Finite Group Databasebeta

← Group #10833324

Character table — Group #10833324

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222244444444444444448888888888888888812121212121216161616161616161616242424242424242424242448
order122222344446662244668812121212242424244466888881212242424242424224488481212121224242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1
χ4111111111111111111111111111111-1-111-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111
χ511111111111111111111-1-11111-1-1-1-1111111-1-1-111-1-1-1-1-1-1111111-1-111-1-111-1-1-11111-1-1-1-1-11-1
χ611111111111111111111-1-11111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-1-1-111111-11
χ711111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-111-1-1-111-11
χ811111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111-1-1111-1-11-1
χ911111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-111-1-1-1-11111-1-11-11111-1-1-1-1111-1-11-1-1-1-1-11
χ1011111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1111-11111-1-1-1-1-1-1-111-111111-1
χ1111111111111111-1-1-1-1111111111111-1-1-1-1111-1-1-1-111-1-1-1-1111111-11-1-1-1-111111-1-1-1-11-1-1111-1
χ1211111111111111-1-1-1-1111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-11111-111-1-1-11
χ1311111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1111-1-1-1-111-111-1-1-11111-1-1
χ1411111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-111-1111-1-1-1-1111-1-1111-1-1-1-111
χ1511111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-111111111111-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ1611111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-1-1-11-1-1-11111-1-1111111-1-111-1-1
χ17222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-122222-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-1000000000000
χ18222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-1-1-2-2222-1-1-1-1-1-1-1-1000000-2-211111111000000000000
χ19222222-12222-1-1-12222-1-1-2-2-1-1-1-1111122-1-122-2-2-2-1-1111111000000-2-2-1-111-1-111000000000000
χ20222222-12222-1-1-12222-1-1-2-2-1-1-1-11111-2-2-1-1-2-2-2-2-2-1-11111110000002211-1-111-1-1000000000000
χ21222222-12222-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-1-12211-2-22-2-211-1-111110000002-2-1-1-1-11111000000000000
χ22222222-12222-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-1-1-2-211222-2-211-1-11111000000-221111-1-1-1-1000000000000
χ23222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-111112211-2-2-2221111-1-1-1-1000000-22-1-11111-1-1000000000000
χ24222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-11111-2-21122-2221111-1-1-1-10000002-211-1-1-1-111000000000000
χ252222-2-222-2-222220000-2-2222-2-222222000000-20000-2-2000022-2-200000000000020000-2000000
χ262222-2-222-2-222220000-2-2222-2-222222000000-20000-2-20000-2-222000000000000-200002000000
χ272222-2-222-2-222220000-2-2-2-22-2-22-2-2-2-20000002000022000022-2-2000000000000-200002000000
χ282222-2-222-2-222220000-2-2-2-22-2-22-2-2-2-200000020000220000-2-22200000000000020000-2000000
χ292222-2-22-222-222222-2-2-2-200-222-20000002200000-2-2000000000022000000000002-20000000-20
χ302222-2-22-222-222222-2-2-2-200-222-20000002200000-2-20000000000-2-200000000000-22000000020
χ312222-2-22-222-2222-2-222-2-200-222-2000000-2-2000002200000000002200000000000-220000000-20
χ322222-2-22-222-2222-2-222-2-200-222-2000000-2-200000220000000000-2-2000000000002-2000000020
χ332-2-222-2222-2-2-2-222-22-22-20022-2-200002i−2i2-22i−2i0002-2000000000000002i−2i002i−2i00000000000000
χ342-2-222-2222-2-2-2-222-22-22-20022-2-20000−2i2i2-2−2i2i0002-200000000000000−2i2i00−2i2i00000000000000
χ352-2-222-2222-2-2-2-22-22-222-20022-2-200002i−2i-22−2i2i000-22000000000000002i−2i00−2i2i00000000000000
χ362-2-222-2222-2-2-2-22-22-222-20022-2-20000−2i2i-222i−2i000-2200000000000000−2i2i002i−2i00000000000000
χ372-2-222-22-2-222-2-2200002-200-2-222000000000002-2000022-2-22-22-20000000000000000002-20000
χ382-2-222-22-2-222-2-2200002-200-2-222000000000002-2000022-2-2-22-22000000000000000000-220000
χ392-2-222-22-2-222-2-2200002-200-2-22200000000000-220000-2-2222-22-2000000000000000000-220000
χ402-2-222-22-2-222-2-2200002-200-2-22200000000000-220000-2-222-22-220000000000000000002-20000
χ412-2-222-2-122-2-211-12-22-2-1100-1-11133−3−32i−2i-112i−2i000-113−33−33−300000000−ii−i3i3−ii−i3i3000000000000
χ422-2-222-2-122-2-211-12-22-2-1100-1-11133−3−3−2i2i-11−2i2i000-113−33−33−300000000i−ii3−i3i−ii3−i3000000000000
χ432-2-222-2-122-2-211-12-22-2-1100-1-111−3−3332i−2i-112i−2i000-11−33−33−3300000000−iii3−i3−iii3−i3000000000000
χ442-2-222-2-122-2-211-12-22-2-1100-1-111−3−333−2i2i-11−2i2i000-11−33−33−3300000000i−i−i3i3i−i−i3i3000000000000
χ452-2-222-2-122-2-211-1-22-22-1100-1-11133−3−32i−2i1-1−2i2i0001-13−3−33−3300000000−ii−i3i3i−ii3−i3000000000000
χ462-2-222-2-122-2-211-1-22-22-1100-1-11133−3−3−2i2i1-12i−2i0001-13−3−33−3300000000i−ii3−i3−ii−i3i3000000000000
χ472-2-222-2-122-2-211-1-22-22-1100-1-111−3−3332i−2i1-1−2i2i0001-1−333−33−300000000−iii3−i3i−i−i3i3000000000000
χ482-2-222-2-122-2-211-1-22-22-1100-1-111−3−333−2i2i1-12i−2i0001-1−333−33−300000000i−i−i3i3−iii3−i3000000000000
χ492-2-22-222-22-22-2-222-2-22-2200-22-220000002-200000-220000002-2-220000000000000002-20000000
χ502-2-22-222-22-22-2-222-2-22-2200-22-220000002-200000-22000000-222-2000000000000000-220000000
χ512-2-22-222-22-22-2-22-222-2-2200-22-22000000-22000002-20000002-2-22000000000000000-220000000
χ522-2-22-222-22-22-2-22-222-2-2200-22-22000000-22000002-2000000-222-20000000000000002-20000000
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
χ564444-4-4-24-4-44-2-2-200002244-222-2-2-2-2-2000000-400002200000000000000000000000000000000
χ574444-4-4-24-4-44-2-2-2000022-4-4-222-2222200000040000-2-200000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-244-4-422002-2-22000000-2-200000220000000000000000000000000000000000
χ594444-4-4-2-444-4-2-2-2-4-44422002-2-220000002200000-2-20000000000000000000000000000000000
χ6044-4-400400004-4-400000022−22000022−2222−2200000000000000000000022−220000000000000000002-200
χ6144-4-400400004-4-400000022−22000022−2222−22000000000000000000000−2222000000000000000000-2200
χ6244-4-400400004-4-4000000−22220000−2222−222200000000000000000000022−22000000000000000000-2200
χ6344-4-400400004-4-4000000−22220000−2222−2222000000000000000000000−22220000000000000000002-200
χ644-4-444-4-2-4-44422-20000-220022-2-2000000000004-40000-2-2220000000000000000000000000000
χ654-4-444-4-2-4-44422-20000-220022-2-200000000000-44000022-2-20000000000000000000000000000
χ664-4-44-4444-44-4-4-440000-44004-44-40000000000000000000000000000000000000000000000000
χ674-4-44-44-24-44-422-200002-200-22-222323−23−2300000000000−232300000000000000000000000000000000
χ684-4-44-44-24-44-422-200002-200-22-22−23−2323230000000000023−2300000000000000000000000000000000
χ694-4-44-44-2-44-4422-24-4-442-2002-22-2000000-22000002-20000000000000000000000000000000000
χ704-4-44-44-2-44-4422-2-444-42-2002-22-20000002-200000-220000000000000000000000000000000000
χ7188-8-800-40000-44400000042−420000−2222−2222000000000000000000000000000000000000000000000
χ7288-8-800-40000-444000000−4242000022−2222−22000000000000000000000000000000000000000000000
χ738-88-80080000-88-80000000000000000000000000000000000000000000000000000000000000
χ748-88-800-400004-4400000000000026−26−2626000000000000000000000000000000000000000000000
χ758-88-800-400004-44000000000000−262626−26000000000000000000000000000000000000000000000

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