Finite Group Databasebeta

← Group #112359

Character table — Group #112359

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1ii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111ii−i−i
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−i−iii
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111−i−iii
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111ii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1ii−i−i
χ172222222222222222222-2-2-22-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ182222222222222222222-2-2-22-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2222-22-2-2-222-20000000000000000000000000000000000002-22-20000
χ20222222222222-2-2-2-2-2-2-2222-22-2-2-222-2000000000000000000000000000000000000-22-220000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-22000000000000000000000000000000002-2-2200000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2200000000000000000000000000000000-222-200000000
χ2322222222-2-2-2-22222-2-2-2222-22-2-22-2-2222-2-2-2-222000000000000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2222-22-2-22-2-22-2-22222-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222222222-2-2-2-20000000000000000000000000000000022-2-200000000
χ2622222222-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000-2-22200000000
χ2722222222-2-2-2-2-2-2-2-2222-2-2-22-2-2-222220000000000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2222-2-2-22-2-2-22222000000000000000000000000000000000000-222-20000
χ29222-2-2-22-222-2-222-2-22-2-200020000000002i−2i002i−2i0000000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ30222-2-2-22-222-2-222-2-22-2-200020000000002i−2i002i−2i00000000−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ31222-2-2-22-222-2-222-2-22-2-20002000000000−2i2i00−2i2i0000000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ32222-2-2-22-222-2-222-2-22-2-20002000000000−2i2i00−2i2i00000000−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ33222-2-2-22-2-2-22222-2-2-222000-20000000002i−2i00−2i2i00000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ34222-2-2-22-2-2-22222-2-2-222000-20000000002i−2i00−2i2i00000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ35222-2-2-22-2-2-22222-2-2-222000-2000000000−2i2i002i−2i00000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ36222-2-2-22-2-2-22222-2-2-222000-2000000000−2i2i002i−2i00000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ372-2-222-22-22-22-22-22-2-22-2000200000002i−2i002i−2i00000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-2-222-22-22-22-22-22-2-22-2000200000002i−2i002i−2i0000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ392-2-222-22-22-22-22-22-2-22-200020000000−2i2i00−2i2i00000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ402-2-222-22-22-22-22-22-2-22-200020000000−2i2i00−2i2i0000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ412-2-222-22-2-22-222-22-22-22000-200000002i−2i00−2i2i0000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ422-2-222-22-2-22-222-22-22-22000-200000002i−2i00−2i2i0000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ432-2-222-22-2-22-222-22-22-22000-20000000−2i2i002i−2i0000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ442-2-222-22-2-22-222-22-22-22000-20000000−2i2i002i−2i0000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ452-2-2-2-22222-2-222-2-22-2-2222-22-22-2-22-220000000000000000000000002-2-222-2-22000000000000
χ462-2-2-2-22222-2-222-2-22-2-2222-22-22-2-22-22000000000000000000000000-222-2-222-2000000000000
χ472-2-2-2-22222-2-222-2-22-2-22-2-2222-222-22-200000000000000002-2-222-2-2200000000000000000000
χ482-2-2-2-22222-2-222-2-22-2-22-2-2222-222-22-20000000000000000-222-2-222-200000000000000000000
χ492-2-2-2-22222-2-22-222-222-222-2-2-2-2222-2-200000000000000000000000000000000000000002i−2i2i−2i
χ502-2-2-2-22222-2-22-222-222-222-2-2-2-2222-2-20000000000000000000000000000000000000000−2i2i−2i2i
χ512-2-2-2-22222-2-22-222-222-2-2-22-222-2-2-2220000000022-2-222-2-20000000000000000000000000000
χ522-2-2-2-22222-2-22-222-222-2-2-22-222-2-2-22200000000-2-222-2-2220000000000000000000000000000
χ532-2-2-2-2222-222-22-2-2222-222-2-2-2-22-2-22200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ542-2-2-2-2222-222-22-2-2222-222-2-2-2-22-2-2220000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ552-2-2-2-2222-222-22-2-2222-2-2-22-222-222-2-20000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ562-2-2-2-2222-222-22-2-2222-2-2-22-222-222-2-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ572-2-2-2-2222-222-2-222-2-2-2222-22-22-22-22-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ582-2-2-2-2222-222-2-222-2-2-2222-22-22-22-22-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ592-2-2-2-2222-222-2-222-2-2-22-2-2222-22-22-2200000000000000000000000000000000000000002-2-22
χ602-2-2-2-2222-222-2-222-2-2-22-2-2222-22-22-220000000000000000000000000000000000000000-222-2
χ61444-4-4-44-444-4-4-4-444-444000-4000000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-4-444-4-4444-4-40004000000000000000000000000000000000000000000000000000
χ6344-44-4-4-44000000000004-440-4000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ6444-44-4-4-44000000000004-440-400000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ6544-44-4-4-4400000000000-44-404000000000000002-22-2-22-220000000000000000000000000000
χ6644-44-4-4-4400000000000-44-40400000000000000-22-222-22-20000000000000000000000000000
χ674-44-44-4-44000000000004-4-404000000000000002-2-22-222-20000000000000000000000000000
χ684-44-44-4-44000000000004-4-40400000000000000-222-22-2-220000000000000000000000000000
χ694-44-44-4-4400000000000-4440-4000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ704-44-44-4-4400000000000-4440-400000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ714-4-444-44-44-44-4-44-444-44000-4000000000000000000000000000000000000000000000000000
χ724-4-444-44-4-44-44-44-44-44-40004000000000000000000000000000000000000000000000000000
χ7388-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000

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