Finite Group Databasebeta

← Group #10846242

Character table — Group #10846242

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444444444466888888888888888881212121212161616161616161616162424242424242424244848
order122222344446666688888812121212242424244424446688812122424242424244448848121212122424242424448888828
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1111-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1
χ3111111111111111111111111111111-1-111111111111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111
χ511111111111111111111-1-11111-1-1-1-111-111-1-1-111-1-1-11111-1-1111-1-1-1-111-1-111-1-1-1-11111-111-1-1
χ611111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-111-1-111-1-111-1-1-1-111-1-1-111
χ711111111111111111111-1-11111-1-1-1-1-1-1-111-1-1-111-1-1-11111-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11-1-111
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1-1111111-1-1111-1-1
χ91111111111111111-1-1-1-1111111111111-111-1-1-1-1-11-1-1-1-1-1-111111111-11111-1-1-1-1-1-111-1-11-1-11-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-1-1-1111-1-1-1-1-1-11111111-11-1-1-1-11111-1-1-1-1-1-1111-11
χ111111111111111111-1-1-1-11111111111-1-1-111-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1-11-11111-1-1-1-111-1-111-111-11
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-11111111111-1-1-11-1
χ131111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-1111-1-1-1111-1-1-1-1111111-1-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-11111-1-1-1-1111-1-111111-111-1-1-1-1-1-1111-1-11-1-1-11111-1-111-1-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-111-1111-1-1-1-111-1-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-111111-111-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-111111-1-1-11
χ172222222-2-2-2-2222222i2i−2i−2i00-2-2-2-2000022000000000002i2i−2i−2i002-2-200000000000000002i−2i00000
χ182222222-2-2-2-2222222i2i−2i−2i00-2-2-2-20000-2-2000000000002i2i−2i−2i00-2220000000000000000−2i2i00000
χ192222222-2-2-2-222222−2i−2i2i2i00-2-2-2-200002200000000000−2i−2i2i2i002-2-20000000000000000−2i2i00000
χ202222222-2-2-2-222222−2i−2i2i2i00-2-2-2-20000-2-200000000000−2i−2i2i2i00-22200000000000000002i−2i00000
χ21222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1002222-1-1222-1-1-1-1-1-1-1-10000022-1-1-1-1-1-1-1-100000000000
χ22222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1002-2-22-1-1-2-22-1-1-1-1-1-1-1-100000-2-21111111100000000000
χ23222222-12222-1-1-1-1-12222-2-2-1-1-1-1111100-222-21122-211-1-1-1-11100000-2-2-1-111-1-11100000000000
χ24222222-12222-1-1-1-1-12222-2-2-1-1-1-1111100-2-2-2-211-2-2-211-1-1-1-111000002211-1-111-1-100000000000
χ25222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-100-222-211-2-22111111-1-1000002-2-1-1-1-1111100000000000
χ26222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-100-2-2-2-211222111111-1-100000-221111-1-1-1-100000000000
χ27222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111002222-1-1-2-2-2-1-111111100000-22-1-11111-1-100000000000
χ28222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111002-2-22-1-122-2-1-1111111000002-211-1-1-1-11100000000000
χ292222-2-222-2-22222-2-2000000-222-2000022200-222000-2-2000000-22-2000000000000-22000000000
χ302222-2-222-2-22222-2-2000000-222-2000022-2002-2-200022000000-22-20000000000002-2000000000
χ312222-2-222-2-22222-2-2000000-222-20000-2-2200-222000-2-20000002-220000000000002-2000000000
χ322222-2-222-2-22222-2-2000000-222-20000-2-2-2002-2-2000220000002-22000000000000-22000000000
χ332222-2-22-222-2222-2-20000222-2-2222222200000000-2000000-2-2-2-22220000000000000000-20000
χ342222-2-22-222-2222-2-20000222-2-222222-2-200000000-2000000-2-222-2-2-2000000000000000020000
χ352222-2-22-222-2222-2-20000-2-22-2-22-2-2-2-22200000000200000022-2-22-2-2000000000000000020000
χ362222-2-22-222-2222-2-20000-2-22-2-22-2-2-2-2-2-20000000020000002222-2220000000000000000-20000
χ372-2-222-2222-2-2-2-222-22i−2i2i−2i0022-2-200000002i−2i0002-20002i−2i2i−2i0000000002i−2i002-20000000000000
χ382-2-222-2222-2-2-2-222-22i−2i2i−2i0022-2-20000000−2i2i000-220002i−2i2i−2i000000000−2i2i00-220000000000000
χ392-2-222-2222-2-2-2-222-2−2i2i−2i2i0022-2-200000002i−2i000-22000−2i2i−2i2i0000000002i−2i00-220000000000000
χ402-2-222-2222-2-2-2-222-2−2i2i−2i2i0022-2-20000000−2i2i0002-2000−2i2i−2i2i000000000−2i2i002-20000000000000
χ412-2-222-22-2-222-2-222-22-2-2200-2-222000000000000000002-2-2200000000000000000002-20002-200
χ422-2-222-22-2-222-2-222-22-2-2200-2-222000000000000000002-2-220000000000000000000-22000-2200
χ432-2-222-22-2-222-2-222-2-222-200-2-22200000000000000000-222-200000000000000000002-2000-2200
χ442-2-222-22-2-222-2-222-2-222-200-2-22200000000000000000-222-20000000000000000000-220002-200
χ452-2-222-2-122-2-211-1-112i−2i2i−2i00-1-11133−3−30002i−2i0−i3i32-20−i3i3−ii−ii3−30000000−ii−i3i3-113−300000000000
χ462-2-222-2-122-2-211-1-112i−2i2i−2i00-1-11133−3−3000−2i2i0−i3i3-220−i3i3−ii−ii3−30000000i−ii3−i31-1−3300000000000
χ472-2-222-2-122-2-211-1-112i−2i2i−2i00-1-111−3−3330002i−2i0i3−i32-20i3−i3−ii−ii−330000000−iii3−i3-11−3300000000000
χ482-2-222-2-122-2-211-1-112i−2i2i−2i00-1-111−3−333000−2i2i0i3−i3-220i3−i3−ii−ii−330000000i−i−i3i31-13−300000000000
χ492-2-222-2-122-2-211-1-11−2i2i−2i2i00-1-11133−3−30002i−2i0i3−i3-220i3−i3i−ii−i3−30000000−ii−i3i31-1−3300000000000
χ502-2-222-2-122-2-211-1-11−2i2i−2i2i00-1-11133−3−3000−2i2i0i3−i32-20i3−i3i−ii−i3−30000000i−ii3−i3-113−300000000000
χ512-2-222-2-122-2-211-1-11−2i2i−2i2i00-1-111−3−3330002i−2i0−i3i3-220−i3i3i−ii−i−330000000−iii3−i31-13−300000000000
χ522-2-222-2-122-2-211-1-11−2i2i−2i2i00-1-111−3−333000−2i2i0−i3i32-20−i3i3i−ii−i−330000000i−i−i3i3-11−3300000000000
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
χ554444-4-4-24-4-44-2-2-2220000002-2-22000000400-4-2-20002200000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-2220000002-2-22000000-400422000-2-200000000000000000000000000000000
χ574444-4-4-2-444-4-2-2-222000044-222-2-2-2-2-20000000000-40000002200000000000000000000000000
χ584444-4-4-2-444-4-2-2-2220000-4-4-222-2222200000000004000000-2-200000000000000000000000000
χ594-44-40040000-44-4000000−2i22i20000−2i22i2−2i22i24i−4i0000000000000000000022−22000000000000000000000
χ604-44-40040000-44-4000000−2i22i20000−2i22i2−2i22i2−4i4i00000000000000000000−2222000000000000000000000
χ614-44-40040000-44-40000002i2−2i200002i2−2i22i2−2i24i−4i00000000000000000000−2222000000000000000000000
χ624-44-40040000-44-40000002i2−2i200002i2−2i22i2−2i2−4i4i0000000000000000000022−22000000000000000000000
χ634-4-444-4-2-4-44422-2-224-4-440022-2-200000000000000000-222-20000000000000000000000000000
χ644-4-444-4-2-4-44422-2-22-444-40022-2-2000000000000000002-2-220000000000000000000000000000
χ654-4-44-4444-44-4-4-44-44000000-44-440000000000000000000000000000000000000000000000000
χ664-4-44-444-44-44-4-44-440000004-44-40000000000000000000000000000000000000000000000000
χ674-4-44-44-24-44-422-22-20000002-22-20000000000−2i32i30002i3−2i300000000000000000000000000000000
χ684-4-44-44-24-44-422-22-20000002-22-200000000002i3−2i3000−2i32i300000000000000000000000000000000
χ694-4-44-44-2-44-4422-22-2000000-22-222323−23−2300000000000000000−232300000000000000000000000000
χ704-4-44-44-2-44-4422-22-2000000-22-22−23−2323230000000000000000023−2300000000000000000000000000
χ7188-8-800800008-8-80000000000000000000000000000000000000000000000000000000000000
χ7288-8-800-40000-4440000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ7388-8-800-40000-444000000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000
χ748-88-800-400004-44000000−4i24i200002i2−2i22i2−2i2000000000000000000000000000000000000000000000
χ758-88-800-400004-440000004i2−4i20000−2i22i2−2i22i2000000000000000000000000000000000000000000000

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