Finite Group Databasebeta

← Group #72341646

Character table — Group #72341646

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111111122226666666666661212121212121212121212121212242424242424242432323232323232323232323232323232484848484848484848484848
order1222444422442222224444442222222444444422444444366666661212121212121212444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111-1-1-1-111111111111111-1-1-1-1-111-1-1-1-1-111-1-1-1-111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1
χ411111111-1-1-1-111111111111111-1-1-1-1-111-1-1-1-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111-1-11111-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1
χ61111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1111
χ71111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-111-1-1111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1111
χ81111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-111-1-111111-1-1-1-11-1-1-1-11111-1-1-1111111-1-1-1
χ92222222222222222222222222222222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1022222222-2-2-2-222222222222222-2-2-2-2-222-2-2-2-2-200000000-1-1-11111-1-1-1-1-11111000000000000
χ112222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2222-2-22222-2-2-200000000-1-1-1-1-1-1-1-111111111000000000000
χ122222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-22222-2-222200000000-1-1-11111-11111-1-1-1-1000000000000
χ132-2-2222-2-20000222-2-2-2222-2-2-22-2000002-200000000000002-2-20000222-2-20000000000000000
χ142-2-2222-2-20000222-2-2-2222-2-2-22-2000002-20000000000000-111−i3−i3i3i3-1-1-111−i3−i3i3i3000000000000
χ152-2-2222-2-20000222-2-2-2222-2-2-22-2000002-20000000000000-111i3i3−i3−i3-1-1-111i3i3−i3−i3000000000000
χ162-2-22-2-2220000222-2-2-2-2-2-2222-22000002-200000000000002-2-200002-2-2220000000000000000
χ172-2-22-2-2220000222-2-2-2-2-2-2222-22000002-20000000000000-111−i3−i3i3i3-111-1-1i3i3−i3−i3000000000000
χ182-2-22-2-2220000222-2-2-2-2-2-2222-22000002-20000000000000-111i3i3−i3−i3-111-1-1−i3−i3i3i3000000000000
χ193333333333333-1-13-1-13-1-13-1-1-1-13-1-1-1-1-1-1-1-13-1-11111111100000000000000001-1-11-1-11-1-11-1-1
χ203333333333333-1-13-1-13-1-13-1-1-1-13-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-1-10000000000000000-111-111-111-111
χ21333333333333-13-1-13-1-13-1-13-1-1-1-13-1-1-1-1-1-1-1-13-1111111110000000000000000-11-1-11-1-11-1-11-1
χ22333333333333-13-1-13-1-13-1-13-1-1-1-13-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-100000000000000001-111-111-111-11
χ23333333333333-1-13-1-13-1-13-1-13-1-1-1-13-1-1-1-1-1-1-1-13111111110000000000000000-1-11-1-11-1-11-1-11
χ24333333333333-1-13-1-13-1-13-1-13-1-1-1-13-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1000000000000000011-111-111-111-1
χ2533333333-3-3-3-33-1-13-1-13-1-13-1-1-1-1-31111-1-111-31111-1-1-1-11100000000000000001-1-11-1-1-111-111
χ2633333333-3-3-3-33-1-13-1-13-1-13-1-1-1-1-31111-1-111-311-1-11111-1-10000000000000000-111-1111-1-11-1-1
χ2733333333-3-3-3-3-13-1-13-1-13-1-13-1-1-11-3111-1-1111-3111-1-1-1-1110000000000000000-11-1-11-11-111-11
χ2833333333-3-3-3-3-13-1-13-1-13-1-13-1-1-11-3111-1-1111-31-1-11111-1-100000000000000001-111-11-11-1-11-1
χ2933333333-3-3-3-3-1-13-1-13-1-13-1-13-1-111-311-1-11111-311-1-1-1-1110000000000000000-1-11-1-1111-111-1
χ3033333333-3-3-3-3-1-13-1-13-1-13-1-13-1-111-311-1-11111-3-1-11111-1-1000000000000000011-111-1-1-11-1-11
χ313333-3-3-3-333-3-33-1-13-1-1-311-311113-1-111-1-1-1-1-3111111-1-1-1-100000000000000001-1-1-1111-1-1-111
χ323333-3-3-3-333-3-33-1-13-1-1-311-311113-1-111-1-1-1-1-311-1-1-1-111110000000000000000-1111-1-1-1111-1-1
χ333333-3-3-3-333-3-3-13-1-13-11-311-3111-13-111-1-1-1-11-311111-1-1-1-10000000000000000-11-11-11-11-11-11
χ343333-3-3-3-333-3-3-13-1-13-11-311-3111-13-111-1-1-1-11-31-1-1-1-1111100000000000000001-11-11-11-11-11-1
χ353333-3-3-3-333-3-3-1-13-1-1311-311-311-1-1311-1-1-1-111-31111-1-1-1-10000000000000000-1-1111-1-1-1111-1
χ363333-3-3-3-333-3-3-1-13-1-1311-311-311-1-1311-1-1-1-111-3-1-1-1-11111000000000000000011-1-1-1111-1-1-11
χ373333-3-3-3-3-3-3333-1-13-1-1-311-31111-311-1-1-1-1113-1-111-1-111-1-100000000000000001-1-1-111-1111-1-1
χ383333-3-3-3-3-3-3333-1-13-1-1-311-31111-311-1-1-1-1113-1-1-1-111-1-1110000000000000000-1111-1-11-1-1-111
χ393333-3-3-3-3-3-333-13-1-13-11-311-31111-31-1-1-1-111-13-111-1-111-1-10000000000000000-11-11-111-11-11-1
χ403333-3-3-3-3-3-333-13-1-13-11-311-31111-31-1-1-1-111-13-1-1-111-1-11100000000000000001-11-11-1-11-11-11
χ413333-3-3-3-3-3-333-1-13-1-1311-311-31111-3-1-1-1-111-1-1311-1-111-1-10000000000000000-1-1111-111-1-1-11
χ423333-3-3-3-3-3-333-1-13-1-1311-311-31111-3-1-1-1-111-1-13-1-111-1-111000000000000000011-1-1-11-1-1111-1
χ4344-4-44i−4i4i−4i4-44i−4i000000000000000000000000002-22-22i−2i2i−2i11-11-11-1-1i−ii−ii−ii−i000000000000
χ4444-4-44i−4i4i−4i4-44i−4i00000000000000000000000000-22-22−2i2i−2i2i11-11-11-1-1i−ii−ii−ii−i000000000000
χ4544-4-44i−4i4i−4i-44−4i4i000000000000000000000000002-2-22−2i2i2i−2i11-1-11-11-1i−ii−i−ii−ii000000000000
χ4644-4-44i−4i4i−4i-44−4i4i00000000000000000000000000-222-22i−2i−2i2i11-1-11-11-1i−ii−i−ii−ii000000000000
χ4744-4-4−4i4i−4i4i4-4−4i4i000000000000000000000000002-22-2−2i2i−2i2i11-11-11-1-1−ii−ii−ii−ii000000000000
χ4844-4-4−4i4i−4i4i4-4−4i4i00000000000000000000000000-22-222i−2i2i−2i11-11-11-1-1−ii−ii−ii−ii000000000000
χ4944-4-4−4i4i−4i4i-444i−4i000000000000000000000000002-2-222i−2i−2i2i11-1-11-11-1−ii−iii−ii−i000000000000
χ5044-4-4−4i4i−4i4i-444i−4i00000000000000000000000000-222-2−2i2i2i−2i11-1-11-11-1−ii−iii−ii−i000000000000
χ51666666666666-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2222222-2-2-2000000000000000000000000000000000000
χ5266666666-6-6-6-6-2-2-2-2-2-2-2-2-2-2-2-222222-2-222-2-2222000000000000000000000000000000000000
χ536666-6-6-6-666-6-6-2-2-2-2-2-2222222-2-2-2-2-2-2-22222222000000000000000000000000000000000000
χ546666-6-6-6-6-6-666-2-2-2-2-2-2222222-2-22222222-2-2-2-2-2000000000000000000000000000000000000
χ556-6-6666-6-600006-2-2-6226-2-2-622-2200000-2200000000000000000000000000000000000000000
χ566-6-6666-6-60000-26-22-62-26-22-62-2200000-2200000000000000000000000000000000000000000
χ576-6-6666-6-60000-2-2622-6-2-2622-6-2200000-2200000000000000000000000000000000000000000
χ586-6-6666-6-60000-2-2-2222-2-2-22222-20004-42-24-4000000000000000000000000000000000000000
χ596-6-6666-6-60000-2-2-2222-2-2-22222-2000-442-2-44000000000000000000000000000000000000000
χ606-6-66-6-66600006-2-2-622-6226-2-22-200000-2200000000000000000000000000000000000000000
χ616-6-66-6-6660000-26-22-622-62-26-22-200000-2200000000000000000000000000000000000000000
χ626-6-66-6-6660000-2-2622-622-6-2-262-200000-2200000000000000000000000000000000000000000
χ636-6-66-6-6660000-2-2-2222222-2-2-2-220004-42-2-44000000000000000000000000000000000000000
χ646-6-66-6-6660000-2-2-2222222-2-2-2-22000-442-24-4000000000000000000000000000000000000000
χ6588-8-88i−8i8i−8i8-88i−8i0000000000000000000000000000000000-1-11-11-111−ii−ii−ii−ii000000000000
χ6688-8-88i−8i8i−8i-88−8i8i0000000000000000000000000000000000-1-111-11-11−ii−iii−ii−i000000000000
χ6788-8-8−8i8i−8i8i8-8−8i8i0000000000000000000000000000000000-1-11-11-111i−ii−ii−ii−i000000000000
χ6888-8-8−8i8i−8i8i-888i−8i0000000000000000000000000000000000-1-111-11-11i−ii−i−ii−ii000000000000
χ698-88-88i−8i−8i8i000000000000000000000000000000000000002-220000-22i−2i−2i2i0000000000000000
χ708-88-88i−8i−8i8i00000000000000000000000000000000000000-11-1−i3i3i3−i31−iii−i3−3−33000000000000
χ718-88-88i−8i−8i8i00000000000000000000000000000000000000-11-1i3−i3−i3i31−iii−i−333−3000000000000
χ728-88-8−8i8i8i−8i000000000000000000000000000000000000002-220000-2−2i2i2i−2i0000000000000000
χ738-88-8−8i8i8i−8i00000000000000000000000000000000000000-11-1−i3i3i3−i31i−i−ii−333−3000000000000
χ748-88-8−8i8i8i−8i00000000000000000000000000000000000000-11-1i3−i3−i3i31i−i−ii3−3−33000000000000

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