Finite Group Databasebeta

← Group #72269833

Character table — Group #72269833

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size111122222233333333333366666666666666666666666666666666663232323232323232323232323232323248484848484848484848484848484848
order1244248888222222444444222222244444448888888888888888888836661212121224242424242424242244444444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1111111-1-1-1-1-1-1
χ4111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1111111
χ511-1-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1-1-111-1-1111-1-1-1111-1-1-1
χ611-1-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-1-111-1-1-1111-1-1-1111
χ711-1-1-11-1-111111111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-111111-1-11111-1-1-1-1-1-1111
χ811-1-1-11-1-111111111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-11111-111-1-1-1-1111111-1-1-1
χ922222222222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ10222222-2-2-2-222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ112222-2-2000022222222222222-2-2-2-2-2-2-2-2-2-222000000000000000000002-2-2222-2-2000000000000000000000000
χ122222-2-2000022222222222222-2-2-2-2-2-2-2-2-2-22200000000000000000000-111-1-1-11133−3−333−3−30000000000000000
χ132222-2-2000022222222222222-2-2-2-2-2-2-2-2-2-22200000000000000000000-111-1-1-111−3−333−3−3330000000000000000
χ1422-2-22-20000222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2000000000000000000002222-2-2-2-2000000000000000000000000
χ1522-2-22-20000222222-2-2-2-2-2-22222222-2-2-2-2-2-2-200000000000000000000-1-1-1-1111133−3−3−3−3330000000000000000
χ1622-2-22-20000222222-2-2-2-2-2-22222222-2-2-2-2-2-2-200000000000000000000-1-1-1-11111−3−33333−3−30000000000000000
χ1722-2-2-2222-2-2222222-2-2-2-2-2-222-2-2-2-2-222222-2-22222222222-2-2-2-2-2-2-2-2-2-2-111-111-1-1-1-1-1-111110000000000000000
χ1822-2-2-22-2-222222222-2-2-2-2-2-222-2-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-111-111-1-11111-1-1-1-10000000000000000
χ192-22i−2i002−2−i2i2222-2-2-22i2i2i−2i−2i−2i2-200000000002i−2i22222−2−2−2−2−2−i2−i2−i2−i2−i2i2i2i2i2i2200-22i−2i002−22−2−i2i2−i2i20000000000000000
χ202-22i−2i002−2−i2i2222-2-2-22i2i2i−2i−2i−2i2-200000000002i−2i22222−2−2−2−2−2−i2−i2−i2−i2−i2i2i2i2i2i2-1−i3i31−ii3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ212-22i−2i002−2−i2i2222-2-2-22i2i2i−2i−2i−2i2-200000000002i−2i22222−2−2−2−2−2−i2−i2−i2−i2−i2i2i2i2i2i2-1i3−i31−ii−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ222-22i−2i00−22i2−i2222-2-2-22i2i2i−2i−2i−2i2-200000000002i−2i−2−2−2−2−222222i2i2i2i2i2−i2−i2−i2−i2−i2200-22i−2i00−22−22i2−i2i2−i20000000000000000
χ232-22i−2i00−22i2−i2222-2-2-22i2i2i−2i−2i−2i2-200000000002i−2i−2−2−2−2−222222i2i2i2i2i2−i2−i2−i2−i2−i2-1−i3i31−ii3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ242-22i−2i00−22i2−i2222-2-2-22i2i2i−2i−2i−2i2-200000000002i−2i−2−2−2−2−222222i2i2i2i2i2−i2−i2−i2−i2−i2-1i3−i31−ii−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ252-2−2i2i002−2i2−i2222-2-2-2−2i−2i−2i2i2i2i2-20000000000−2i2i22222−2−2−2−2−2i2i2i2i2i2−i2−i2−i2−i2−i2200-2−2i2i002−22−2i2−i2i2−i20000000000000000
χ262-2−2i2i002−2i2−i2222-2-2-2−2i−2i−2i2i2i2i2-20000000000−2i2i22222−2−2−2−2−2i2i2i2i2i2−i2−i2−i2−i2−i2-1−i3i31i−i−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ272-2−2i2i002−2i2−i2222-2-2-2−2i−2i−2i2i2i2i2-20000000000−2i2i22222−2−2−2−2−2i2i2i2i2i2−i2−i2−i2−i2−i2-1i3−i31i−i3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ282-2−2i2i00−22−i2i2222-2-2-2−2i−2i−2i2i2i2i2-20000000000−2i2i−2−2−2−2−222222−i2−i2−i2−i2−i2i2i2i2i2i2200-2−2i2i00−22−22−i2i2−i2i20000000000000000
χ292-2−2i2i00−22−i2i2222-2-2-2−2i−2i−2i2i2i2i2-20000000000−2i2i−2−2−2−2−222222−i2−i2−i2−i2−i2i2i2i2i2i2-1−i3i31i−i−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ302-2−2i2i00−22−i2i2222-2-2-2−2i−2i−2i2i2i2i2-20000000000−2i2i−2−2−2−2−222222−i2−i2−i2−i2−i2i2i2i2i2i2-1i3−i31i−i3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ3133333333333-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-1000000000000000011111-1-11-1-11-1-11-1-1
χ3233333333333-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-10000000000000000-1-1-1-1-111-111-111-111
χ333333333333-13-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-100000000000000001111-11-1-11-1-11-1-11-1
χ343333333333-13-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-10000000000000000-1-1-1-11-111-111-111-11
χ353333333333-1-13-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-100000000000000001111-1-11-1-11-1-11-1-11
χ363333333333-1-13-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-10000000000000000-1-1-1-111-111-111-111-1
χ37333333-3-3-3-33-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-1-1-31111-31111-31111-3111100000000000000001-11-11-1-11-1-1-111-111
χ38333333-3-3-3-33-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-1-1-31111-31111-31111-311110000000000000000-11-11-111-1111-1-11-1-1
χ39333333-3-3-3-3-13-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-11-31111-31111-31111-311100000000000000001-11-1-11-1-11-11-111-11
χ40333333-3-3-3-3-13-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-1-11-31111-31111-31111-31110000000000000000-11-111-111-11-11-1-11-1
χ41333333-3-3-3-3-1-13-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-111-31111-31111-31111-31100000000000000001-11-1-1-11-1-1111-111-1
χ42333333-3-3-3-3-1-13-1-13-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-111-31111-31111-31111-3110000000000000000-11-1111-111-1-1-11-1-11
χ4333-3-3-3333-3-33-1-13-1-1-311-311-1-1-311113-1-1-1-1113-1-1-1-13-1-1-1-1-31111-31111000000000000000011-1-11-1-1-1111-1-1-111
χ4433-3-3-3333-3-33-1-13-1-1-311-311-1-1-311113-1-1-1-1113-1-1-1-13-1-1-1-1-31111-311110000000000000000-1-111-1111-1-1-1111-1-1
χ4533-3-3-3333-3-3-13-1-13-11-311-31-1-11-3111-13-1-1-111-13-1-1-1-13-1-1-11-31111-3111000000000000000011-1-1-11-11-11-11-11-11
χ4633-3-3-3333-3-3-13-1-13-11-311-31-1-11-3111-13-1-1-111-13-1-1-1-13-1-1-11-31111-31110000000000000000-1-1111-11-11-11-11-11-1
χ4733-3-3-3333-3-3-1-13-1-1311-311-3-1-111-311-1-13-1-111-1-13-1-1-1-13-1-111-31111-311000000000000000011-1-1-1-1111-1-1-1111-1
χ4833-3-3-3333-3-3-1-13-1-1311-311-3-1-111-311-1-13-1-111-1-13-1-1-1-13-1-111-31111-3110000000000000000-1-11111-1-1-1111-1-1-11
χ4933-3-3-33-3-3333-1-13-1-1-311-311-1-1-311113-1-1-1-111-31111-311113-1-1-1-13-1-1-1-100000000000000001-1-111-1-1-111-1111-1-1
χ5033-3-3-33-3-3333-1-13-1-1-311-311-1-1-311113-1-1-1-111-31111-311113-1-1-1-13-1-1-1-10000000000000000-111-1-1111-1-11-1-1-111
χ5133-3-3-33-3-333-13-1-13-11-311-31-1-11-3111-13-1-1-1111-31111-3111-13-1-1-1-13-1-1-100000000000000001-1-11-11-11-111-11-11-1
χ5233-3-3-33-3-333-13-1-13-11-311-31-1-11-3111-13-1-1-1111-31111-3111-13-1-1-1-13-1-1-10000000000000000-111-11-11-11-1-11-11-11
χ5333-3-3-33-3-333-1-13-1-1311-311-3-1-111-311-1-13-1-11111-31111-311-1-13-1-1-1-13-1-100000000000000001-1-11-1-1111-111-1-1-11
χ5433-3-3-33-3-333-1-13-1-1311-311-3-1-111-311-1-13-1-11111-31111-311-1-13-1-1-1-13-1-10000000000000000-111-111-1-1-11-1-1111-1
χ556666666666-2-2-2-2-2-2-2-2-2-2-2-222-2-2-222-2-2-22222-2-2-222-2-2-222-2-2-222-2-2-22200000000000000000000000000000000
χ56666666-6-6-6-6-2-2-2-2-2-2-2-2-2-2-2-222-2-2-222-2-2-22222222-2-2222-2-2222-2-2222-2-200000000000000000000000000000000
χ576666-6-600006-2-26-2-26-2-26-2-2-2-2-62222-62222-2-20000000000000000000000000000000000000000000000000000
χ586666-6-60000-26-2-26-2-26-2-26-2-2-22-62222-6222-2-20000000000000000000000000000000000000000000000000000
χ596666-6-60000-2-26-2-26-2-26-2-26-2-222-62222-622-2-20000000000000000000000000000000000000000000000000000
χ606666-6-60000-2-2-2-2-2-2-2-2-2-2-2-222222-2-2222-2-2220004i−4i0004i−4i0004i−4i0004i−4i00000000000000000000000000000000
χ616666-6-60000-2-2-2-2-2-2-2-2-2-2-2-222222-2-2222-2-222000−4i4i000−4i4i000−4i4i000−4i4i00000000000000000000000000000000
χ6266-6-66-600006-2-26-2-2-622-622-2-26-2-2-2-2-62222220000000000000000000000000000000000000000000000000000
χ6366-6-66-60000-26-2-26-22-622-62-2-2-26-2-2-22-6222220000000000000000000000000000000000000000000000000000
χ6466-6-66-60000-2-26-2-2622-622-6-2-2-2-26-2-222-622220000000000000000000000000000000000000000000000000000
χ6566-6-66-60000-2-2-2-2-2-222222222-2-2-222222-2-2-2-20004i−4i0004i−4i000−4i4i000−4i4i00000000000000000000000000000000
χ6666-6-66-60000-2-2-2-2-2-222222222-2-2-222222-2-2-2-2000−4i4i000−4i4i0004i−4i0004i−4i00000000000000000000000000000000
χ6766-6-6-6666-6-6-2-2-2-2-2-222222222222-2-2-2-2-222-2-2-2-2-222-2-2-222222-2-2222-2-200000000000000000000000000000000
χ6866-6-6-66-6-666-2-2-2-2-2-222222222222-2-2-2-2-222-2-2222-2-2222-2-2-2-2-222-2-2-22200000000000000000000000000000000
χ696-66i−6i0032−32−3i23i26-2-2-6226i−2i−2i−6i2i2i-220000000000−2i2i32−2−2−2−2−322222−3i2i2i2i2i23i2−i2−i2−i2−i200000000000000000000000000000000
χ706-66i−6i0032−32−3i23i2-26-22-62−2i6i−2i2i−6i2i-220000000000−2i2i−232−2−2−22−32222i2−3i2i2i2i2−i23i2−i2−i2−i200000000000000000000000000000000
χ716-66i−6i0032−32−3i23i2-2-2622-6−2i−2i6i2i2i−6i-220000000000−2i2i−2−232−2−222−3222i2i2−3i2i2i2−i2−i23i2−i2−i200000000000000000000000000000000
χ726-66i−6i0032−32−3i23i2-2-2-2222−2i−2i−2i2i2i2i2-20004-40004i−4i2i−2i−2−2−2−3ζ5−ζ7−3ζ13−ζ23ζ5+3ζ7+ζ13+3ζ232223ζ5+ζ7+3ζ13+ζ23−ζ5−3ζ7−ζ13−3ζ23i2i2i2ζ5−3ζ7+ζ13−3ζ23−3ζ5+ζ7−3ζ13+ζ23−i2−i2−i2−ζ5+3ζ7−ζ13+3ζ233ζ5−ζ7+3ζ13−ζ2300000000000000000000000000000000
χ736-66i−6i0032−32−3i23i2-2-2-2222−2i−2i−2i2i2i2i2-2000-44000−4i4i2i−2i−2−2−2ζ5+3ζ7+ζ13+3ζ23−3ζ5−ζ7−3ζ13−ζ23222−ζ5−3ζ7−ζ13−3ζ233ζ5+ζ7+3ζ13+ζ23i2i2i2−3ζ5+ζ7−3ζ13+ζ23ζ5−3ζ7+ζ13−3ζ23−i2−i2−i23ζ5−ζ7+3ζ13−ζ23−ζ5+3ζ7−ζ13+3ζ2300000000000000000000000000000000
χ746-66i−6i00−32323i2−3i26-2-2-6226i−2i−2i−6i2i2i-220000000000−2i2i−32222232−2−2−2−23i2−i2−i2−i2−i2−3i2i2i2i2i200000000000000000000000000000000
χ756-66i−6i00−32323i2−3i2-26-22-62−2i6i−2i2i−6i2i-220000000000−2i2i2−32222−232−2−2−2−i23i2−i2−i2−i2i2−3i2i2i2i200000000000000000000000000000000
χ766-66i−6i00−32323i2−3i2-2-2622-6−2i−2i6i2i2i−6i-220000000000−2i2i22−3222−2−232−2−2−i2−i23i2−i2−i2i2i2−3i2i2i200000000000000000000000000000000
χ776-66i−6i00−32323i2−3i2-2-2-2222−2i−2i−2i2i2i2i2-20004-40004i−4i2i−2i2223ζ5+ζ7+3ζ13+ζ23−ζ5−3ζ7−ζ13−3ζ23−2−2−2−3ζ5−ζ7−3ζ13−ζ23ζ5+3ζ7+ζ13+3ζ23−i2−i2−i2−ζ5+3ζ7−ζ13+3ζ233ζ5−ζ7+3ζ13−ζ23i2i2i2ζ5−3ζ7+ζ13−3ζ23−3ζ5+ζ7−3ζ13+ζ2300000000000000000000000000000000
χ786-66i−6i00−32323i2−3i2-2-2-2222−2i−2i−2i2i2i2i2-2000-44000−4i4i2i−2i222−ζ5−3ζ7−ζ13−3ζ233ζ5+ζ7+3ζ13+ζ23−2−2−2ζ5+3ζ7+ζ13+3ζ23−3ζ5−ζ7−3ζ13−ζ23−i2−i2−i23ζ5−ζ7+3ζ13−ζ23−ζ5+3ζ7−ζ13+3ζ23i2i2i2−3ζ5+ζ7−3ζ13+ζ23ζ5−3ζ7+ζ13−3ζ2300000000000000000000000000000000
χ796-6−6i6i0032−323i2−3i26-2-2-622−6i2i2i6i−2i−2i-2200000000002i−2i32−2−2−2−2−3222223i2−i2−i2−i2−i2−3i2i2i2i2i200000000000000000000000000000000
χ806-6−6i6i0032−323i2−3i2-26-22-622i−6i2i−2i6i−2i-2200000000002i−2i−232−2−2−22−32222−i23i2−i2−i2−i2i2−3i2i2i2i200000000000000000000000000000000
χ816-6−6i6i0032−323i2−3i2-2-2622-62i2i−6i−2i−2i6i-2200000000002i−2i−2−232−2−222−3222−i2−i23i2−i2−i2i2i2−3i2i2i200000000000000000000000000000000
χ826-6−6i6i0032−323i2−3i2-2-2-22222i2i2i−2i−2i−2i2-20004-4000−4i4i−2i2i−2−2−2ζ5+3ζ7+ζ13+3ζ23−3ζ5−ζ7−3ζ13−ζ23222−ζ5−3ζ7−ζ13−3ζ233ζ5+ζ7+3ζ13+ζ23−i2−i2−i23ζ5−ζ7+3ζ13−ζ23−ζ5+3ζ7−ζ13+3ζ23i2i2i2−3ζ5+ζ7−3ζ13+ζ23ζ5−3ζ7+ζ13−3ζ2300000000000000000000000000000000
χ836-6−6i6i0032−323i2−3i2-2-2-22222i2i2i−2i−2i−2i2-2000-440004i−4i−2i2i−2−2−2−3ζ5−ζ7−3ζ13−ζ23ζ5+3ζ7+ζ13+3ζ232223ζ5+ζ7+3ζ13+ζ23−ζ5−3ζ7−ζ13−3ζ23−i2−i2−i2−ζ5+3ζ7−ζ13+3ζ233ζ5−ζ7+3ζ13−ζ23i2i2i2ζ5−3ζ7+ζ13−3ζ23−3ζ5+ζ7−3ζ13+ζ2300000000000000000000000000000000
χ846-6−6i6i00−3232−3i23i26-2-2-622−6i2i2i6i−2i−2i-2200000000002i−2i−32222232−2−2−2−2−3i2i2i2i2i23i2−i2−i2−i2−i200000000000000000000000000000000
χ856-6−6i6i00−3232−3i23i2-26-22-622i−6i2i−2i6i−2i-2200000000002i−2i2−32222−232−2−2−2i2−3i2i2i2i2−i23i2−i2−i2−i200000000000000000000000000000000
χ866-6−6i6i00−3232−3i23i2-2-2622-62i2i−6i−2i−2i6i-2200000000002i−2i22−3222−2−232−2−2i2i2−3i2i2i2−i2−i23i2−i2−i200000000000000000000000000000000
χ876-6−6i6i00−3232−3i23i2-2-2-22222i2i2i−2i−2i−2i2-20004-4000−4i4i−2i2i222−ζ5−3ζ7−ζ13−3ζ233ζ5+ζ7+3ζ13+ζ23−2−2−2ζ5+3ζ7+ζ13+3ζ23−3ζ5−ζ7−3ζ13−ζ23i2i2i2−3ζ5+ζ7−3ζ13+ζ23ζ5−3ζ7+ζ13−3ζ23−i2−i2−i23ζ5−ζ7+3ζ13−ζ23−ζ5+3ζ7−ζ13+3ζ2300000000000000000000000000000000
χ886-6−6i6i00−3232−3i23i2-2-2-22222i2i2i−2i−2i−2i2-2000-440004i−4i−2i2i2223ζ5+ζ7+3ζ13+ζ23−ζ5−3ζ7−ζ13−3ζ23−2−2−2−3ζ5−ζ7−3ζ13−ζ23ζ5+3ζ7+ζ13+3ζ23i2i2i2ζ5−3ζ7+ζ13−3ζ23−3ζ5+ζ7−3ζ13+ζ23−i2−i2−i2−ζ5+3ζ7−ζ13+3ζ233ζ5−ζ7+3ζ13−ζ2300000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.