Finite Group Databasebeta

← Group #112352

Character table — Group #112352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888244444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111
χ911111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-11-1ii−i−i
χ1011111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-11−i−iii
χ1111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11-1-111-11ii−i−i
χ1211111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-1−i−iii
χ1311111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1111-1-1-11−i−iii
χ1411111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-1-1111-1ii−i−i
χ1511111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-1-1-1111-1−i−iii
χ1611111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1-11ii−i−i
χ1722222222222222-2-2-2-2-2-222-2-222-2-2-2-200000000000000000000000000000000002-22-2000000
χ1822222222222222-2-2-2-2-2-222-2-222-2-2-2-20000000000000000000000000000000000-22-22000000
χ19222222222222-2-22222-2-2-2-2-2-2-2-2-2-22222-2-222-2-2000000000000000000000000000000000000
χ20222222222222-2-22222-2-2-2-2-2-2-2-2-2-222-2-222-2-222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-222-2-222-2-222-2-200000000000000000000000000000000220000-2-20000
χ22222222222222-2-2-2-2-2-222-2-222-2-222-2-200000000000000000000000000000000-2-20000220000
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
χ2522222222-2-2-2-222-2-2-2-2-2-222-2-2-2-22222000000000000000000000000000000002-20000-220000
χ2622222222-2-2-2-222-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000-2200002-20000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-22200000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-2220000000000000000000000000000000000-222-2000000
χ2922-22-2-22-200002i−2i22-2-22i−2i2i−2i2i−2i000000002i−2i2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3022-22-2-22-200002i−2i22-2-22i−2i2i−2i2i−2i000000002i−2i2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3122-22-2-22-200002i−2i22-2-22i−2i2i−2i2i−2i00000000−2i2i-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3222-22-2-22-200002i−2i22-2-22i−2i2i−2i2i−2i00000000−2i2i-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3322-22-2-22-20000−2i2i22-2-2−2i2i−2i2i−2i2i000000002i−2i-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ3422-22-2-22-20000−2i2i22-2-2−2i2i−2i2i−2i2i000000002i−2i-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3522-22-2-22-20000−2i2i22-2-2−2i2i−2i2i−2i2i00000000−2i2i2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3622-22-2-22-20000−2i2i22-2-2−2i2i−2i2i−2i2i00000000−2i2i2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ372-22-22-22-200002i−2i2-22-22i−2i−2i2i−2i2i0000002i−2i00002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ382-22-22-22-200002i−2i2-22-22i−2i−2i2i−2i2i0000002i−2i00002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ392-22-22-22-200002i−2i2-22-22i−2i−2i2i−2i2i000000−2i2i0000-221−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ402-22-22-22-200002i−2i2-22-22i−2i−2i2i−2i2i000000−2i2i0000-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ412-22-22-22-20000−2i2i2-22-2−2i2i2i−2i2i−2i0000002i−2i0000-221+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ422-22-22-22-20000−2i2i2-22-2−2i2i2i−2i2i−2i0000002i−2i0000-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ432-22-22-22-20000−2i2i2-22-2−2i2i2i−2i2i−2i000000−2i2i00002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ442-22-22-22-20000−2i2i2-22-2−2i2i2i−2i2i−2i000000−2i2i00002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ452-2-2-2-222222-2-2222-2-2222-2-2-2-22-22-2-22000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ462-2-2-2-222222-2-2222-2-2222-2-2-2-22-22-2-2200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ472-2-2-2-222222-2-222-222-2-2-2-2-2222-2-222-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ482-2-2-2-222222-2-222-222-2-2-2-2-2222-2-222-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ492-2-2-2-222222-2-2-2-22-2-22-2-22222-22-22-220000000000000000000000002-2-222-2-22000000000000
χ502-2-2-2-222222-2-2-2-22-2-22-2-22222-22-22-22000000000000000000000000-222-2-222-2000000000000
χ512-2-2-2-222222-2-2-2-2-222-22222-2-2-222-22-200000000000000000000000000000000000000002i−2i2i−2i
χ522-2-2-2-222222-2-2-2-2-222-22222-2-2-222-22-20000000000000000000000000000000000000000−2i2i−2i2i
χ532-2-2-2-2222-2-222222-2-2222-2-2-2-2-22-222-20000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ542-2-2-2-2222-2-222222-2-2222-2-2-2-2-22-222-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ552-2-2-2-2222-2-22222-222-2-2-2-2-222-222-2-2200000000000000000000000000000000000000002-2-22
χ562-2-2-2-2222-2-22222-222-2-2-2-2-222-222-2-220000000000000000000000000000000000000000-222-2
χ572-2-2-2-2222-2-222-2-22-2-22-2-222222-22-22-2000000002-2-222-2-220000000000000000000000000000
χ582-2-2-2-2222-2-222-2-22-2-22-2-222222-22-22-200000000-222-2-222-20000000000000000000000000000
χ592-2-2-2-2222-2-222-2-2-222-22222-2-22-2-22-22000000000000000022-2-2-2-22200000000000000000000
χ602-2-2-2-2222-2-222-2-2-222-22222-2-22-2-22-220000000000000000-2-22222-2-200000000000000000000
χ6144-44-4-44-400004i−4i-4-444−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6244-44-4-44-40000−4i4i-4-4444i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6344-4-444-4-44-44-400000000000000000000000000000000002-22-22-22-200000000000000000000
χ6444-4-444-4-44-44-40000000000000000000000000000000000-22-22-22-2200000000000000000000
χ6544-4-444-4-4-44-4400000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ6644-4-444-4-4-44-440000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ674-444-44-4-44-4-4400000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ684-444-44-4-44-4-440000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ694-444-44-4-4-444-400000000000000000000000000000000002-2-22-222-200000000000000000000
χ704-444-44-4-4-444-40000000000000000000000000000000000-222-22-2-2200000000000000000000
χ714-44-44-44-400004i−4i-44-44−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ724-44-44-44-40000−4i4i-44-444i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ73888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000

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