Finite Group Databasebeta

← Group #72245747

Character table — Group #72245747

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111111122226666666666661212121212121212121212121212242424242424242432323232323232323232323232323232484848484848484848484848
order12224444444422222244444422444444444444222244443666121212121212121212121212444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1111-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1111-1-1-1111-1-1-1
χ61111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1111-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1111
χ71111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111
χ81111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-1
χ92222222222222222222222222222222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1022222222-2-2-2-2222222222222-2-22222-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-111111111000000000000
χ112222-2-2-2-222-2-2222222-2-2-2-2-2-22222-2-2222-2-2-2-2-200000000-1-1-1-11111-1-1-1-11111000000000000
χ122222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222-2-2-2-2-22222200000000-1-1-1-111111111-1-1-1-1000000000000
χ1322-2-22i2i−2i−2i0000222-2-2-22i2i2i−2i−2i−2i002-22i−2i000000000000000022-2-22i2i−2i−2i00000000000000000000
χ1422-2-22i2i−2i−2i0000222-2-2-22i2i2i−2i−2i−2i002-22i−2i0000000000000000-1-111−i−iii−i3−i3i3i333−3−3000000000000
χ1522-2-22i2i−2i−2i0000222-2-2-22i2i2i−2i−2i−2i002-22i−2i0000000000000000-1-111−i−iiii3i3−i3−i3−3−333000000000000
χ1622-2-2−2i−2i2i2i0000222-2-2-2−2i−2i−2i2i2i2i002-2−2i2i000000000000000022-2-2−2i−2i2i2i00000000000000000000
χ1722-2-2−2i−2i2i2i0000222-2-2-2−2i−2i−2i2i2i2i002-2−2i2i0000000000000000-1-111ii−i−i−i3−i3i3i3−3−333000000000000
χ1822-2-2−2i−2i2i2i0000222-2-2-2−2i−2i−2i2i2i2i002-2−2i2i0000000000000000-1-111ii−i−ii3i3−i3−i333−3−3000000000000
χ193333333333333-1-13-1-13-1-13-1-1-1-1-1-1-1-13-1-13-1-1-1-11111111100000000000000001-1-11-1-11-1-11-1-1
χ203333333333333-1-13-1-13-1-13-1-1-1-1-1-1-1-13-1-13-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-111-111-111-111
χ21333333333333-13-1-13-1-13-1-13-1-1-1-1-1-1-1-13-1-13-1-1-1111111110000000000000000-11-1-11-1-11-1-11-1
χ22333333333333-13-1-13-1-13-1-13-1-1-1-1-1-1-1-13-1-13-1-1-1-1-1-1-1-1-1-1-100000000000000001-111-111-111-11
χ23333333333333-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-13-1-13-1-1111111110000000000000000-1-11-1-11-1-11-1-11
χ24333333333333-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-13-1-13-1-1-1-1-1-1-1-1-1-1000000000000000011-111-111-111-1
χ2533333333-3-3-3-33-1-13-1-13-1-13-1-111-1-1-1-1-311-3111111-1-111-1-100000000000000001-1-11-1-1-111-111
χ2633333333-3-3-3-33-1-13-1-13-1-13-1-111-1-1-1-1-311-31111-1-111-1-1110000000000000000-111-1111-1-11-1-1
χ2733333333-3-3-3-3-13-1-13-1-13-1-13-111-1-1-1-11-311-311111-1-111-1-10000000000000000-11-1-11-11-111-11
χ2833333333-3-3-3-3-13-1-13-1-13-1-13-111-1-1-1-11-311-3111-1-111-1-11100000000000000001-111-11-11-1-11-1
χ2933333333-3-3-3-3-1-13-1-13-1-13-1-1311-1-1-1-111-311-31111-1-111-1-10000000000000000-1-11-1-1111-111-1
χ3033333333-3-3-3-3-1-13-1-13-1-13-1-1311-1-1-1-111-311-311-1-111-1-111000000000000000011-111-1-1-11-1-11
χ313333-3-3-3-333-3-33-1-13-1-1-311-311-1-1-1-1113-1-1-3111111-1-1-1-11100000000000000001-1-1-1111-1-1-111
χ323333-3-3-3-333-3-33-1-13-1-1-311-311-1-1-1-1113-1-1-31111-1-11111-1-10000000000000000-1111-1-1-1111-1-1
χ333333-3-3-3-333-3-3-13-1-13-11-311-31-1-1-1-111-13-11-311111-1-1-1-1110000000000000000-11-11-11-11-11-11
χ343333-3-3-3-333-3-3-13-1-13-11-311-31-1-1-1-111-13-11-3111-1-11111-1-100000000000000001-11-11-11-11-11-1
χ353333-3-3-3-333-3-3-1-13-1-1311-311-3-1-1-1-111-1-1311-31111-1-1-1-1110000000000000000-1-1111-1-1-1111-1
χ363333-3-3-3-333-3-3-1-13-1-1311-311-3-1-1-1-111-1-1311-311-1-11111-1-1000000000000000011-1-1-1111-1-1-11
χ373333-3-3-3-3-3-3333-1-13-1-1-311-31111-1-111-3113-1-1-1-11111-1-1-1-100000000000000001-1-1-111-1111-1-1
χ383333-3-3-3-3-3-3333-1-13-1-1-311-31111-1-111-3113-1-1-1-1-1-1-1-111110000000000000000-1111-1-11-1-1-111
χ393333-3-3-3-3-3-333-13-1-13-11-311-3111-1-1111-31-13-1-1-11111-1-1-1-10000000000000000-11-11-111-11-11-1
χ403333-3-3-3-3-3-333-13-1-13-11-311-3111-1-1111-31-13-1-1-1-1-1-1-1111100000000000000001-11-11-1-11-11-11
χ413333-3-3-3-3-3-333-1-13-1-1311-311-311-1-11111-3-1-13-1-11111-1-1-1-10000000000000000-1-1111-111-1-1-11
χ423333-3-3-3-3-3-333-1-13-1-1311-311-311-1-11111-3-1-13-1-1-1-1-1-11111000000000000000011-1-1-11-1-1111-1
χ434-44-44i−4i4i−4i4i−4i4-4000000000000000000000000002-22-22i−2i2i−2i1-11-1i−ii−ii−ii−i1-11-1000000000000
χ444-44-44i−4i4i−4i4i−4i4-400000000000000000000000000-22-22−2i2i−2i2i1-11-1i−ii−ii−ii−i1-11-1000000000000
χ454-44-44i−4i4i−4i−4i4i-44000000000000000000000000002-2-222i−2i−2i2i1-11-1i−ii−i−ii−ii-11-11000000000000
χ464-44-44i−4i4i−4i−4i4i-4400000000000000000000000000-222-2−2i2i2i−2i1-11-1i−ii−i−ii−ii-11-11000000000000
χ474-44-4−4i4i−4i4i4i−4i-44000000000000000000000000002-2-22−2i2i2i−2i1-11-1−ii−iii−ii−i-11-11000000000000
χ484-44-4−4i4i−4i4i4i−4i-4400000000000000000000000000-222-22i−2i−2i2i1-11-1−ii−iii−ii−i-11-11000000000000
χ494-44-4−4i4i−4i4i−4i4i4-4000000000000000000000000002-22-2−2i2i−2i2i1-11-1−ii−ii−ii−ii1-11-1000000000000
χ504-44-4−4i4i−4i4i−4i4i4-400000000000000000000000000-22-222i−2i2i−2i1-11-1−ii−ii−ii−ii1-11-1000000000000
χ51666666666666-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222000000000000000000000000000000000000
χ5266666666-6-6-6-6-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2000000000000000000000000000000000000
χ536666-6-6-6-666-6-6-2-2-2-2-2-22222222222-2-2-2-2-2222-2-2000000000000000000000000000000000000
χ546666-6-6-6-6-6-666-2-2-2-2-2-2222222-2-222-2-2222-2-2-222000000000000000000000000000000000000
χ5566-6-66i6i−6i−6i00006-2-2-6226i−2i−2i−6i2i2i00-22−2i2i00000000000000000000000000000000000000000000
χ5666-6-66i6i−6i−6i0000-26-22-62−2i6i−2i2i−6i2i00-22−2i2i00000000000000000000000000000000000000000000
χ5766-6-66i6i−6i−6i0000-2-2622-6−2i−2i6i2i2i−6i00-22−2i2i00000000000000000000000000000000000000000000
χ5866-6-66i6i−6i−6i0000-2-2-2222−2i−2i−2i2i2i2i4-42-22i−2i0000004i−4i000000000000000000000000000000000000
χ5966-6-66i6i−6i−6i0000-2-2-2222−2i−2i−2i2i2i2i-442-22i−2i000000−4i4i000000000000000000000000000000000000
χ6066-6-6−6i−6i6i6i00006-2-2-622−6i2i2i6i−2i−2i00-222i−2i00000000000000000000000000000000000000000000
χ6166-6-6−6i−6i6i6i0000-26-22-622i−6i2i−2i6i−2i00-222i−2i00000000000000000000000000000000000000000000
χ6266-6-6−6i−6i6i6i0000-2-2622-62i2i−6i−2i−2i6i00-222i−2i00000000000000000000000000000000000000000000
χ6366-6-6−6i−6i6i6i0000-2-2-22222i2i2i−2i−2i−2i4-42-2−2i2i000000−4i4i000000000000000000000000000000000000
χ6466-6-6−6i−6i6i6i0000-2-2-22222i2i2i−2i−2i−2i-442-2−2i2i0000004i−4i000000000000000000000000000000000000
χ658-88-88i−8i8i−8i8i−8i8-80000000000000000000000000000000000-11-11−ii−ii−ii−ii-11-11000000000000
χ668-88-88i−8i8i−8i−8i8i-880000000000000000000000000000000000-11-11−ii−iii−ii−i1-11-1000000000000
χ678-88-8−8i8i−8i8i8i−8i-880000000000000000000000000000000000-11-11i−ii−i−ii−ii1-11-1000000000000
χ688-88-8−8i8i−8i8i−8i8i8-80000000000000000000000000000000000-11-11i−ii−ii−ii−i-11-11000000000000
χ698-8-888-8-88000000000000000000000000000000000000002-2-222-2-2200000000000000000000
χ708-8-888-8-8800000000000000000000000000000000000000-111-1-111-13−3−33−333−3000000000000
χ718-8-888-8-8800000000000000000000000000000000000000-111-1-111-1−333−33−3−33000000000000
χ728-8-88-888-8000000000000000000000000000000000000002-2-22-222-200000000000000000000
χ738-8-88-888-800000000000000000000000000000000000000-111-11-1-113−3−333−3−33000000000000
χ748-8-88-888-800000000000000000000000000000000000000-111-11-1-11−333−3−333−3000000000000

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