Finite Group Databasebeta

← Group #72271500

Character table — Group #72271500

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112222222222244444444444488888888888888888121212121212161616161616161616161616161616161616161616161616162424242424242424243232323232484848484848484896
order12222344446886668881212121224244444441212121216161616242424222244224466812121212121216162424484848484848484848888161616164612121224444416164
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111111-11-1111111111-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1
χ411111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-11-11-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1111
χ511111111111111111111111111111-1-1-1-1-1-1111111111-1-111-11-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-11111-111-1-11111-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-11111111-1-111-1-1-11-11-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-111-1-1-1-1-1-111111
χ711111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-111-1-1-1-1-1-11-1-111-1-111-1-1111
χ811111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-11111111-1-11111-1-111-1-1-1
χ91111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1
χ101111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ111111111111111111111111111-1-1-1-1111111-1-1-1-1111111111-11-11-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-11
χ121111111111111111111111111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-11-11-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111111-1
χ131111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1111-11-111-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-111111-1-111-1-1-1-111-1-11
χ141111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-11-11-111-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-111-1-1-1-11-1-1111111-1-111-1
χ151111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111111-111-1-1-1-111-1-1-1-1-1-11111-111-1-1-1-1-1-1-111-1-111-1-11111-1
χ161111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1111111-111-1-1-1-111-1-1-1-1-1-111111-1-1111111-111-1-1-1-111-1-1-1-11
χ1722222222222-2-2222-2-2-22222-2-200002222220000-2-2-2222222000000-200000000-2-2000000002-2-2-2-2000000000000000000
χ1822222222222-2-2222-2-2-22222-2-200002222220000-2-2-2-2-2-2-2-2-2000000-200000000-2-200000000-22222000000000000000000
χ1922222222222-2-2222-2-2-22222-2-20000-2-2-2-2-2-20000-2-2-222-2-2220000002000000002200000000-2-2-222000000000000000000
χ2022222222222-2-2222-2-2-22222-2-20000-2-2-2-2-2-20000-2-2-2-2-222-2-20000002000000002200000000222-2-2000000000000000000
χ21222222-2-2-2-2200222000-2-2-2-20000002-222-2-222−2−20002-2222-200000000000002−20022−2−222−2−2-2000022−2−2000000000002−20
χ22222222-2-2-2-2200222000-2-2-2-20000002-222-2-222−2−2000-22-2-2-2200000000000002−20022−2−222−2−220000−2−22200000000000−220
χ23222222-2-2-2-2200222000-2-2-2-20000002-222-2-2−2−2220002-2222-20000000000000−2200−2−222−2−222-20000−2−22200000000000−220
χ24222222-2-2-2-2200222000-2-2-2-20000002-222-2-2−2−222000-22-2-2-220000000000000−2200−2−222−2−2222000022−2−2000000000002−20
χ25222222-2-2-2-2200222000-2-2-2-2000000-22-2-22222−2−20002-2-2-22-20000000000000−220022−2−2−2−2222000022−2−200000000000−220
χ26222222-2-2-2-2200222000-2-2-2-2000000-22-2-22222−2−2000-2222-220000000000000−220022−2−2−2−222-20000−2−222000000000002−20
χ27222222-2-2-2-2200222000-2-2-2-2000000-22-2-222−2−2220002-2-2-22-200000000000002−200−2−22222−2−220000−2−222000000000002−20
χ28222222-2-2-2-2200222000-2-2-2-2000000-22-2-222−2−222000-2222-2200000000000002−200−2−22222−2−2-2000022−2−200000000000−220
χ2922222-12222-122-1-1-1222-1-1-1-1-1-1222222-1-1-1-12222-1-1-10000002222-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000000002-1-1-1-1000000000
χ3022222-12222-122-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-10000002-22-2-1-12-1-1-1-1-1-1-2-2-1-111111111000000000-21111000000000
χ3122222-12222-122-1-1-1222-1-1-1-1-1-12222-2-211112222-1-1-1000000-22-2211-211-1-1-1-1-2-211-1-1-1-11111000000000-2-1-111000000000
χ3222222-12222-122-1-1-1222-1-1-1-1-1-12222-2-21111-2-2-2-2-1-1-1000000-2-2-2-211-211-1-1-1-122111111-1-1-1-1000000000211-1-1000000000
χ3322222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-222-1-1-1-12222-1-1-1000000-2-2-2-211211111122-1-1-1-1-1-1-1-1-1-1000000000-21111000000000
χ3422222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1000000-22-22112111111-2-2-1-1111111110000000002-1-1-1-1000000000
χ3522222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-211112222-1-1-10000002-22-2-1-1-2-1-11111-2-211-1-1-1-11111000000000211-1-1000000000
χ3622222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-21111-2-2-2-2-1-1-10000002222-1-1-2-1-1111122111111-1-1-1-1000000000-2-1-111000000000
χ37222-2-222-2-222-2-2-22-22-222-22-2-2-22i2i−2i−2i000000000022-20000000000000002i2i−2i−2i000000000000000002i−2i2i−2i000002-20000000
χ38222-2-222-2-222-2-2-22-22-222-22-2-2-22i2i−2i−2i000000000022-20000000000000002i2i−2i−2i00000000000000000−2i2i−2i2i00000-220000000
χ39222-2-222-2-222-2-2-22-22-222-22-2-2-2−2i−2i2i2i000000000022-2000000000000000−2i−2i2i2i000000000000000002i−2i2i−2i00000-220000000
χ40222-2-222-2-222-2-2-22-22-222-22-2-2-2−2i−2i2i2i000000000022-2000000000000000−2i−2i2i2i00000000000000000−2i2i−2i2i000002-20000000
χ4122-22-22-22-222-2-22-2-222-2-222-2-2-22i−2i2i−2i0000002i−2i2i−2i2-22000000020-2000002i−2i2i−2i00002i−2i2i−2i000000000000002-200000000000
χ4222-22-22-22-222-2-22-2-222-2-222-2-2-22i−2i2i−2i000000−2i2i−2i2i2-220000000-202000002i−2i2i−2i0000−2i2i−2i2i00000000000000-2200000000000
χ4322-22-22-22-222-2-22-2-222-2-222-2-2-2−2i2i−2i2i0000002i−2i2i−2i2-220000000-20200000−2i2i−2i2i00002i−2i2i−2i00000000000000-2200000000000
χ4422-22-22-22-222-2-22-2-222-2-222-2-2-2−2i2i−2i2i000000−2i2i−2i2i2-22000000020-200000−2i2i−2i2i0000−2i2i−2i2i000000000000002-200000000000
χ4522-22-2-1-22-22-1-2-2-11122-21-1-11112i−2i2i−2i003−33−32i−2i2i−2i-11-1000000020-2−i3i30−i3i3−ii−ii003−3−ii−ii−i3i3−i3i30000000000-113−3000000000
χ4622-22-2-1-22-22-1-2-2-11122-21-1-11112i−2i2i−2i003−33−3−2i2i−2i2i-11-10000000-202−i3i30−i3i3−ii−ii003−3i−ii−ii3−i3i3−i300000000001-1−33000000000
χ4722-22-2-1-22-22-1-2-2-11122-21-1-11112i−2i2i−2i00−33−332i−2i2i−2i-11-1000000020-2i3−i30i3−i3−ii−ii00−33−ii−iii3−i3i3−i30000000000-11−33000000000
χ4822-22-2-1-22-22-1-2-2-11122-21-1-11112i−2i2i−2i00−33−33−2i2i−2i2i-11-10000000-202i3−i30i3−i3−ii−ii00−33i−ii−i−i3i3−i3i300000000001-13−3000000000
χ4922-22-2-1-22-22-1-2-2-11122-21-1-1111−2i2i−2i2i003−33−32i−2i2i−2i-11-10000000-202i3−i30i3−i3i−ii−i003−3−ii−ii−i3i3−i3i300000000001-1−33000000000
χ5022-22-2-1-22-22-1-2-2-11122-21-1-1111−2i2i−2i2i003−33−3−2i2i−2i2i-11-1000000020-2i3−i30i3−i3i−ii−i003−3i−ii−ii3−i3i3−i30000000000-113−3000000000
χ5122-22-2-1-22-22-1-2-2-11122-21-1-1111−2i2i−2i2i00−33−332i−2i2i−2i-11-10000000-202−i3i30−i3i3i−ii−i00−33−ii−iii3−i3i3−i300000000001-13−3000000000
χ5222-22-2-1-22-22-1-2-2-11122-21-1-1111−2i2i−2i2i00−33−33−2i2i−2i2i-11-1000000020-2−i3i30−i3i3i−ii−i00−33i−ii−i−i3i3−i3i30000000000-11−33000000000
χ5322-2-222-2-222222-2-222-2-2-2-222222-2-2200000000002-2-22-200-220000000002-2-2200000000000002-200000000000002-200000
χ5422-2-222-2-222222-2-222-2-2-2-222222-2-2200000000002-2-2-22002-20000000002-2-220000000000000-220000000000000-2200000
χ5522-2-222-2-222222-2-222-2-2-2-22222-222-200000000002-2-22-200-22000000000-222-200000000000002-20000000000000-2200000
χ5622-2-222-2-222222-2-222-2-2-2-22222-222-200000000002-2-2-22002-2000000000-222-20000000000000-2200000000000002-200000
χ5722-2-222-2-2222-2-2-2-22-222-2-222-2-200000000000000-2222-200-2220-20220-2-200000000000000000-220000000000000002-2000
χ5822-2-222-2-2222-2-2-2-22-222-2-222-2-200000000000000-2222-200-22-2020-2-202200000000000000000-22000000000000000-22000
χ5922-2-222-2-2222-2-2-2-22-222-2-222-2-200000000000000-222-22002-220-20220-2-2000000000000000002-2000000000000000-22000
χ6022-2-222-2-2222-2-2-2-22-222-2-222-2-200000000000000-222-22002-2-2020-2-2022000000000000000002-20000000000000002-2000
χ6144444-24444-2-4-4-2-2-2-4-4-4-2-2-2-222000044-2-2-2-20000222000000000000-400000000220000000000000000000000000000000
χ6244444-24444-2-4-4-2-2-2-4-4-4-2-2-2-2220000-4-422220000222000000000000400000000-2-20000000000000000000000000000000
χ6344444-2-4-4-4-4-200-2-2-200022220000004-4-2-2222222−22−22000000000000000000000022−2200−2−222−2−22200000000000000000000000
χ6444444-2-4-4-4-4-200-2-2-200022220000004-4-2-222−22−2222220000000000000000000000−22220022−2−222−2−200000000000000000000000
χ6544444-2-4-4-4-4-200-2-2-20002222000000-4422-2-22222−22−220000000000000000000000−222200−2−22222−2−200000000000000000000000
χ6644444-2-4-4-4-4-200-2-2-20002222000000-4422-2-2−22−222222000000000000000000000022−220022−2−2−2−22200000000000000000000000
χ67444-4-444-4-44444-44-4-44-44-44-44400000000000000-4-44000000000000000000000000000000000000000000000000000000
χ68444-4-44-444-4400-44-4000-44-440000000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ69444-4-44-444-4400-44-4000-44-4400000000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ70444-4-4-24-4-44-2442-22-44-4-22-22-2-20000000000000022-20000000000−2i32i302i3−2i3000000000000000000000000000000000000000
χ71444-4-4-24-4-44-2442-22-44-4-22-22-2-20000000000000022-200000000002i3−2i30−2i32i3000000000000000000000000000000000000000
χ72444-4-4-24-4-44-2-4-42-224-44-22-22224i4i−4i−4i0000000000-2-22000000000000000−2i−2i2i2i00000000000000000000000000000000000
χ73444-4-4-24-4-44-2-4-42-224-44-22-2222−4i−4i4i4i0000000000-2-220000000000000002i2i−2i−2i00000000000000000000000000000000000
χ7444-44-444-44-44004-4-40004-4-44000000000000−2i22i22i2−2i200000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ7544-44-444-44-44004-4-40004-4-440000000000002i2−2i2−2i22i2000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ7644-44-44-44-444444-4-4-4-44-444-44400000000000000-44-4000000000000000000000000000000000000000000000000000000
χ7744-44-4-24-44-4-200-222000-222-20000000023−23−2323−2i22i22i2−2i200000000000000000000000000i2−i2−i2i2i6−i6−i6i600000000000000000000000
χ7844-44-4-24-44-4-200-222000-222-20000000023−23−23232i2−2i2−2i22i200000000000000000000000000−i2i2i2−i2−i6i6i6−i600000000000000000000000
χ7944-44-4-24-44-4-200-222000-222-200000000−232323−23−2i22i22i2−2i200000000000000000000000000i2−i2−i2i2−i6i6i6−i600000000000000000000000
χ8044-44-4-24-44-4-200-222000-222-200000000−232323−232i2−2i2−2i22i200000000000000000000000000−i2i2i2−i2i6−i6−i6i600000000000000000000000
χ8144-44-4-2-44-44-244-222-4-442-2-22-2-200000023−2323−2300002-22000000000000000000000−23230000000000000000000000000000000
χ8244-44-4-2-44-44-244-222-4-442-2-22-2-2000000−2323−232300002-2200000000000000000000023−230000000000000000000000000000000
χ8344-4-44444-4-4400-4-4400044-4-400000000000000000004400-4-4000000000000000000000000000000000000000000000000
χ8444-4-44444-4-4400-4-4400044-4-40000000000000000000-4-40044000000000000000000000000000000000000000000000000
χ8544-4-44-2-4-444-24422-24-4-422-2-2-2-24-4-440000000000-222000000000000000-222-200000000000000000000000000000000000
χ8644-4-44-2-4-444-24422-24-4-422-2-2-2-2-444-40000000000-2220000000000000002-2-2200000000000000000000000000000000000
χ8744-4-44-2-4-444-2-4-422-2-44422-2-222000000000000002-2-200000040-40-2-2022000000000000000000000000000000000000000
χ8844-4-44-2-4-444-2-4-422-2-44422-2-222000000000000002-2-2000000-4040220-2-2000000000000000000000000000000000000000
χ89888-8-8-4-888-8-4004-440004-44-40000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-88-488-8-8-40044-4000-4-4440000000000000000000000000000000000000000000000000000000000000000000000000
χ918-800080000-8−4i24i20000000000−4i24i200000000000000000004-4000000000000000000000000000000−2i22i2000000000000000000
χ928-800080000-8−4i24i20000000000−4i24i20000000000000000000-440000000000000000000000000000002i2−2i2000000000000000000
χ938-800080000-84i2−4i200000000004i2−4i200000000000000000004-40000000000000000000000000000002i2−2i2000000000000000000
χ948-800080000-84i2−4i200000000004i2−4i20000000000000000000-44000000000000000000000000000000−2i22i2000000000000000000
χ9516-16000-800008−8i28i200000000004i2−4i200000000000000000000000000000000000000000000000000000000000000000000000
χ9616-16000-8000088i2−8i20000000000−4i24i200000000000000000000000000000000000000000000000000000000000000000000000

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