Finite Group Databasebeta

← Group #10843144

Character table — Group #10843144

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222244444444448888888888888888888888888812121212121212121616161616161624242424242424244848
order12222234444666444466121212122222444466668812121212121212121212121222448888668242424242444888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-11111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1111-1-1-1
χ411111111111111111111111111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-11-1-1-1111
χ5111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-111-1-11111-1-1-11-1-1
χ6111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111-1-1-1-1-1-1111-111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11-1-111-111-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-1111-1-111111-1-1
χ911111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-11-1-11-111-1-11
χ1011111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-11-1-111-1
χ1111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111-1-1-1-1-11111-1
χ1211111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11
χ1311111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111-1-1111-1-111-1-1-11-1
χ1411111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111-111-1-1111-11
χ1511111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111111111-1-1-111-1-1-1-1-1-11-1-11-11
χ1611111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-11-1
χ17222222-12222-1-1-12222-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000-1-12-1-1-1-10000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-122-2-222-2-2-1-1-1-1-2-2-1-1-1-1-1-1-1-111110000000011-211110000000000
χ19222222-12222-1-1-12222-1-1-1-1-1-1-2-222-2-2-2-2111122-1-1-1-11111111100000000-1-1-2-1-1110000000000
χ20222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2221111-2-2-1-1-1-11111-1-1-1-10000000011211-1-10000000000
χ21222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-12222-2-222-1-1-1-1-2-211111111-1-1-1-100000000-1-1-211110000000000
χ22222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-12211111111111100000000112-1-1-1-10000000000
χ23222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-22222-2-21111-2-21111-1-1-1-1111100000000-1-1211-1-10000000000
χ24222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-222221111221111-1-1-1-1-1-1-1-10000000011-2-1-1110000000000
χ252222-2-222-2-2222222-2-2-2-22-22-20000000000000022-2-200000000000000220000000-2002000-200
χ262222-2-222-2-2222222-2-2-2-22-22-20000000000000022-2-200000000000000-2-20000000200-2000200
χ272222-2-222-2-22222-2-222-2-22-22-200000000000000-2-22200000000000000220000000200-2000-200
χ282222-2-222-2-22222-2-222-2-22-22-200000000000000-2-22200000000000000-2-20000000-2002000200
χ292222-2-22-222-22220000-2-2-22-2200002-200000000000022-2-2000022-2-2-2-20000000000000200000
χ302222-2-22-222-22220000-2-2-22-2200002-200000000000022-2-20000-2-222220000000000000-200000
χ312222-2-22-222-22220000-2-2-22-220000-22000000000000-2-222000022-2-2220000000000000-200000
χ322222-2-22-222-22220000-2-2-22-220000-22000000000000-2-2220000-2-222-2-20000000000000200000
χ332-2-222-222-22-22-2-22i−2i2i−2i2-22-2-22000000000000002i−2i2i−2i000000002-22-20000000000002i−2i0000000
χ342-2-222-222-22-22-2-22i−2i2i−2i2-22-2-22000000000000002i−2i2i−2i00000000-22-22000000000000−2i2i0000000
χ352-2-222-222-22-22-2-2−2i2i−2i2i2-22-2-2200000000000000−2i2i−2i2i000000002-22-2000000000000−2i2i0000000
χ362-2-222-222-22-22-2-2−2i2i−2i2i2-22-2-2200000000000000−2i2i−2i2i00000000-22-220000000000002i−2i0000000
χ372-2-22-22222-2-22-2-22i−2i−2i2i-2222-2-2002-2000000002i−2i2i−2i−2i2i00000000000000002-202i−2i000000000000
χ382-2-22-22222-2-22-2-22i−2i−2i2i-2222-2-200-2200000000−2i2i2i−2i−2i2i0000000000000000-220−2i2i000000000000
χ392-2-22-22222-2-22-2-2−2i2i2i−2i-2222-2-2002-200000000−2i2i−2i2i2i−2i00000000000000002-20−2i2i000000000000
χ402-2-22-22222-2-22-2-2−2i2i2i−2i-2222-2-200-22000000002i−2i−2i2i2i−2i0000000000000000-2202i−2i000000000000
χ412-2-22-222-2-2222-2-20000-22-2-2222-200000022-2-2000000000000002-2-2200000000000000002-2000
χ422-2-22-222-2-2222-2-20000-22-2-2222-200000022-2-200000000000000-222-20000000000000000-22000
χ432-2-22-222-2-2222-2-20000-22-2-222-22000000-2-222000000000000002-2-220000000000000000-22000
χ442-2-22-222-2-2222-2-20000-22-2-222-22000000-2-22200000000000000-222-200000000000000002-2000
χ452-2-22-22-122-2-2-1112i−2i−2i2i1-1-1-111002-20000−i3i3−i3i32i−2i−iii−i3−33−3−i3−i3i3i300000000-110−ii3−30000000000
χ462-2-22-22-122-2-2-1112i−2i−2i2i1-1-1-111002-20000i3−i3i3−i32i−2i−iii−i−33−33i3i3−i3−i300000000-110−ii−330000000000
χ472-2-22-22-122-2-2-1112i−2i−2i2i1-1-1-11100-220000−i3i3−i3i3−2i2i−iii−i3−33−3i3i3−i3−i3000000001-10i−i−330000000000
χ482-2-22-22-122-2-2-1112i−2i−2i2i1-1-1-11100-220000i3−i3i3−i3−2i2i−iii−i−33−33−i3−i3i3i3000000001-10i−i3−30000000000
χ492-2-22-22-122-2-2-111−2i2i2i−2i1-1-1-111002-20000−i3i3−i3i3−2i2ii−i−ii−33−33−i3−i3i3i300000000-110i−i−330000000000
χ502-2-22-22-122-2-2-111−2i2i2i−2i1-1-1-111002-20000i3−i3i3−i3−2i2ii−i−ii3−33−3i3i3−i3−i300000000-110i−i3−30000000000
χ512-2-22-22-122-2-2-111−2i2i2i−2i1-1-1-11100-220000−i3i3−i3i32i−2ii−i−ii−33−33i3i3−i3−i3000000001-10−ii3−30000000000
χ522-2-22-22-122-2-2-111−2i2i2i−2i1-1-1-11100-220000i3−i3i3−i32i−2ii−i−ii3−33−3−i3−i3i3i3000000001-10−ii−330000000000
χ534444444-4-4-4-4444000044-4-4-4-4000000000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-20000-2-2222200000000−2i32i32i3−2i3000000000000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-20000-2-22222000000002i3−2i3−2i32i3000000000000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-244-4-422-22-2200000000000000-2-222000000000000000000000000000000000
χ574444-4-4-24-4-44-2-2-2-4-44422-22-220000000000000022-2-2000000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-20000222-22-200004-4000000000000-2-22200000000000000000000000000000
χ594444-4-4-2-444-4-2-2-20000222-22-20000-4400000000000022-2-200000000000000000000000000000
χ6044-4-40040000-44-400000000000000002-2000000000000002-22-20000−2i22i2−2i22i200000000000000000
χ6144-4-40040000-44-400000000000000002-2000000000000002-22-200002i2−2i22i2−2i200000000000000000
χ6244-4-40040000-44-40000000000000000-2200000000000000-22-220000−2i22i22i2−2i200000000000000000
χ6344-4-40040000-44-40000000000000000-2200000000000000-22-2200002i2−2i2−2i22i200000000000000000
χ644-4-444-44-44-444-4-400004-4-444-4000000000000000000000000000000000000000000000000000
χ654-4-444-4-24-44-4-2224i−4i4i−4i-22-222-200000000000000−2i2i−2i2i000000000000000000000000000000000
χ664-4-444-4-24-44-4-222−4i4i−4i4i-22-222-2000000000000002i−2i2i−2i000000000000000000000000000000000
χ674-4-444-4-2-44-44-2220000-222-2-2200000000000000000023−23−232300000000000000000000000000000
χ684-4-444-4-2-44-44-2220000-222-2-22000000000000000000−232323−2300000000000000000000000000000
χ694-4-44-44-2-4-444-22200002-222-2-24-4000000-2-222000000000000000000000000000000000000000
χ704-4-44-44-2-4-444-22200002-222-2-2-4400000022-2-2000000000000000000000000000000000000000
χ7188-8-800-400004-4400000000000000004-400000000000000-22-220000000000000000000000000
χ7288-8-800-400004-440000000000000000-44000000000000002-22-20000000000000000000000000
χ738-88-80080000-8-880000000000000000000000000000000000000000000000000000000000000
χ748-88-800-4000044-400000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000
χ758-88-800-4000044-4000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000

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