Finite Group Databasebeta

← Group #10696470

Character table — Group #10696470

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111111112222222244444444448888888888888888161616161616161616161616242424242424242448484848
order12222222366666664444441212121288881212121224242424242424242244666612121212888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1-11
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ922222222222222222-2-22-2-222220000-2-2-2-200000000002-2000022-2-2000000000000
χ1022222222222222222-2-22-2-222220000-2-2-2-20000000000-220000-2-222000000000000
χ112222222222222222-22-2-22-2-2-2-2-2000022-2-2000000000000000000000000000002-20
χ122222222222222222-22-2-22-2-2-2-2-2000022-2-200000000000000000000000000000-220
χ132222222222222222-2-22-2-22-2-2-2-20000-2-2220000000000000000000000000000200-2
χ142222222222222222-2-22-2-22-2-2-2-20000-2-2220000000000000000000000000000-2002
χ1522222222-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1622222222-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1722222222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ1822222222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ1922222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111−i3−i3−i3−i3i3i3i3i3002-2−i3−i3i3i3-1-111000000000000
χ2022222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111−i3−i3−i3−i3i3i3i3i300-22i3i3−i3−i311-1-1000000000000
χ2122222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111i3i3i3i3−i3−i3−i3−i3002-2i3i3−i3−i3-1-111000000000000
χ2222222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111i3i3i3i3−i3−i3−i3−i300-22−i3−i3i3i311-1-1000000000000
χ232-2-222-2-222-2-2-2-2222222-2-2-222-2-200002-22-2000000000000000000002i2i−2i−2i00000000
χ242-2-222-2-222-2-2-2-2222222-2-2-222-2-200002-22-200000000000000000000−2i−2i2i2i00000000
χ252-2-222-2-222-2-2-2-22222-2-2-22222-2-20000-22-2200000000000000000000000022-2-20000
χ262-2-222-2-222-2-2-2-22222-2-2-22222-2-20000-22-22000000000000000000000000-2-2220000
χ272-2-222-2-222-2-2-2-2222-22-22-22-2-22200002-2-22000000002-2002-22-20000000000000000
χ282-2-222-2-222-2-2-2-2222-22-22-22-2-22200002-2-2200000000-2200-22-220000000000000000
χ292-2-222-2-222-2-2-2-2222-2-2222-2-2-22222-2-2-222-222-2-222-2-2000000000000000000000000
χ302-2-222-2-222-2-2-2-2222-2-2222-2-2-222-2-222-222-2-2-222-2-222000000000000000000000000
χ312-2-222-2-22-11111-1-1-1-22-22-2211-1-10000-111-1−i3−i3i3i3i3i3−i3−i32-200-11-11−i3i3−i3i3000000000000
χ322-2-222-2-22-11111-1-1-1-22-22-2211-1-10000-111-1−i3−i3i3i3i3i3−i3−i3-22001-11-1i3−i3i3−i3000000000000
χ332-2-222-2-22-11111-1-1-1-22-22-2211-1-10000-111-1i3i3−i3−i3−i3−i3i3i32-200-11-11i3−i3i3−i3000000000000
χ342-2-222-2-22-11111-1-1-1-22-22-2211-1-10000-111-1i3i3−i3−i3−i3−i3i3i3-22001-11-1−i3i3−i3i3000000000000
χ352-2-222-2-22-11111-1-1-1-2-2222-211-1-122-2-21-1-11-1-111-1-1110000−i3i3i3−i3−i3i3i3−i3000000000000
χ362-2-222-2-22-11111-1-1-1-2-2222-211-1-122-2-21-1-11-1-111-1-1110000i3−i3−i3i3i3−i3−i3i3000000000000
χ372-2-222-2-22-11111-1-1-1-2-2222-211-1-1-2-2221-1-1111-1-111-1-10000−i3i3i3−i3i3−i3−i3i3000000000000
χ382-2-222-2-22-11111-1-1-1-2-2222-211-1-1-2-2221-1-1111-1-111-1-10000i3−i3−i3i3−i3i3i3−i3000000000000
χ3944444444-2-2-2-2-2-2-2-2-44-4-44-422220000-2-22200000000000000000000000000000000
χ4044444444-2-2-2-2-2-2-2-2-4-44-4-442222000022-2-200000000000000000000000000000000
χ41444-44-4-4-4444-4-4-44-4000000000000000000000000000000000000002i−2i2i−2i00000000
χ42444-44-4-4-4444-4-4-44-400000000000000000000000000000000000000−2i2i−2i2i00000000
χ4344-44-44-4-444-44-44-4-400000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ4444-44-44-4-444-44-44-4-40000000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ4544-44-44-4-4-2-22-22-222000000−2i32i3−2i32i32i−2i2i−2i00002ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ11000000000000000000000000
χ4644-44-44-4-4-2-22-22-222000000−2i32i3−2i32i3−2i2i−2i2i0000−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11000000000000000000000000
χ4744-44-44-4-4-2-22-22-2220000002i3−2i32i3−2i32i−2i2i−2i00002ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ7000000000000000000000000
χ4844-44-44-4-4-2-22-22-2220000002i3−2i32i3−2i3−2i2i−2i2i0000−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7000000000000000000000000
χ4944-4-4-4-44444-4-44-4-440000000000000000000000000000000000000000002-22-20000
χ5044-4-4-4-44444-4-44-4-44000000000000000000000000000000000000000000-22-220000
χ514-444-4-44-44-44-444-4-400000000002i−2i−2i2i00002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ524-444-4-44-44-44-444-4-40000000000−2i2i2i−2i0000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ534-444-4-44-4-22-22-2-222000000−2i32i32i3−2i32i−2i−2i2i00002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ7000000000000000000000000
χ544-444-4-44-4-22-22-2-222000000−2i32i32i3−2i3−2i2i2i−2i0000−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ7000000000000000000000000
χ554-444-4-44-4-22-22-2-2220000002i3−2i3−2i32i32i−2i−2i2i00002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ11000000000000000000000000
χ564-444-4-44-4-22-22-2-2220000002i3−2i3−2i32i3−2i2i2i−2i0000−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ11000000000000000000000000
χ574-44-4-44-444-444-4-4-440000000000000000000000000000000000000000002-2-220000
χ584-44-4-44-444-444-4-4-44000000000000000000000000000000000000000000-222-20000
χ594-4-444-4-44-22222-2-2-2444-4-4-4-2-2220000-22-2200000000000000000000000000000000
χ604-4-444-4-44-22222-2-2-24-4-4-444-2-22200002-22-200000000000000000000000000000000
χ614-4-4-4444-44-4-444-44-4000000000000000000000000000000000000002-2-2200000000
χ624-4-4-4444-44-4-444-44-400000000000000000000000000000000000000-222-200000000
χ63888-88-8-8-8-4-4-4444-4400000000000000000000000000000000000000000000000000
χ6488-8-8-8-888-4-444-444-400000000000000000000000000000000000000000000000000
χ658-88-8-88-88-44-4-4444-400000000000000000000000000000000000000000000000000
χ668-8-8-8888-8-444-4-44-4400000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.