Finite Group Databasebeta

← Group #72239818

Character table — Group #72239818

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11233333366666666666666612121212121212121212121248484848484848484848484848484848128128128128
order1242222222244444444444444444444444442244444488888888361212
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311-111111111-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-111-1-11-11111-1-1-1-111-1-1
χ411-111111111-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-1-111-11-1-1-1-1111111-1-1
χ52222222222222222222222222222222222220000000000000000-1-1-1-1
χ622-222222222-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-20000000000000000-1-111
χ73333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-10000
χ83333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111110000
χ93333-13-1-1-1-1-13-1-1-1-1−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2i1111−1+2i−1−2i111-11-1-1-1ii−i−iii−i−i0000
χ103333-13-1-1-1-1-13-1-1-1-1−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2i1111−1+2i−1−2i-1-1-11-1111−i−iii−i−iii0000
χ113333-13-1-1-1-1-13-1-1-1-1−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2i1111−1−2i−1+2i111-11-1-1-1−i−iii−i−iii0000
χ123333-13-1-1-1-1-13-1-1-1-1−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2i1111−1−2i−1+2i-1-1-11-1111ii−i−iii−i−i0000
χ13333-13-13-1-1-1-1-13-1-1-1−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i1111−1+2i−1−2i1111-11-11-1-1i−ii−ii−ii−i0000
χ14333-13-13-1-1-1-1-13-1-1-1−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i1111−1+2i−1−2i11-1-11-11-111−ii−ii−ii−ii0000
χ15333-13-13-1-1-1-1-13-1-1-1−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i1111−1−2i−1+2i1111-11-11-1-1−ii−ii−ii−ii0000
χ16333-13-13-1-1-1-1-13-1-1-1−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i1111−1−2i−1+2i11-1-11-11-111i−ii−ii−ii−i0000
χ17333-1-1-1-133-1-1-1-13-1-13-1-133-1-133-1-1-1-1-13-1-1-1-1-111-1-1-1-1111-1-111-1-110000
χ18333-1-1-1-133-1-1-1-13-1-13-1-133-1-133-1-1-1-1-13-1-1-1-1-1-1-11111-1-1-111-1-111-10000
χ19333-1-1-1-133-1-1-1-13-1-1-133-1-133-1-13-1-1-1-1-13-1-1-1-111-1-1-1-111-111-1-111-10000
χ20333-1-1-1-133-1-1-1-13-1-1-133-1-133-1-13-1-1-1-1-13-1-1-1-1-1-11111-1-11-1-111-1-110000
χ2133-333333333-3-3-3-3-31111-1-1-1-1-1-1-1-1-1-11111111-111-1-11-1-1-1-1-111110000
χ2233-333333333-3-3-3-3-31111-1-1-1-1-1-1-1-1-1-1111111-11-1-111-111111-1-1-1-10000
χ2333-33-13-1-1-1-1-1-311111+2i1+2i1−2i1−2i−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2i-1-1-1-11+2i1−2i1-11-1-11-11−i−iiiii−i−i0000
χ2433-33-13-1-1-1-1-1-311111+2i1+2i1−2i1−2i−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2i-1-1-1-11+2i1−2i-11-111-11-1ii−i−i−i−iii0000
χ2533-33-13-1-1-1-1-1-311111−2i1−2i1+2i1+2i−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2i-1-1-1-11−2i1+2i1-11-1-11-11ii−i−i−i−iii0000
χ2633-33-13-1-1-1-1-1-311111−2i1−2i1+2i1+2i−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2i-1-1-1-11−2i1+2i-11-111-11-1−i−iiiii−i−i0000
χ2733-3-13-13-1-1-1-11-31111+2i1−2i1+2i1−2i−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i11-1-11+2i1−2i-1-11-1-111-1-11−ii−iii−ii−i0000
χ2833-3-13-13-1-1-1-11-31111+2i1−2i1+2i1−2i−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i11-1-11+2i1−2i-1-1-111-1-111-1i−ii−i−ii−ii0000
χ2933-3-13-13-1-1-1-11-31111−2i1+2i1−2i1+2i−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i11-1-11−2i1+2i-1-11-1-111-1-11i−ii−i−ii−ii0000
χ3033-3-13-13-1-1-1-11-31111−2i1+2i1−2i1+2i−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i11-1-11−2i1+2i-1-1-111-1-111-1−ii−iii−ii−i0000
χ3133-3-1-1-1-133-1-111-3111-3-31-133-1-13-1-1-1-11-311111-1-1-1111-1-111-11-1-110000
χ3233-3-1-1-1-133-1-111-3111-3-31-133-1-13-1-1-1-11-31111-1111-1-1-111-1-11-111-10000
χ3333-3-1-1-1-133-1-111-311-311-33-1-133-1-1-1-1-1-3111111-1-1-1111-11-1-11-111-10000
χ3433-3-1-1-1-133-1-111-311-311-33-1-133-1-1-1-1-1-311111-1111-1-1-11-111-11-1-110000
χ354-40-4-444-444-4000000000000000000000000000000000000000001-13−3
χ364-40-4-444-444-4000000000000000000000000000000000000000001-1−33
χ374-40-4-444-444-400000000000000000000000000000000000000000-2200
χ386666-26-2-2-2-2-26-2-2-2-222222222-2-2-2-222-2-2-2-22200000000000000000000
χ39666-26-26-2-2-2-2-26-2-2-222222222-2-222-2-2-2-222-2-200000000000000000000
χ40666-2-2-2-266-2-2-2-26-2-2-2-2-2-2-2-2-2-2-2-22222-2-2222200000000000000000000
χ41666-2-2-2-2-2-222-2-2-2222−2+4i−2−4i22−2+4i−2−4i2-222i−2i−2i2i-222i−2i−2i2i00000000000000000000
χ42666-2-2-2-2-2-222-2-2-2222−2−4i−2+4i22−2−4i−2+4i2-22−2i2i2i−2i-22−2i2i2i−2i00000000000000000000
χ43666-2-2-2-2-2-222-2-2-222−2+4i22−2−4i−2+4i22−2−4i2-2−2i2i−2i2i2-2−2i2i−2i2i00000000000000000000
χ44666-2-2-2-2-2-222-2-2-222−2−4i22−2+4i−2−4i22−2+4i2-22i−2i2i−2i2-22i−2i2i−2i00000000000000000000
χ4566-66-26-2-2-2-2-2-62222-2-2-2-22222-2-2-2-2222222-2-200000000000000000000
χ4666-6-26-26-2-2-2-22-6222-2-2-2-22222-2-222-2-222-2-22200000000000000000000
χ4766-6-2-2-2-266-2-222-6222222-2-2-2-2-2-2222222-2-2-2-200000000000000000000
χ4866-6-2-2-2-2-2-222222-2-2-22+4i2−4i-22−2−4i−2+4i2-22−2i2i2i−2i2-22i−2i−2i2i00000000000000000000
χ4966-6-2-2-2-2-2-222222-2-2-22−4i2+4i-22−2+4i−2−4i2-222i−2i−2i2i2-2−2i2i2i−2i00000000000000000000
χ5066-6-2-2-2-2-2-222222-2-22+4i-2-22−4i−2−4i22−2+4i2-22i−2i2i−2i-22−2i2i−2i2i00000000000000000000
χ5166-6-2-2-2-2-2-222222-2-22−4i-2-22+4i−2+4i22−2−4i2-2−2i2i−2i2i-222i−2i2i−2i00000000000000000000
χ5212-12044-4-44-44-40008i−8i0000000000000000000000000000000000000000
χ5312-12044-4-44-44-4000−8i8i0000000000000000000000000000000000000000
χ5412-12044-4-4-1212-44000000000000000000000000000000000000000000000
χ5512-1204-12-4124-4-44000000000000000000000000000000000000000000000
χ5612-120-12412-44-4-44000000000000000000000000000000000000000000000

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