Finite Group Databasebeta

← Group #102166

Character table — Group #102166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222222244444444444444444488888888888888888888888888888888444444442444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ1011111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ1111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ1211111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ1311111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ1411111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ1511111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ1611111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ19222222222222-2-22222-2-2-2-2-2-222-2-2-2-200000000000000000000000022-2-222-2-2000000000000
χ20222222222222-2-22222-2-2-2-2-2-222-2-2-2-2000000000000000000000000-2-222-2-222000000000000
χ21222222222222-2-2-2-2-2-22222-2-2-2-2-2-222000000000000000022-2-222-2-200000000000000000000
χ22222222222222-2-2-2-2-2-22222-2-2-2-2-2-2220000000000000000-2-222-2-22200000000000000000000
χ2322222222-2-2-2-2222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000
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
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-22-22-2-200002-22i2i−2i−2i2i2i−2i−2i2-2000000000022-2-22i2i−2i−2i000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ3022-22-22-2-200002-22i2i−2i−2i2i2i−2i−2i2-2000000000022-2-22i2i−2i−2i00000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ3122-22-22-2-200002-22i2i−2i−2i2i2i−2i−2i2-20000000000-2-222−2i−2i2i2i000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ3222-22-22-2-200002-22i2i−2i−2i2i2i−2i−2i2-20000000000-2-222−2i−2i2i2i00000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ3322-22-22-2-200002-2−2i−2i2i2i−2i−2i2i2i2-2000000000022-2-2−2i−2i2i2i000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ3422-22-22-2-200002-2−2i−2i2i2i−2i−2i2i2i2-2000000000022-2-2−2i−2i2i2i00000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ3522-22-22-2-200002-2−2i−2i2i2i−2i−2i2i2i2-20000000000-2-2222i2i−2i−2i000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ3622-22-22-2-200002-2−2i−2i2i2i−2i−2i2i2i2-20000000000-2-2222i2i−2i−2i00000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ372-222-2-22-22-22-22-200000000-22002-20000002i−2i2i−2i00002i2i−2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ382-222-2-22-22-22-22-200000000-22002-20000002i−2i2i−2i00002i2i−2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ392-222-2-22-22-22-22-200000000-22002-2000000−2i2i−2i2i0000−2i−2i2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ402-222-2-22-22-22-22-200000000-22002-2000000−2i2i−2i2i0000−2i−2i2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ412-222-2-22-22-22-2-22000000002-200-22002i2i−2i−2i00002i−2i2i−2i0000i2−i2−i2i2i2−i2−i2i22−2−222−2−22000000000000
χ422-222-2-22-22-22-2-22000000002-200-22002i2i−2i−2i00002i−2i2i−2i0000−i2i2i2−i2−i2i2i2−i2−222−2−222−2000000000000
χ432-222-2-22-22-22-2-22000000002-200-2200−2i−2i2i2i0000−2i2i−2i2i0000i2−i2−i2i2i2−i2−i2i2−222−2−222−2000000000000
χ442-222-2-22-22-22-2-22000000002-200-2200−2i−2i2i2i0000−2i2i−2i2i0000−i2i2i2−i2−i2i2i2−i22−2−222−2−22000000000000
χ452-222-2-22-2-22-222-200000000-2200-220000002i−2i2i−2i0000−2i−2i2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ462-222-2-22-2-22-222-200000000-2200-220000002i−2i2i−2i0000−2i−2i2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ472-222-2-22-2-22-222-200000000-2200-22000000−2i2i−2i2i00002i2i−2i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ482-222-2-22-2-22-222-200000000-2200-22000000−2i2i−2i2i00002i2i−2i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ492-222-2-22-2-22-22-22000000002-2002-2002i2i−2i−2i0000−2i2i−2i2i00002−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ502-222-2-22-2-22-22-22000000002-2002-2002i2i−2i−2i0000−2i2i−2i2i0000−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ512-222-2-22-2-22-22-22000000002-2002-200−2i−2i2i2i00002i−2i2i−2i00002−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ522-222-2-22-2-22-22-22000000002-2002-200−2i−2i2i2i00002i−2i2i−2i0000−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ53444-4-4-4-440000004i−4i4i−4i0000000000002i2−2i22i2−2i20000000022−2222−220000000000000000000000000000
χ54444-4-4-4-440000004i−4i4i−4i000000000000−2i22i2−2i22i200000000−2222−22220000000000000000000000000000
χ55444-4-4-4-44000000−4i4i−4i4i0000000000002i2−2i22i2−2i200000000−2222−22220000000000000000000000000000
χ56444-4-4-4-44000000−4i4i−4i4i000000000000−2i22i2−2i22i20000000022−2222−220000000000000000000000000000
χ5744-44-44-4-40000-444i4i−4i−4i−4i−4i4i4i-4400000000000000000000000000000000000000000000000000
χ5844-44-44-4-40000-44−4i−4i4i4i4i4i−4i−4i-4400000000000000000000000000000000000000000000000000
χ5944-4-44-44-444-4-4004-4-440000004-4000000000000000000000000000000000000000000000000
χ6044-4-44-44-444-4-400-444-4000000-44000000000000000000000000000000000000000000000000
χ6144-4-44-44-4-4-444004-4-44000000-44000000000000000000000000000000000000000000000000
χ6244-4-44-44-4-4-44400-444-40000004-4000000000000000000000000000000000000000000000000
χ634-44-444-4-400000000004i−4i4i−4i0000000022−22−2222000000002i2−2i2−2i22i20000000000000000000000000000
χ644-44-444-4-400000000004i−4i4i−4i00000000−222222−2200000000−2i22i22i2−2i20000000000000000000000000000
χ654-44-444-4-40000000000−4i4i−4i4i0000000022−22−222200000000−2i22i22i2−2i20000000000000000000000000000
χ664-44-444-4-40000000000−4i4i−4i4i00000000−222222−22000000002i2−2i2−2i22i20000000000000000000000000000
χ674-4-444-4-4400004400000000-4-400000000004i−4i−4i4i000000000000000000000000000000000000
χ684-4-444-4-4400004400000000-4-40000000000−4i4i4i−4i000000000000000000000000000000000000
χ694-4-444-4-440000-4-40000000044000000000000004-4-4400000000000000000000000000000000
χ704-4-444-4-440000-4-4000000004400000000000000-444-400000000000000000000000000000000
χ714-4-4-4-44444-4-440000004-4-440000004-400000000000000000000000000000000000000000000
χ724-4-4-4-44444-4-44000000-444-4000000-4400000000000000000000000000000000000000000000
χ734-4-4-4-4444-444-40000004-4-44000000-4400000000000000000000000000000000000000000000
χ744-4-4-4-4444-444-4000000-444-40000004-400000000000000000000000000000000000000000000

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