Finite Group Databasebeta

← Group #113149

Character table — Group #113149

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ91-1-11-1-11111-1-11111-1-1-1-1-111-111-11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-111-1-11-1ii−i−i
χ101-1-11-1-11111-1-11111-1-1-1-1-111-111-11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1111-1-1-11−i−iii
χ111-1-11-1-11111-1-11111-1-1-1-1-111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-11-1-111-11−i−iii
χ121-1-11-1-11111-1-11111-1-1-1-1-111-111-11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii1-1-1-1111-1ii−i−i
χ131-1-11-1-11111-1-11111-1-1-1-1-111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-11-1-111-11ii−i−i
χ141-1-11-1-11111-1-11111-1-1-1-1-111-111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i1-1-1-1111-1−i−iii
χ151-1-11-1-11111-1-11111-1-1-1-1-111-111-11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-111-1-11-1−i−iii
χ161-1-11-1-11111-1-11111-1-1-1-1-111-111-11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1111-1-1-11ii−i−i
χ172222222222222222222-2-2-2-22-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ182222222222222222222-2-2-2-22-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-22222-2-2-2-222-200000000000000000000000000000000002-22-2000000
χ20222222222222-2-2-2-2-2-2-22222-2-2-2-222-20000000000000000000000000000000000-22-22000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-220000000022-2-222-2-20000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2200000000-2-222-2-2220000000000000000000000000000
χ2322222222-2-2-2-222-2-222-22222-22-2-2-2-22000000000000000022-2-222-2-200000000000000000000
χ2422222222-2-2-2-222-2-222-22222-22-2-2-2-220000000000000000-2-222-2-22200000000000000000000
χ2522222222-2-2-2-222-2-222-2-2-2-2-2-2-22222-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-2-2-2-22222-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-222-2-2222222-222-2-2-200000000000000000000000000000000220000-2-20000
χ2822222222-2-2-2-2-2-222-2-2222222-222-2-2-200000000000000000000000000000000-2-20000220000
χ2922222222-2-2-2-2-2-222-2-22-2-2-2-222-2-222200000000000000000000000000000000000000002-22-2
χ3022222222-2-2-2-2-2-222-2-22-2-2-2-222-2-22220000000000000000000000000000000000000000-22-22
χ3122-222-2-2-22-22-22-22-22-220000-2000000002-2002-2000000002−22−22−22−22−22−22−22−2000000000000
χ3222-222-2-2-22-22-22-22-22-220000-2000000002-2002-200000000−22−22−22−22−22−22−22−22000000000000
χ3322-222-2-2-22-22-22-22-22-220000-200000000-2200-22000000002−22−22−22−2−22−22−22−22000000000000
χ3422-222-2-2-22-22-22-22-22-220000-200000000-2200-2200000000−22−22−22−222−22−22−22−2000000000000
χ3522-222-2-2-2-22-222-2-222-2-2000020000002i−2i002i−2i00000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ3622-222-2-2-2-22-222-2-222-2-2000020000002i−2i002i−2i0000000000−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ3722-222-2-2-2-22-222-2-222-2-200002000000−2i2i00−2i2i00000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ3822-222-2-2-2-22-222-2-222-2-200002000000−2i2i00−2i2i0000000000−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ392-222-22-2-22-2-222-22-2-22-200002000000002i−2i00−2i2i000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ402-222-22-2-22-2-222-22-2-22-200002000000002i−2i00−2i2i00000000−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ412-222-22-2-22-2-222-22-2-22-20000200000000−2i2i002i−2i000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ422-222-22-2-22-2-222-22-2-22-20000200000000−2i2i002i−2i00000000−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ432-222-22-2-2-222-22-2-22-2220000-20000002-200-2200000000002−2−22−222−22−2−22−222−2000000000000
χ442-222-22-2-2-222-22-2-22-2220000-20000002-200-220000000000−222−22−2−22−222−22−2−22000000000000
χ452-222-22-2-2-222-22-2-22-2220000-2000000-22002-200000000002−2−22−222−2−222−22−2−22000000000000
χ462-222-22-2-2-222-22-2-22-2220000-2000000-22002-20000000000−222−22−2−222−2−22−222−2000000000000
χ472-2-22-2-22222-2-22222-2-2-222-2-2-2-2-22-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ482-2-22-2-22222-2-22222-2-2-222-2-2-2-2-22-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ492-2-22-2-22222-2-2-2-2-2-222222-2-2222-2-22-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ502-2-22-2-22222-2-2-2-2-2-222222-2-2222-2-22-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ512-2-22-2-22222-2-2-2-2-2-2222-2-2222-2-222-2200000000000000000000000000000000002-2-22000000
χ522-2-22-2-22222-2-2-2-2-2-2222-2-2222-2-222-220000000000000000000000000000000000-222-2000000
χ532-2-22-2-222-2-22222-2-2-2-2222-2-22-22-22-2200000000000000000000000022-2-2-2-222000000000000
χ542-2-22-2-222-2-22222-2-2-2-2222-2-22-22-22-22000000000000000000000000-2-22222-2-2000000000000
χ552-2-22-2-222-2-22222-2-2-2-22-2-22222-22-22-2000000000000000022-2-2-2-22200000000000000000000
χ562-2-22-2-222-2-22222-2-2-2-22-2-22222-22-22-20000000000000000-2-22222-2-200000000000000000000
χ572-2-22-2-222-2-222-2-22222-222-2-2-22-222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ582-2-22-2-222-2-222-2-22222-222-2-2-22-222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ592-2-22-2-222-2-222-2-22222-2-2-222-2-22-2-222000000000000000000000000000000002-20000-220000
χ602-2-22-2-222-2-222-2-22222-2-2-222-2-22-2-22200000000000000000000000000000000-2200002-20000
χ61444-4-4-4-44000000000004-44-40000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ62444-4-4-4-44000000000004-44-4000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ63444-4-4-4-4400000000000-44-440000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ64444-4-4-4-4400000000000-44-44000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ6544-444-4-4-44-44-4-44-44-44-40000400000000000000000000000000000000000000000000000000
χ6644-444-4-4-4-44-44-444-4-4440000-400000000000000000000000000000000000000000000000000
χ674-444-44-4-44-4-44-44-444-440000-400000000000000000000000000000000000000000000000000
χ684-444-44-4-4-444-4-444-44-4-40000400000000000000000000000000000000000000000000000000
χ694-4-4-444-44000000000004-4-440000000000000002-2-22-222-20000000000000000000000000000
χ704-4-4-444-44000000000004-4-44000000000000000-222-22-2-220000000000000000000000000000
χ714-4-4-444-4400000000000-444-40000000000000002-22-2-22-220000000000000000000000000000
χ724-4-4-444-4400000000000-444-4000000000000000-22-222-22-20000000000000000000000000000
χ7388-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000
χ748-88-88-88-8000000000000000000000000000000000000000000000000000000000000000000

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