Finite Group Databasebeta

← Group #10843147

Character table — Group #10843147

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222224444444444444488888888888888888888121212121616161616161616162424242424242424242424242424
order122222344446662244444466121212124444661212121212121212121212121212888848812122424242422222444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1111-1-1-1
χ4111111111111111111111111111111-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1111
χ51111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-11-1-111-1-1-1-1-1-1-111-11-1-1111
χ61111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-111111-1-11-111-1-1-1
χ71111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-111-1-111-1-11111111-1-1-1-1-1
χ81111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-111-1-11111-1-1-1-1-1-1-111111
χ911111111111111-1-11111-1-1111111-1-111-1-11111-1-1-1-1-1-111111111-11-1-1-1-1-111-1-11-1-1-1-111111-1-1
χ1011111111111111-1-11111-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-11111-11111-1-1-1-1-111
χ1111111111111111-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11-111111-1-1-1-1-111-1-1-1111-111
χ1211111111111111-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111111-1-1111-1-1111-1-1-11-1-1
χ1311111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1111111111-1-111-1-1-1-111-111-1-1-11-1-11-1-1
χ1411111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-111-1-1-1-1-1-11-1-1111-111-111
χ1511111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-11111111-1-1-1-111-1-1-111
χ1611111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-11111-1-1-11111-1-1111-1-1
χ17222222-12222-1-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000222-1-1-1-1-1-100000000000000
χ18222222-12222-1-1-122222222-1-1-1-1-1-122-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000-2-2-211111100000000000000
χ19222222-12222-1-1-122-2-2-2-222-1-1-1-1-1-1-2-222-1-111111111-1-1-1-1-1-10000-2-2211-1-11100000000000000
χ20222222-12222-1-1-122-2-2-2-222-1-1-1-1-1-1-2-2-2-2-1-111111111-1-11111000022-2-1-111-1-100000000000000
χ21222222-12222-1-1-1-2-22222-2-2-1-1-1-1-1-1-2-22211-1-1-1-1111111-1-1-1-10000-22-21111-1-100000000000000
χ22222222-12222-1-1-1-2-22222-2-2-1-1-1-1-1-1-2-2-2-211-1-1-1-1111111111100002-22-1-1-1-11100000000000000
χ23222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-12222111111-1-1-1-111-1-1-1-100002-2-2-1-1111100000000000000
χ24222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-122-2-2111111-1-1-1-11111110000-22211-1-1-1-100000000000000
χ252222-2-222-2-222220022-2-200-2-22-22-200000022-2-20000000000002200000000000-200002000-200
χ262222-2-222-2-222220022-2-200-2-22-22-200000022-2-2000000000000-2-20000000000020000-2000200
χ272222-2-222-2-2222200-2-22200-2-22-22-2000000-2-222000000000000220000000000020000-2000-200
χ282222-2-222-2-2222200-2-22200-2-22-22-2000000-2-222000000000000-2-200000000000-200002000200
χ292222-2-22-222-2222220000-2-2-2-2-22-2200002200000000-2-20000220000000000000000-220-200000
χ302222-2-22-222-2222220000-2-2-2-2-22-2200002200000000-2-20000-2-200000000000000002-20200000
χ312222-2-22-222-2222-2-2000022-2-2-22-220000-2-2000000002200002200000000000000002-20-200000
χ322222-2-22-222-2222-2-2000022-2-2-22-220000-2-200000000220000-2-20000000000000000-220200000
χ332-2-222-222-22-2-2-222-22i−2i2i−2i2-22-22-2-222i−2i002-22i−2i2i−2i2i2i−2i−2i2-20000000000000000000000000000000
χ342-2-222-222-22-2-2-222-2−2i2i−2i2i2-22-22-2-22−2i2i002-2−2i2i−2i2i−2i−2i2i2i2-20000000000000000000000000000000
χ352-2-222-222-22-2-2-22-222i−2i2i−2i-222-22-2-22−2i2i00-222i−2i2i−2i−2i−2i2i2i-220000000000000000000000000000000
χ362-2-222-222-22-2-2-22-22−2i2i−2i2i-222-22-2-222i−2i00-22−2i2i−2i2i2i2i−2i−2i-220000000000000000000000000000000
χ372-2-222-2-12-22-211-12-22i−2i2i−2i2-2-11-111-12i−2i00-11−ii−ii−i−iii-1133−3−30000000−i3i33−3−i3i300000000000000
χ382-2-222-2-12-22-211-12-22i−2i2i−2i2-2-11-111-12i−2i00-11−ii−ii−i−iii-11−3−3330000000i3−i3−33i3−i300000000000000
χ392-2-222-2-12-22-211-12-2−2i2i−2i2i2-2-11-111-1−2i2i00-11i−ii−iii−i−i-1133−3−30000000i3−i33−3i3−i300000000000000
χ402-2-222-2-12-22-211-12-2−2i2i−2i2i2-2-11-111-1−2i2i00-11i−ii−iii−i−i-11−3−3330000000−i3i3−33−i3i300000000000000
χ412-2-222-2-12-22-211-1-222i−2i2i−2i-22-11-111-1−2i2i001-1−ii−iiii−i−i1-133−3−30000000i3−i3−33−i3i300000000000000
χ422-2-222-2-12-22-211-1-222i−2i2i−2i-22-11-111-1−2i2i001-1−ii−iiii−i−i1-1−3−3330000000−i3i33−3i3−i300000000000000
χ432-2-222-2-12-22-211-1-22−2i2i−2i2i-22-11-111-12i−2i001-1i−ii−i−i−iii1-133−3−30000000−i3i3−33i3−i300000000000000
χ442-2-222-2-12-22-211-1-22−2i2i−2i2i-22-11-111-12i−2i001-1i−ii−i−i−iii1-1−3−3330000000i3−i33−3−i3i300000000000000
χ452-2-22-22222-2-2-2-22002i−2i−2i2i00-2222-2-20000002i−2i−2i2i000000000000000000000000002-200000002i−2i
χ462-2-22-22222-2-2-2-22002i−2i−2i2i00-2222-2-20000002i−2i−2i2i00000000000000000000000000-220000000−2i2i
χ472-2-22-22222-2-2-2-2200−2i2i2i−2i00-2222-2-2000000−2i2i2i−2i000000000000000000000000002-20000000−2i2i
χ482-2-22-22222-2-2-2-2200−2i2i2i−2i00-2222-2-2000000−2i2i2i−2i00000000000000000000000000-2200000002i−2i
χ492-2-22-222-2-222-2-222-20000-22-22-2-22200002-200000000-22000000000000000002-200000002-2000
χ502-2-22-222-2-222-2-222-20000-22-22-2-22200002-200000000-2200000000000000000-220000000-22000
χ512-2-22-222-2-222-2-22-2200002-2-22-2-2220000-22000000002-2000000000000000002-20000000-22000
χ522-2-22-222-2-222-2-22-2200002-2-22-2-2220000-22000000002-200000000000000000-2200000002-2000
χ534444444-4-4-4-44440000000044-4-4-4-400000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-200000000-2-222220000000000−2i32i3−2i32i3000000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-200000000-2-2222200000000002i3−2i32i3−2i3000000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-20044-4-40022-22-22000000-2-2220000000000000000000000000000000000000
χ574444-4-4-24-4-44-2-2-200-4-4440022-22-2200000022-2-20000000000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-2440000-4-4222-22-20000-2-200000000220000000000000000000000000000000
χ594444-4-4-2-444-4-2-2-2-4-4000044222-22-200002200000000-2-20000000000000000000000000000000
χ6044-4-400400004-4-400000000000000002-20000000000002-22-2−2i22i2−2i22i200000000000000000000000
χ6144-4-400400004-4-400000000000000002-20000000000002-22-22i2−2i22i2−2i200000000000000000000000
χ6244-4-400400004-4-40000000000000000-22000000000000-22-22−2i22i22i2−2i200000000000000000000000
χ6344-4-400400004-4-40000000000000000-22000000000000-22-222i2−2i2−2i22i200000000000000000000000
χ644-4-444-44-44-44-4-44000000004-4-444-400000000000000000000000000000000000000000000000
χ654-4-444-4-2-44-4422-200000000-222-2-22000000000023−23−2323000000000000000000000000000000000
χ664-4-444-4-2-44-4422-200000000-222-2-220000000000−232323−23000000000000000000000000000000000
χ674-4-44-44-244-4-422-2004i−4i−4i4i002-2-2-222000000−2i2i2i−2i0000000000000000000000000000000000000
χ684-4-44-44-244-4-422-200−4i4i4i−4i002-2-2-2220000002i−2i−2i2i0000000000000000000000000000000000000
χ694-4-44-44-2-4-44422-24-40000-442-222-2-20000-22000000002-20000000000000000000000000000000
χ704-4-44-44-2-4-44422-2-4400004-42-222-2-200002-200000000-220000000000000000000000000000000
χ7188-8-800-40000-44400000000000000004-4000000000000-22-22000000000000000000000000000
χ7288-8-800-40000-4440000000000000000-440000000000002-22-2000000000000000000000000000
χ738-88-80080000-88-80000000000000000000000000000000000000000000000000000000000000
χ748-88-800-400004-4400000000000000000000000000000023−23−2323000000000000000000000000000
χ758-88-800-400004-44000000000000000000000000000000−232323−23000000000000000000000000000

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