Finite Group Databasebeta

← Group #72231577

Character table — Group #72231577

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122222224444444444444488888888888888816161616161616161616161616161616161616161616161624242424242424243232323232324848484896969696
order122223666222222446666662222444666666121244444466612121212121212121212121212121222224444441212121244444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-111-1-1111111111-1-111111-1-1-1-1-1-11-1-11111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111-1-111-1-1111111111-1-111111-1-1-1-1-1-11-1-111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111-1-111-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-111
χ811111111111111111111111-1-111-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-1
χ91111111111111-1-11111-1-1-1-111-1-111-11111-1-111-1-1ii−i−i-111-1-1-1-1-111iiii−i−i−i−i11111111i−iii−i−i-1-1-1-1i−ii−i
χ101111111111111-1-11111-1-1-1-111-1-111-11111-1-111-1-1ii−i−i-111-1-1-1-1-111iiii−i−i−i−i-1-1-1-1-1-1-1-1i−iii−i−i1111−ii−ii
χ111111111111111-1-11111-1-1-1-111-1-111-11111-1-111-1-1−i−iii-111-1-1-1-1-111−i−i−i−iiiii11111111−ii−i−iii-1-1-1-1−ii−ii
χ121111111111111-1-11111-1-1-1-111-1-111-11111-1-111-1-1−i−iii-111-1-1-1-1-111−i−i−i−iiiii-1-1-1-1-1-1-1-1−ii−i−iii1111i−ii−i
χ131111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-11111ii−i−i-1-1-11111-1-1-1iiii−i−i−i−i11-1-111-1-1−ii−i−iii-1-111i−i−ii
χ141111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-11111ii−i−i-1-1-11111-1-1-1iiii−i−i−i−i-1-111-1-111−ii−i−iii11-1-1−iii−i
χ151111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-11111−i−iii-1-1-11111-1-1-1−i−i−i−iiiii11-1-111-1-1i−iii−i−i-1-111−iii−i
χ161111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-11111−i−iii-1-1-11111-1-1-1−i−i−i−iiiii-1-111-1-111i−iii−i−i11-1-1i−i−ii
χ1722222222222-2-222-2-222222200-2200-222-2-2-2-2-2-20000002000000-200000000002-2002-2000000002-2000000
χ1822222222222-2-222-2-222222200-2200-222-2-2-2-2-2-20000002000000-20000000000-2200-2200000000-22000000
χ1922222222222-2-2-2-2-2-222-2-2-2-2002-200222-2-222-2-2000000-2000000200000000002-2002-200000000-22000000
χ2022222222222-2-2-2-2-2-222-2-2-2-2002-200222-2-222-2-2000000-200000020000000000-2200-22000000002-2000000
χ21222222222-2-22222-2-22222222-22-22-2-2-2-22222-2-22-20000-22-222-2-2-22-2000000000000000000000000000000
χ22222222222-2-22222-2-2222222-222-2-22-2-2-22222-2-2-220000-2-22-2-222-2-22000000000000000000000000000000
χ23222222222-2-222-2-2-2-222-2-2-2-22-2-222-22-2-222-2-2-2-2-22000022-2-2-22222-2000000000000000000000000000000
χ24222222222-2-222-2-2-2-222-2-2-2-2-22-22-222-2-222-2-2-2-22-200002-2222-2-22-22000000000000000000000000000000
χ25222222222-2-2-2-2222222222200-2-2002-2-2-2-2-2-222000000-200000020000000000002-2002-2000000002-20000
χ26222222222-2-2-2-2222222222200-2-2002-2-2-2-2-2-222000000-20000002000000000000-2200-2200000000-220000
χ27222222222-2-2-2-2-2-22222-2-2-2-2002200-2-2-2-2-222220000002000000-20000000000002-2002-200000000-220000
χ28222222222-2-2-2-2-2-22222-2-2-2-2002200-2-2-2-2-222220000002000000-2000000000000-2200-22000000002-20000
χ2922222-1-1-1-122222222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-100000000
χ3022222-1-1-1-122222222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-2111100000000
χ3122222-1-1-1-122222222-1-1-1-1-1-1-2-222-2-22-1-1-1-1-1-1-1-1-2-22222-1111111-111-1-1-1-1-1-1-1-100000000-2-2111100000000
χ3222222-1-1-1-122222222-1-1-1-1-1-1-2-222-2-22-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1111111-111111111110000000022-1-1-1-100000000
χ3322222-1-1-1-12222-2-222-1-1111122-2-222-2-1-1-1-111-1-1-2-22i2i−2i−2i1-1-111111-1-1−i−i−i−iiiii000000002i−2i−i−iii00000000
χ3422222-1-1-1-12222-2-222-1-1111122-2-222-2-1-1-1-111-1-1-2-2−2i−2i2i2i1-1-111111-1-1iiii−i−i−i−i00000000−2i2iii−i−i00000000
χ3522222-1-1-1-12222-2-222-1-11111-2-2-2-2-2-2-2-1-1-1-111-1-1222i2i−2i−2i111-1-1-1-1111−i−i−i−iiiii00000000−2i2iii−i−i00000000
χ3622222-1-1-1-12222-2-222-1-11111-2-2-2-2-2-2-2-1-1-1-111-1-122−2i−2i2i2i111-1-1-1-1111iiii−i−i−i−i000000002i−2i−i−iii00000000
χ3722222-1-1-1-1-2-22222-2-2-1-1-1-1-1-12-22-22-2-211-1-1-1-1112-200001-11-1-1111-11−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i300000000
χ3822222-1-1-1-1-2-22222-2-2-1-1-1-1-1-12-22-22-2-211-1-1-1-1112-200001-11-1-1111-11i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i300000000
χ3922222-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-222-2-22-211-1-1-1-111-22000011-111-1-111-1−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i300000000
χ4022222-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-222-2-22-211-1-1-1-111-22000011-111-1-111-1i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i300000000
χ4122222-1-1-1-1-2-222-2-2-2-2-1-111112-2-222-2211-1-11111-220000-1-1111-1-1-1-1133−3−3−3−33300000000003−3−3300000000
χ4222222-1-1-1-1-2-222-2-2-2-2-1-111112-2-222-2211-1-11111-220000-1-1111-1-1-1-11−3−33333−3−30000000000−333−300000000
χ4322222-1-1-1-1-2-222-2-2-2-2-1-11111-22-22-22211-1-111112-20000-11-1-1-111-11-133−3−3−3−3330000000000−333−300000000
χ4422222-1-1-1-1-2-222-2-2-2-2-1-11111-22-22-22211-1-111112-20000-11-1-1-111-11-1−3−33333−3−300000000003−3−3300000000
χ4544444-2-2-2-244-4-444-4-4-2-2-2-2-2-200-4400-4-2-2222222000000-2000000200000000000000000000000000000000
χ4644444-2-2-2-244-4-4-4-4-4-4-2-22222004-4004-2-222-2-2220000002000000-200000000000000000000000000000000
χ4744444-2-2-2-2-4-4-4-44444-2-2-2-2-2-200-4-4004222222-2-20000002000000-200000000000000000000000000000000
χ4844444-2-2-2-2-4-4-4-4-4-444-2-22222004400-42222-2-2-2-2000000-2000000200000000000000000000000000000000
χ49444-4-44444004-40000-4-4000004000-40004-40000000000004000000-4000000000000000000000000000000
χ50444-4-44444004-40000-4-400000-400040004-4000000000000-40000004000000000000000000000000000000
χ51444-4-4444400-440000-4-400004000-40000-44000000000004000000-40000000000000000000000000000000
χ52444-4-4444400-440000-4-40000-400040000-4400000000000-400000040000000000000000000000000000000
χ53444-4-4-2-2-2-2004-4000022−2i32i3−2i32i304000-4000-22−2i32i30000000000-200−2i32i3002000000000000000000000000000000
χ54444-4-4-2-2-2-2004-4000022−2i32i3−2i32i30-40004000-22−2i32i300000000002002i3−2i300-2000000000000000000000000000000
χ55444-4-4-2-2-2-2004-40000222i3−2i32i3−2i304000-4000-222i3−2i30000000000-2002i3−2i3002000000000000000000000000000000
χ56444-4-4-2-2-2-2004-40000222i3−2i32i3−2i30-40004000-222i3−2i30000000000200−2i32i300-2000000000000000000000000000000
χ57444-4-4-2-2-2-200-44000022−2i32i3−2i32i34000-400002-22i3−2i3000000000-20−2i32i300020000000000000000000000000000000
χ58444-4-4-2-2-2-200-44000022−2i32i3−2i32i3-4000400002-22i3−2i3000000000202i3−2i3000-20000000000000000000000000000000
χ59444-4-4-2-2-2-200-440000222i3−2i32i3−2i34000-400002-2−2i32i3000000000-202i3−2i300020000000000000000000000000000000
χ60444-4-4-2-2-2-200-440000222i3−2i32i3−2i3-4000400002-2−2i32i300000000020−2i32i3000-20000000000000000000000000000000
χ6144-44-44-4-440000004-44-4000000000000000004-40000000000000000000000000004000-400000000000000
χ6244-44-44-4-440000004-44-4000000000000000004-4000000000000000000000000000-4000400000000000000
χ6344-44-44-4-44000000-444-400000000000000000-44000000000000000000000000004000-4000000000000000
χ6444-44-44-4-44000000-444-400000000000000000-4400000000000000000000000000-40004000000000000000
χ6544-4-444-4-444-4000000-44000000000004-400000000000000000000000000000004000-40000000000000000
χ6644-4-444-4-444-4000000-44000000000004-40000000000000000000000000000000-400040000000000000000
χ6744-4-444-4-44-44000000-4400000000000-440000000000000000000000000000004000-400000000000000000
χ6844-4-444-4-44-44000000-4400000000000-44000000000000000000000000000000-4000400000000000000000
χ6988-88-8-444-40000008-8-4400000000000000000-440000000000000000000000000000000000000000000000
χ7088-88-8-444-4000000-88-44000000000000000004-40000000000000000000000000000000000000000000000
χ7188-8-88-444-48-80000004-400000000000-440000000000000000000000000000000000000000000000000000
χ7288-8-88-444-4-880000004-4000000000004-40000000000000000000000000000000000000000000000000000
χ738-8000800-800004-4000044-4-4000000000000000002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ748-8000800-800004-4000044-4-400000000000000000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ758-8000800-80000-440000-4-444000000000000000002-2-2200000000002-22-2-22-220000000000000000000000
χ768-8000800-80000-440000-4-44400000000000000000-222-20000000000-22-222-22-20000000000000000000000
χ778-8000-4−4i34i3400004-40000−2−2i3−2+2i32+2i32−2i3000000000000000002i−2i2i−2i00000000002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ788-8000-4−4i34i3400004-40000−2−2i3−2+2i32+2i32−2i300000000000000000−2i2i−2i2i0000000000−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ798-8000-4−4i34i340000-4400002+2i32−2i3−2−2i3−2+2i3000000000000000002-2-220000000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000
χ808-8000-4−4i34i340000-4400002+2i32−2i3−2−2i3−2+2i300000000000000000-222-200000000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000
χ818-8000-44i3−4i3400004-40000−2+2i3−2−2i32−2i32+2i3000000000000000002i−2i2i−2i00000000002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ828-8000-44i3−4i3400004-40000−2+2i3−2−2i32−2i32+2i300000000000000000−2i2i−2i2i0000000000−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ838-8000-44i3−4i340000-4400002−2i32+2i3−2+2i3−2−2i3000000000000000002-2-220000000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000
χ848-8000-44i3−4i340000-4400002−2i32+2i3−2+2i3−2−2i300000000000000000-222-200000000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000

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