Finite Group Databasebeta

← Group #10844975

Character table — Group #10844975

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444444444466888888888888888881212121212161616161616161616162424242424242424244848
order12222234444666668888881212121224242424444444888121212122424242424244448848121212122424242444448888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1
χ3111111111111111111111111111111-1-111111111111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111
χ511111111111111111111-1-11111-1-1-1-111-111-111-1-1-1-1-11111-1-1111-1-1-1-111-1-111-1-1-1-1111111-1-1-1
χ611111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-111-1-111-1-111-1-1-1-1-1-111-111
χ711111111111111111111-1-11111-1-1-1-1-1-1-111-111-1-1-1-1-11111-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1111
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1-111111111-1-11-1-1
χ91111111111111111-1-1-1-1111111111111-111-1-1-11-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-111-1-1-1-111-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111111-11-1-1-1-11111-1-1-1-111-1-11-11
χ111111111111111111-1-1-1-11111111111-1-1-111-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-11-11111-1-1-1-111-1-11111-1-11
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-111111111-1-111-11-1
χ131111111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1111-1-1-1111-1-1-1-1111111-1-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1111-11111-1-1-1-1-1-1111-1-11-1-1-11111-1-111-1-111-1-1-11-1
χ151111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-111-1111-1-1-1-111-1-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-11111-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-111-1-1111-11
χ172222222-2-2-2-2222222i2i−2i−2i00-2-2-2-2000022000000000002i2i−2i−2i002-2-20000000000000000002i−2i000
χ182222222-2-2-2-2222222i2i−2i−2i00-2-2-2-20000-2-2000000000002i2i−2i−2i00-222000000000000000000−2i2i000
χ192222222-2-2-2-222222−2i−2i2i2i00-2-2-2-200002200000000000−2i−2i2i2i002-2-2000000000000000000−2i2i000
χ202222222-2-2-2-222222−2i−2i2i2i00-2-2-2-20000-2-200000000000−2i−2i2i2i00-2220000000000000000002i−2i000
χ21222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1002222222-1-1-1-1-1-1-1-1-1-10000022-1-1-1-1-1-1-1-100000000000
χ22222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1002-2-22-2-22-1-1-1-1-1-1-1-1-1-100000-2-21111111100000000000
χ23222222-12222-1-1-1-1-12222-2-2-1-1-1-1111100-222-222-21111-1-1-1-11100000-2-2-1-111-1-11100000000000
χ24222222-12222-1-1-1-1-12222-2-2-1-1-1-1111100-2-2-2-2-2-2-21111-1-1-1-111000002211-1-111-1-100000000000
χ25222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-100-222-2-2-2211111111-1-1000002-2-1-1-1-1111100000000000
χ26222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-100-2-2-2-222211111111-1-100000-221111-1-1-1-100000000000
χ27222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111002222-2-2-2-1-1-1-111111100000-22-1-11111-1-100000000000
χ28222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111002-2-2222-2-1-1-1-1111111000002-211-1-1-1-11100000000000
χ292222-2-222-2-22222-2-2000022-222-2222222000000-200000000-2-2-22-222000000000000000000-200
χ302222-2-222-2-22222-2-2000022-222-22222-2-2000000-200000000-2-22-22-2-2000000000000000000200
χ312222-2-222-2-22222-2-20000-2-2-222-2-2-2-2-22200000020000000022-22-2-2-2000000000000000000200
χ322222-2-222-2-22222-2-20000-2-2-222-2-2-2-2-2-2-2000000200000000222-2222000000000000000000-200
χ332222-2-22-222-2222-2-20000002-2-22000022200-200022-2-2000000-2-220000000000002-2000000000
χ342222-2-22-222-2222-2-20000002-2-22000022-2002000-2-222000000-2-22000000000000-22000000000
χ352222-2-22-222-2222-2-20000002-2-220000-2-2200-200022-2-200000022-2000000000000-22000000000
χ362222-2-22-222-2222-2-20000002-2-220000-2-2-2002000-2-22200000022-20000000000002-2000000000
χ372-22-22-222-22-2-2-222-22-22-200-22-22000000000000000002-22-200000000000000000002i−2i2i−2i00000
χ382-22-22-222-22-2-2-222-22-22-200-22-22000000000000000002-22-20000000000000000000−2i2i−2i2i00000
χ392-22-22-222-22-2-2-222-2-22-2200-22-2200000000000000000-22-2200000000000000000002i−2i−2i2i00000
χ402-22-22-222-22-2-2-222-2-22-2200-22-2200000000000000000-22-220000000000000000000−2i2i2i−2i00000
χ412-22-22-22-22-22-2-222-22i−2i−2i2i002-22-200000002-202i−2i000002i−2i−2i2i0000000002-2002i−2i0000000000000
χ422-22-22-22-22-22-2-222-22i−2i−2i2i002-22-20000000-220−2i2i000002i−2i−2i2i000000000-2200−2i2i0000000000000
χ432-22-22-22-22-22-2-222-2−2i2i2i−2i002-22-200000002-20−2i2i00000−2i2i2i−2i0000000002-200−2i2i0000000000000
χ442-22-22-22-22-22-2-222-2−2i2i2i−2i002-22-20000000-2202i−2i00000−2i2i2i−2i000000000-22002i−2i0000000000000
χ452-22-22-2-1-22-2211-1-112i−2i−2i2i00-11-11−i3−i3i3i30002-202i−2i03−33−3−iii−i−i3i30000000-11−i3i3−ii3−300000000000
χ462-22-22-2-1-22-2211-1-112i−2i−2i2i00-11-11−i3−i3i3i3000-220−2i2i03−33−3−iii−i−i3i300000001-1i3−i3i−i−3300000000000
χ472-22-22-2-1-22-2211-1-112i−2i−2i2i00-11-11i3i3−i3−i30002-202i−2i0−33−33−iii−ii3−i30000000-11i3−i3−ii−3300000000000
χ482-22-22-2-1-22-2211-1-112i−2i−2i2i00-11-11i3i3−i3−i3000-220−2i2i0−33−33−iii−ii3−i300000001-1−i3i3i−i3−300000000000
χ492-22-22-2-1-22-2211-1-11−2i2i2i−2i00-11-11−i3−i3i3i30002-20−2i2i0−33−33i−i−ii−i3i30000000-11−i3i3i−i−3300000000000
χ502-22-22-2-1-22-2211-1-11−2i2i2i−2i00-11-11−i3−i3i3i3000-2202i−2i0−33−33i−i−ii−i3i300000001-1i3−i3−ii3−300000000000
χ512-22-22-2-1-22-2211-1-11−2i2i2i−2i00-11-11i3i3−i3−i30002-20−2i2i03−33−3i−i−iii3−i30000000-11i3−i3i−i3−300000000000
χ522-22-22-2-1-22-2211-1-11−2i2i2i−2i00-11-11i3i3−i3−i3000-2202i−2i03−33−3i−i−iii3−i300000001-1−i3i3−ii−3300000000000
χ53444444-2-4-4-4-4-2-2-2-2-24i4i−4i−4i00222200000000000000000−2i−2i2i2i0000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-2−4i−4i4i4i002222000000000000000002i2i−2i−2i0000000000000000000000000000
χ554444-4-4-24-4-44-2-2-2220000442-2-22-2-2-2-200000000-4000000002200000000000000000000000000
χ564444-4-4-24-4-44-2-2-2220000-4-42-2-22222200000000400000000-2-200000000000000000000000000
χ574444-4-4-2-444-4-2-2-222000000-222-2000000400-4000-2-22200000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-222000000-222-2000000-400400022-2-200000000000000000000000000000000
χ5944-4-400400004-4-400000022−22000022−2222−224-40000000000000000000022−22000000000000000000000
χ6044-4-400400004-4-400000022−22000022−2222−22-4400000000000000000000−2222000000000000000000000
χ6144-4-400400004-4-4000000−22220000−2222−22224-400000000000000000000−2222000000000000000000000
χ6244-4-400400004-4-4000000−22220000−2222−2222-440000000000000000000022−22000000000000000000000
χ634-44-44-4-24-44-422-2-224-44-4002-22-200000000000000000-22-220000000000000000000000000000
χ644-44-44-4-24-44-422-2-22-44-44002-22-2000000000000000002-22-20000000000000000000000000000
χ654-44-4-44444-4-4-4-44-4400000044-4-40000000000000000000000000000000000000000000000000
χ664-44-4-444-4-444-4-44-44000000-4-4440000000000000000000000000000000000000000000000000
χ674-44-4-44-244-4-422-22-2000000-2-222000000000000023−23−232300000000000000000000000000000000
χ684-44-4-44-244-4-422-22-2000000-2-2220000000000000−232323−2300000000000000000000000000000000
χ694-44-4-44-2-4-44422-22-200000022-2-2−2i3−2i32i32i3000000000000000002i3−2i300000000000000000000000000
χ704-44-4-44-2-4-44422-22-200000022-2-22i32i3−2i3−2i300000000000000000−2i32i300000000000000000000000000
χ7188-8-800-40000-44400000042−420000−2222−2222000000000000000000000000000000000000000000000
χ7288-8-800-40000-444000000−4242000022−2222−22000000000000000000000000000000000000000000000
χ738-8-880080000-88-80000000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400004-440000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ758-8-8800-400004-44000000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000

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