Finite Group Databasebeta

← Group #10858715

Character table — Group #10858715

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222244444444444444448888888888888888812121212121216161616161616161616242424242424242424242448
order12222234444666444466881212121224242424448888812121212242424242424224488481212121224242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1
χ4111111111111111111111111111111-1-1111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111
χ511111111111111111111-1-11111-1-1-1-111-1-1-1111111-1-1-1-1-1-1111111-1-111-1-111-1-1-11-1-111-11-1-11-1
χ611111111111111111111-1-11111-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-111-1-11-111-11
χ711111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-111-11
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-111-1-11-1
χ911111111111111-1-1-1-111111111111111-1-11-1-1-1-1-1-111-1-1-1-11111-1-11-11111-1-1-1-111-1-1-1-111-1-1-11
χ1011111111111111-1-1-1-111111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-11111-1-1-1-1-1-11111-1-1111-1
χ1111111111111111-1-1-1-1111111111111-1-1-1-1111-1-1-1-111-1-1-1-1111111-11-1-1-1-111111-1-1-1-1-11-1111-1
χ1211111111111111-1-1-1-1111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-111111-11-1-1-11
χ1311111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111111111-1-1-1111-1-1-1-111-1111-1-1-1111-1-1
χ1411111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1111-1-1-1-1111-1-1-1111-1-1-111
χ1511111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-111-1-1-1-1-1-111111111111-1-1-11111-1-1-1-111-1-1-1-1-1-111
χ1611111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-11111-1-111-1-1111111-1-1
χ17222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-1000000000000
χ18222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2222-2-2-1-1-1-1-1-1-1-1-1-1000000-2-211111111000000000000
χ19222222-12222-1-1-12222-1-1-2-2-1-1-1-1111122-2-2-222-1-1-1-1111111000000-2-2-1-111-1-111000000000000
χ20222222-12222-1-1-12222-1-1-2-2-1-1-1-11111-2-2-2-2-2-2-2-1-1-1-11111110000002211-1-111-1-1000000000000
χ21222222-12222-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-1-122-2-22-2-21111-1-111110000002-2-1-1-1-11111000000000000
χ22222222-12222-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-1-1-2-2-2-22221111-1-11111000000-221111-1-1-1-1000000000000
χ23222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-111112222-2-2-2111111-1-1-1-1000000-22-1-11111-1-1000000000000
χ24222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-11111-2-222-222111111-1-1-1-10000002-211-1-1-1-111000000000000
χ252222-2-222-2-2222222-2-2-2-2002-2-220000000000022-2-200000000002200000000000200000-200-20
χ262222-2-222-2-2222222-2-2-2-2002-2-220000000000022-2-20000000000-2-200000000000-20000020020
χ272222-2-222-2-22222-2-222-2-2002-2-2200000000000-2-22200000000002200000000000-200000200-20
χ282222-2-222-2-22222-2-222-2-2002-2-2200000000000-2-2220000000000-2-200000000000200000-20020
χ292222-2-22-222-22220000-2-222-222-222220000-2000000-2-2000022-2-2000000000000200000-200000
χ302222-2-22-222-22220000-2-222-222-222220000-2000000-2-20000-2-222000000000000-200000200000
χ312222-2-22-222-22220000-2-2-2-2-222-2-2-2-2-20000200000022000022-2-2000000000000-200000200000
χ322222-2-22-222-22220000-2-2-2-2-222-2-2-2-2-200002000000220000-2-222000000000000200000-200000
χ332-22-22-2222-2-22-2-200002-20022-2-20000002-200000000022-2-22-22-2000000000000002-200000000
χ342-22-22-2222-2-22-2-200002-20022-2-20000002-200000000022-2-2-22-2200000000000000-2200000000
χ352-22-22-2222-2-22-2-200002-20022-2-2000000-22000000000-2-2222-22-200000000000000-2200000000
χ362-22-22-2222-2-22-2-200002-20022-2-2000000-22000000000-2-222-22-22000000000000002-200000000
χ372-22-22-22-2-2222-2-22i−2i2i−2i2-200-2-22200002i−2i0002-22i−2i2i−2i000000000000002i−2i002-200000000000000
χ382-22-22-22-2-2222-2-22i−2i2i−2i2-200-2-2220000−2i2i000-222i−2i2i−2i00000000000000−2i2i00-2200000000000000
χ392-22-22-22-2-2222-2-2−2i2i−2i2i2-200-2-22200002i−2i000-22−2i2i−2i2i000000000000002i−2i00-2200000000000000
χ402-22-22-22-2-2222-2-2−2i2i−2i2i2-200-2-2220000−2i2i0002-2−2i2i−2i2i00000000000000−2i2i002-200000000000000
χ412-22-22-2-1-2-222-1112i−2i2i−2i-110011-1-1−i3−i3i3i32i−2i0002-2−ii−ii−i3i33−33−300000000−ii3−3-11−i3i3000000000000
χ422-22-22-2-1-2-222-1112i−2i2i−2i-110011-1-1−i3−i3i3i3−2i2i000-22−ii−ii−i3i33−33−300000000i−i−331-1i3−i3000000000000
χ432-22-22-2-1-2-222-1112i−2i2i−2i-110011-1-1i3i3−i3−i32i−2i0002-2−ii−iii3−i3−33−3300000000−ii−33-11i3−i3000000000000
χ442-22-22-2-1-2-222-1112i−2i2i−2i-110011-1-1i3i3−i3−i3−2i2i000-22−ii−iii3−i3−33−3300000000i−i3−31-1−i3i3000000000000
χ452-22-22-2-1-2-222-111−2i2i−2i2i-110011-1-1−i3−i3i3i32i−2i000-22i−ii−i−i3i3−33−3300000000−ii3−31-1i3−i3000000000000
χ462-22-22-2-1-2-222-111−2i2i−2i2i-110011-1-1−i3−i3i3i3−2i2i0002-2i−ii−i−i3i3−33−3300000000i−i−33-11−i3i3000000000000
χ472-22-22-2-1-2-222-111−2i2i−2i2i-110011-1-1i3i3−i3−i32i−2i000-22i−ii−ii3−i33−33−300000000−ii−331-1−i3i3000000000000
χ482-22-22-2-1-2-222-111−2i2i−2i2i-110011-1-1i3i3−i3−i3−2i2i0002-2i−ii−ii3−i33−33−300000000i−i3−3-11i3−i3000000000000
χ492-22-2-222-22-222-2-22i−2i−2i2i-2200-22-22000000000002i−2i−2i2i0000002-2-2200000000000000002i−2i000000
χ502-22-2-222-22-222-2-22i−2i−2i2i-2200-22-22000000000002i−2i−2i2i000000-222-20000000000000000−2i2i000000
χ512-22-2-222-22-222-2-2−2i2i2i−2i-2200-22-2200000000000−2i2i2i−2i0000002-2-220000000000000000−2i2i000000
χ522-22-2-222-22-222-2-2−2i2i2i−2i-2200-22-2200000000000−2i2i2i−2i000000-222-200000000000000002i−2i000000
χ534444444-4-4-4-444400004400-4-4-4-40000000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-20000-2-20022220000000000000000023−23−23230000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-20000-2-200222200000000000000000−232323−230000000000000000000000000000
χ564444-4-4-24-4-44-2-2-244-4-42200-222-200000000000-2-2220000000000000000000000000000000000
χ574444-4-4-24-4-44-2-2-2-4-4442200-222-20000000000022-2-20000000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-2000022442-2-22-2-2-2-20000-40000002200000000000000000000000000000000
χ594444-4-4-2-444-4-2-2-2000022-4-42-2-22222200004000000-2-200000000000000000000000000000000
χ6044-4-40040000-44-400000022−22000022−2222−2200000000000000000000022−220000000000000000002-200
χ6144-4-40040000-44-400000022−22000022−2222−22000000000000000000000−2222000000000000000000-2200
χ6244-4-40040000-44-4000000−22220000−2222−222200000000000000000000022−22000000000000000000-2200
χ6344-4-40040000-44-4000000−22220000−2222−2222000000000000000000000−22220000000000000000002-200
χ644-44-44-4-244-4-4-2220000-2200-2-2220000004-4000000000-2-2220000000000000000000000000000
χ654-44-44-4-244-4-4-2220000-2200-2-222000000-4400000000022-2-20000000000000000000000000000
χ664-44-4-4444-44-44-4-40000-44004-44-40000000000000000000000000000000000000000000000000
χ674-44-4-44-24-44-4-22200002-200-22-22−2i3−2i32i32i3000000000002i3−2i300000000000000000000000000000000
χ684-44-4-44-24-44-4-22200002-200-22-222i32i3−2i3−2i300000000000−2i32i300000000000000000000000000000000
χ694-44-4-44-2-44-44-2224i−4i−4i4i2-2002-22-200000000000−2i2i2i−2i0000000000000000000000000000000000
χ704-44-4-44-2-44-44-222−4i4i4i−4i2-2002-22-2000000000002i−2i−2i2i0000000000000000000000000000000000
χ7188-8-800-400004-4400000042−420000−2222−2222000000000000000000000000000000000000000000000
χ7288-8-800-400004-44000000−4242000022−2222−22000000000000000000000000000000000000000000000
χ738-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000
χ748-8-8800-4000044-40000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ758-8-8800-4000044-4000000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000

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