Finite Group Databasebeta

← Group #72247748

Character table — Group #72247748

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size112224466666666666612121212121212121212121212123232323248484848484848484848484848484848646464646464
order122448822222244444422448888888888361212224444448888888861224242424
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ311111-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-1
χ411111-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ5111-1-1i−i1-1-11-1-111-111-111-1-1iiiii−i−i−i−i−i11-1-11-11-1ii−i−ii−i11-1-1i−i1-1ii−i−i
χ6111-1-1i−i1-1-11-1-111-111-111-1-1iiiii−i−i−i−i−i11-1-1-11-11−i−iii−ii-1-111−ii1-1ii−i−i
χ7111-1-1−ii1-1-11-1-111-111-111-1-1−i−i−i−i−iiiiii11-1-11-11-1−i−iii−ii11-1-1−ii1-1−i−iii
χ8111-1-1−ii1-1-11-1-111-111-111-1-1−i−i−i−i−iiiiii11-1-1-11-11ii−i−ii−i-1-111i−i1-1−i−iii
χ9222222222222222222222222222222222-1-1-1-10000000000000000-1-1-1-1-1-1
χ1022222-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-1-1-1-10000000000000000-1-11111
χ11222-2-22i−2i2-2-22-2-222-222-222-2-22i2i2i2i2i−2i−2i−2i−2i−2i-1-1110000000000000000-11−i−iii
χ12222-2-2−2i2i2-2-22-2-222-222-222-2-2−2i−2i−2i−2i−2i2i2i2i2i2i-1-1110000000000000000-11ii−i−i
χ1322-22-200-2-2-2222-2-2-22222-22-2000000000022-2-20000000000000000-220000
χ1422-22-200-2-2-2222-2-2-22222-22-20000000000-1-11100000000000000001-13−33−3
χ1522-22-200-2-2-2222-2-2-22222-22-20000000000-1-11100000000000000001-1−33−33
χ1622-2-2200-2222-2-2-2-2222-22-2-22000000000022220000000000000000-2-20000
χ1722-2-2200-2222-2-2-2-2222-22-2-220000000000-1-1-1-1000000000000000011−i3i3i3−i3
χ1822-2-2200-2222-2-2-2-2222-22-2-220000000000-1-1-1-1000000000000000011i3−i3−i3i3
χ1933333333-1-13-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-100001111-1-1-1-111-1-1-1-111000000
χ2033333333-1-13-1-1-1-13-1-13-1-1-1-13-1-1-1-13-1-1-1-10000-1-1-1-11111-1-11111-1-1000000
χ213333333-13-1-13-13-1-13-1-1-1-1-1-1-13-1-1-1-13-1-1-1000011-1-11-11-1111-11-1-1-1000000
χ223333333-13-1-13-13-1-13-1-1-1-1-1-1-13-1-1-1-13-1-1-10000-1-111-11-11-1-1-11-1111000000
χ233333333-1-13-1-13-13-1-13-1-1-1-1-1-1-13-1-1-1-13-1-1000011-1-1-11-1111-11-11-1-1000000
χ243333333-1-13-1-13-13-1-13-1-1-1-1-1-1-13-1-1-1-13-1-10000-1-1111-11-1-1-11-11-111000000
χ2533333-3-33-1-13-1-1-1-13-1-13-1-1-1-1-31111-31111000011111111-1-1-1-1-1-1-1-1000000
χ2633333-3-33-1-13-1-1-1-13-1-13-1-1-1-1-31111-311110000-1-1-1-1-1-1-1-111111111000000
χ2733333-3-3-13-1-13-13-1-13-1-1-1-1-1-11-31111-3111000011-1-1-11-11-1-11-11-111000000
χ2833333-3-3-13-1-13-13-1-13-1-1-1-1-1-11-31111-31110000-1-1111-11-111-11-11-1-1000000
χ2933333-3-3-1-13-1-13-13-1-13-1-1-1-1-111-31111-311000011-1-11-11-1-1-1-11-1111000000
χ3033333-3-3-1-13-1-13-13-1-13-1-1-1-1-111-31111-3110000-1-111-11-11111-11-1-1-1000000
χ31333-3-33i−3i311311-1-1-3-1-1-3-1-1113i−i−i−i−i−3iiiii00001-11-1−i−iiii−i-1-111i−i000000
χ32333-3-33i−3i311311-1-1-3-1-1-3-1-1113i−i−i−i−i−3iiiii0000-11-11ii−i−i−ii11-1-1−ii000000
χ33333-3-33i−3i-11-3-11-3-131-131-1-111−i−i3i−i−iii−3iii00001-1-11−iii−ii−i-111-1−ii000000
χ34333-3-33i−3i-11-3-11-3-131-131-1-111−i−i3i−i−iii−3iii0000-111-1i−i−ii−ii1-1-11i−i000000
χ35333-3-33i−3i-1-31-1-313-113-11-1-111−i3i−i−i−ii−3iiii00001-1-11i−i−iii−i1-1-11−ii000000
χ36333-3-33i−3i-1-31-1-313-113-11-1-111−i3i−i−i−ii−3iiii0000-111-1−iii−i−ii-111-1i−i000000
χ37333-3-3−3i3i311311-1-1-3-1-1-3-1-111−3iiiii3i−i−i−i−i00001-11-1ii−i−i−ii-1-111−ii000000
χ38333-3-3−3i3i311311-1-1-3-1-1-3-1-111−3iiiii3i−i−i−i−i0000-11-11−i−iiii−i11-1-1i−i000000
χ39333-3-3−3i3i-11-3-11-3-131-131-1-111ii−3iii−i−i3i−i−i00001-1-11i−i−ii−ii-111-1i−i000000
χ40333-3-3−3i3i-11-3-11-3-131-131-1-111ii−3iii−i−i3i−i−i0000-111-1−iii−ii−i1-1-11−ii000000
χ41333-3-3−3i3i-1-31-1-313-113-11-1-111i−3iiii−i3i−i−i−i00001-1-11−iii−i−ii1-1-11i−i000000
χ42333-3-3−3i3i-1-31-1-313-113-11-1-111i−3iiii−i3i−i−i−i0000-111-1i−i−iii−i-111-1−ii000000
χ436666666-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-222-2-2-22200000000000000000000000000
χ4466666-6-6-2-2-2-2-2-2-2-2-2-2-2-22222222-2-2222-2-200000000000000000000000000
χ45666-6-66i−6i-222-222-2-22-2-2222-2-2−2i−2i−2i2i2i2i2i2i−2i−2i00000000000000000000000000
χ46666-6-6−6i6i-222-222-2-22-2-2222-2-22i2i2i−2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ4766-66-600222-2-2-2222-2-2-22-22-20004i−4i0004i−4i00000000000000000000000000
χ4866-66-600222-2-2-2222-2-2-22-22-2000−4i4i000−4i4i00000000000000000000000000
χ4966-66-60022-6-2-262-62-26-2-22-22000000000000000000000000000000000000
χ5066-66-6002-62-26-2-6226-2-2-22-22000000000000000000000000000000000000
χ5166-66-600-6226-2-222-6-2-26-22-22000000000000000000000000000000000000
χ5266-6-660026-2-2-62-62-26-22-222-2000000000000000000000000000000000000
χ5366-6-66002-26-22-62-6-2-262-222-2000000000000000000000000000000000000
χ5466-6-66002-2-2-22222-2-2-222-2-220004-4000-4400000000000000000000000000
χ5566-6-66002-2-2-22222-2-2-222-2-22000-440004-400000000000000000000000000
χ5666-6-6600-6-2-2622226-2-2-6-222-2000000000000000000000000000000000000
χ5716-1600000000000000000000000000000004-4000000000000000000000000
χ5816-160000000000000000000000000000000-2223−230000000000000000000000
χ5916-160000000000000000000000000000000-22−23230000000000000000000000

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