1-111-1-1-1-111-111-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i11-1-1
χ1511111111-1-1-1-111-1-1-1-111-1-1-1-111-111-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii11-1-1
χ1611111111-1-1-1-111-1-1-1-111-1-1-1-111-111-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i-1-111
χ1722222222222222-2-2-2-222-2-2-2-2-2-22-2-222222-2-2-2-2000000000000000000000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-22-2-22-2-2-2-22222000000000000000000000000000000000000
χ19222222222222-2-22222-2-2-2-2-2-222-2-2-2-20000000000000000000000000000000000002i−2i2i−2i0000
χ20222222222222-2-22222-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000000000−2i2i−2i2i0000
χ21222222222222-2-2-2-2-2-2-2-22222-2-2-222-2000000000000000022-2-222-2-200000000000000000000
χ22222222222222-2-2-2-2-2-2-2-22222-2-2-222-20000000000000000-2-222-2-22200000000000000000000
χ2322222222-2-2-2-2222222222222-2-2-2-2-2-222-2-2-2-222000000000000000000000000000000000000
χ2422222222-2-2-2-2222222222222-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-220000000000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-22000000000000000000000000000000000000-222-20000
χ2922-22-22-2-200002-22i2i−2i−2i2-22i2i−2i−2i000000002-22i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3022-22-22-2-200002-22i2i−2i−2i2-22i2i−2i−2i000000002-22i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3122-22-22-2-200002-22i2i−2i−2i2-22i2i−2i−2i00000000-22−2i2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3222-22-22-2-200002-22i2i−2i−2i2-22i2i−2i−2i00000000-22−2i2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3322-22-22-2-200002-2−2i−2i2i2i2-2−2i−2i2i2i000000002-2−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3422-22-22-2-200002-2−2i−2i2i2i2-2−2i−2i2i2i000000002-2−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ3522-22-22-2-200002-2−2i−2i2i2i2-2−2i−2i2i2i00000000-222i−2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ3622-22-22-2-200002-2−2i−2i2i2i2-2−2i−2i2i2i00000000-222i−2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ372-222-2-22-20000-222i−2i2i−2i2-22i−2i2i−2i0000002-200002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ382-222-2-22-20000-222i−2i2i−2i2-22i−2i2i−2i0000002-200002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ392-222-2-22-20000-222i−2i2i−2i2-22i−2i2i−2i000000-220000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ402-222-2-22-20000-222i−2i2i−2i2-22i−2i2i−2i000000-220000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ412-222-2-22-20000-22−2i2i−2i2i2-2−2i2i−2i2i0000002-20000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ422-222-2-22-20000-22−2i2i−2i2i2-2−2i2i−2i2i0000002-20000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ432-222-2-22-20000-22−2i2i−2i2i2-2−2i2i−2i2i000000-2200002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ442-222-2-22-20000-22−2i2i−2i2i2-2−2i2i−2i2i000000-2200002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ452-2-222-2-2222-2-2222-2-22-2-2-222-22-2-22-22000000000000000000000000000000002i−2i2i−2i00000000
χ462-2-222-2-2222-2-2222-2-22-2-2-222-22-2-22-2200000000000000000000000000000000−2i2i−2i2i00000000
χ472-2-222-2-2222-2-222-222-2-2-22-2-22-22-2-22200000000000000000000000000000000000000002i−2i2i−2i
χ482-2-222-2-2222-2-222-222-2-2-22-2-22-22-2-2220000000000000000000000000000000000000000−2i2i−2i2i
χ492-2-222-2-2222-2-2-2-22-2-22222-2-222-22-22-20000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ502-2-222-2-2222-2-2-2-22-2-22222-2-222-22-22-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ512-2-222-2-2222-2-2-2-2-222-222-222-2-2222-2-2000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ522-2-222-2-2222-2-2-2-2-222-222-222-2-2222-2-200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ532-2-222-2-22-2-222222-2-22-2-2-222-2-222-22-200000000000000000000000000000000000000002i−2i−2i2i
χ542-2-222-2-22-2-222222-2-22-2-2-222-2-222-22-20000000000000000000000000000000000000000−2i2i2i−2i
χ552-2-222-2-22-2-22222-222-2-2-22-2-222-222-2-2000000000000000000000000000000002i−2i−2i2i00000000
χ562-2-222-2-22-2-22222-222-2-2-22-2-222-222-2-200000000000000000000000000000000−2i2i2i−2i00000000
χ572-2-222-2-22-2-222-2-22-2-22222-2-22-22-22-22000000002-2-222-2-220000000000000000000000000000
χ582-2-222-2-22-2-222-2-22-2-22222-2-22-22-22-2200000000-222-2-222-20000000000000000000000000000
χ592-2-222-2-22-2-222-2-2-222-222-222-22-2-2-2220000000000000000000000002-2-222-2-22000000000000
χ602-2-222-2-22-2-222-2-2-222-222-222-22-2-2-222000000000000000000000000-222-2-222-2000000000000
χ61444-44-4-4-44-44-400000000000000000000000000000000000022−220022−2200000000000000000000
χ62444-44-4-4-44-44-4000000000000000000000000000000000000−222200−222200000000000000000000
χ63444-44-4-4-4-44-440000000000000000000000000000000000002i2−2i200−2i22i200000000000000000000
χ64444-44-4-4-4-44-44000000000000000000000000000000000000−2i22i2002i2−2i200000000000000000000
χ6544-44-44-4-40000-444i4i−4i−4i-44−4i−4i4i4i00000000000000000000000000000000000000000000000000
χ6644-44-44-4-40000-44−4i−4i4i4i-444i4i−4i−4i00000000000000000000000000000000000000000000000000
χ674-444-4-44-400004-44i−4i4i−4i-44−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ684-444-4-44-400004-4−4i4i−4i4i-444i−4i4i−4i00000000000000000000000000000000000000000000000000
χ694-4-4-4444-44-4-44000000000000000000000000000000000022−220022−220000000000000000000000
χ704-4-4-4444-44-4-440000000000000000000000000000000000−222200−22220000000000000000000000
χ714-4-4-4444-4-444-400000000000000000000000000000000002i2−2i200−2i22i20000000000000000000000
χ724-4-4-4444-4-444-40000000000000000000000000000000000−2i22i2002i2−2i20000000000000000000000
χ7388-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000

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