Finite Group Databasebeta

← Group #10830426

Character table — Group #10830426

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222224444444444888888888888888888888888121212121616161616161616242424242424242424244848
order1222223444466644446612121212224444446666121212121212121212121212444488121224242424222244444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-1
χ911111111111111-1-1-1-11111111-11-111-1-111-1-1-1-1-1-111-1-1-1-1-1-111111-11111-1-11-111-1-11-1-1-11-1
χ1011111111111111-1-1-1-11111111-11-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-1-11-1-111-1111-11
χ1111111111111111-1-1-1-11111111-11-1-1-11111-1-1-1-1-1-111-1-111111111-11-1-1-1-1111-1-1-1-1-11-111-11
χ1211111111111111-1-1-1-11111111-11-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-1-1-111-111111-11-1-11-1
χ1311111111111111-1-1-1-1111111-11-1111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1111-1-111-1111-1-1-11-1-1-11
χ1411111111111111-1-1-1-1111111-11-1111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1111-1111-1
χ1511111111111111-1-1-1-1111111-11-11-1-111-1-111-1-1-1-1-1-111111111111-1-1-111-1-1-11-1-1-1-1-11111-1
χ1611111111111111-1-1-1-1111111-11-11-1-111-1-111-1-1-1-1-1-1111111-1-1-1-11-1-1-111-1-11-111111-1-1-1-11
χ172222222-2-2-2-222222-2-222-2-2-2-200000000000022-2-20000000022-2-20000000000002-2000000
χ182222222-2-2-2-222222-2-222-2-2-2-200000000000022-2-200000000-2-222000000000000-22000000
χ192222222-2-2-2-2222-2-22222-2-2-2-2000000000000-2-2220000000022-2-2000000000000-22000000
χ202222222-2-2-2-2222-2-22222-2-2-2-2000000000000-2-22200000000-2-2220000000000002-2000000
χ21222222-12222-1-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000-2-2111111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-222221111-1-1-1-11111-1-1-1-10000-2-2-1-11111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-11111111100002211-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-12-22-222-2-2-1-1111111-1-111111100002-2-1-1-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-12-22-2-2-222-1-1111111-1-111-1-1-1-10000-221111-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-22-2222-2-211-1-1111111-1-111110000-22-1-111-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-22-22-2-22211-1-1111111-1-1-1-1-1-100002-211-1-111000000000000
χ292222-2-222-22-22220000-2-22-22-2020-200000022000000-2-200002-22-2000000000200000-20000
χ302222-2-222-22-22220000-2-22-22-2020-200000022000000-2-20000-22-22000000000-20000020000
χ312222-2-222-22-22220000-2-22-22-20-202000000-2-20000002200002-22-2000000000-20000020000
χ322222-2-222-22-22220000-2-22-22-20-202000000-2-2000000220000-22-22000000000200000-20000
χ332222-2-22-22-222220000-2-2-22-2220-20000022000000-2-20000002-2-2200000000200000-200000
χ342222-2-22-22-222220000-2-2-22-2220-20000022000000-2-2000000-222-200000000-200000200000
χ352222-2-22-22-222220000-2-2-22-22-20200000-2-2000000220000002-2-2200000000-200000200000
χ362222-2-22-22-222220000-2-2-22-22-20200000-2-200000022000000-222-200000000200000-200000
χ372-22-2-22222-2-2-2-222-22-22-222-2-200002i−2i2i−2i00002-22-200002i2i−2i−2i0000002i−2i0000000000000000
χ382-22-2-22222-2-2-2-222-22-22-222-2-20000−2i2i−2i2i00002-22-20000−2i−2i2i2i000000−2i2i0000000000000000
χ392-22-2-22222-2-2-2-22-22-222-222-2-200002i−2i−2i2i0000-22-220000−2i−2i2i2i0000002i−2i0000000000000000
χ402-22-2-22222-2-2-2-22-22-222-222-2-20000−2i2i2i−2i0000-22-2200002i2i−2i−2i000000−2i2i0000000000000000
χ412-22-2-222-2-222-2-222-2-222-2-2-2220000000000002-2-2200000000000000000000002-200002-200
χ422-22-2-222-2-222-2-222-2-222-2-2-2220000000000002-2-220000000000000000000000-220000-2200
χ432-22-2-222-2-222-2-22-222-22-2-2-222000000000000-222-200000000000000000000002-20000-2200
χ442-22-2-222-2-222-2-22-222-22-2-2-222000000000000-222-20000000000000000000000-2200002-200
χ452-22-2-22-122-2-211-12-22-2-11-1-11100002i−2i2i−2i−i3i3−i3i3-11-11−i3i3−i3i3−i−iii000000−ii3−33−3000000000000
χ462-22-2-22-122-2-211-12-22-2-11-1-11100002i−2i2i−2ii3−i3i3−i3-11-11i3−i3i3−i3−i−iii000000−ii−33−33000000000000
χ472-22-2-22-122-2-211-12-22-2-11-1-1110000−2i2i−2i2i−i3i3−i3i3-11-11−i3i3−i3i3ii−i−i000000i−i−33−33000000000000
χ482-22-2-22-122-2-211-12-22-2-11-1-1110000−2i2i−2i2ii3−i3i3−i3-11-11i3−i3i3−i3ii−i−i000000i−i3−33−3000000000000
χ492-22-2-22-122-2-211-1-22-22-11-1-11100002i−2i−2i2i−i3i3i3−i31-11-1−i3i3i3−i3ii−i−i000000−ii3−3−33000000000000
χ502-22-2-22-122-2-211-1-22-22-11-1-11100002i−2i−2i2ii3−i3−i3i31-11-1i3−i3−i3i3ii−i−i000000−ii−333−3000000000000
χ512-22-2-22-122-2-211-1-22-22-11-1-1110000−2i2i2i−2i−i3i3i3−i31-11-1−i3i3i3−i3−i−iii000000i−i−333−3000000000000
χ522-22-2-22-122-2-211-1-22-22-11-1-1110000−2i2i2i−2ii3−i3−i3i31-11-1i3−i3−i3i3−i−iii000000i−i3−3−33000000000000
χ53444444-2-4-4-4-4-2-2-244-4-4-2-22222000000000000-2-22200000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-444-2-2222200000000000022-2-200000000000000000000000000000000
χ554444-4-4-24-44-4-2-2-2000022-22-22040-4000000-2-2000000220000000000000000000000000000
χ564444-4-4-24-44-4-2-2-2000022-22-220-40400000022000000-2-20000000000000000000000000000
χ574444-4-4-2-44-44-2-2-20000222-22-240-400000-2-200000022000000000000000000000000000000
χ584444-4-4-2-44-44-2-2-20000222-22-2-4040000022000000-2-2000000000000000000000000000000
χ594-44-44-444-4-44-4-440000-444-4-44000000000000000000000000000000000000000000000000
χ604-44-44-44-444-4-4-440000-44-444-4000000000000000000000000000000000000000000000000
χ614-44-44-4-24-4-4422-200002-2-222-20000000000−2i32i30000002i3−2i30000000000000000000000000000
χ624-44-44-4-24-4-4422-200002-2-222-200000000002i3−2i3000000−2i32i30000000000000000000000000000
χ634-44-44-4-2-444-422-200002-22-2-2200000000−2i32i30000002i3−2i3000000000000000000000000000000
χ644-44-44-4-2-444-422-200002-22-2-22000000002i3−2i3000000−2i32i3000000000000000000000000000000
χ654-44-4-44-2-4-44422-24-4-44-2222-2-2000000000000-222-200000000000000000000000000000000
χ664-44-4-44-2-4-44422-2-444-4-2222-2-20000000000002-2-2200000000000000000000000000000000
χ6788-8-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-444000000000000000000000000000000−2i32i3−2i32i3000000000000000000000000
χ6988-8-800-40000-4440000000000000000000000000000002i3−2i32i3−2i3000000000000000000000000
χ708-8-880080000-88-80000000000000000000000000000000000000000000000000000000000
χ718-8-8800-400004-4400000000000000000000000000000023−23−2323000000000000000000000000
χ728-8-8800-400004-44000000000000000000000000000000−232323−23000000000000000000000000

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