Finite Group Databasebeta

← Group #72253572

Character table — Group #72253572

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1133446666121212121212121212122424242432324848484848484848484848484848484896969696969696969696128128128128128128128128
order1222222222222222222244444422444444444444444444444444366612121212
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ3111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ51-1-111-11-11-1111-1-111-1-1-111-1-1i−i1-1i−ii−i1-111-1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i
χ61-1-111-11-11-1111-1-111-1-1-111-1-1i−i-11−ii−ii-11-1-111−i−iiii−i-1-111−i−iii11-1-1ii−i−i
χ71-1-111-11-11-1111-1-111-1-1-111-1-1−ii1-1−ii−ii1-111-1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii
χ81-1-111-11-11-1111-1-111-1-1-111-1-1−ii-11i−ii−i-11-1-111ii−i−i−ii-1-111ii−i−i11-1-1−i−iii
χ92222222222222222222222222200000000000000002200000000-1-1-1-1-1-1-1-1
χ10222222222222222222222222-2-20000000000000000-2-200000000-1-1-1-11111
χ112222-2-2222222-2222222-2-2-2-2-200000000000000000000000000002-22-20000
χ122222-2-2222222-2222222-2-2-2-2-20000000000000000000000000000-11-113−33−3
χ132222-2-2222222-2222222-2-2-2-2-20000000000000000000000000000-11-11−33−33
χ142-2-222-22-22-2222-2-222-2-2-222-2-22i−2i00000000000000002i−2i00000000-1-111−i−iii
χ152-2-222-22-22-2222-2-222-2-2-222-2-2−2i2i0000000000000000−2i2i00000000-1-111ii−i−i
χ162-2-22-222-22-222-2-2-222-2-22-2-22200000000000000000000000000002-2-220000
χ172-2-22-222-22-222-2-2-222-2-22-2-2220000000000000000000000000000-111-1−i3i3i3−i3
χ182-2-22-222-22-222-2-2-222-2-22-2-2220000000000000000000000000000-111-1i3−i3−i3i3
χ193333333333-1-13-1-1-1-1-1-13-1-1-1-1331111111111111111-1-1-1-1-1-1-1-1-1-100000000
χ203333333333-1-13-1-1-1-1-1-13-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111100000000
χ213333333333-1-13-1-1-1-1-1-13-1-1-1-1-3-311-1-1-1-1111111-1-1-1-111-1-1-1-1111100000000
χ223333333333-1-13-1-1-1-1-1-13-1-1-1-1-3-3-1-11111-1-1-1-1-1-11111111111-1-1-1-100000000
χ233-3-333-33-33-3-1-1311-1-111-3-1-1113i−3i1-1i−ii−i1-111-1-1ii−i−i−ii-1-111−i−iii00000000
χ243-3-333-33-33-3-1-1311-1-111-3-1-1113i−3i-11−ii−ii-11-1-111−i−iii−ii11-1-1ii−i−i00000000
χ253-3-333-33-33-3-1-1311-1-111-3-1-111−3i3i1-1−ii−ii1-111-1-1−i−iiii−i-1-111ii−i−i00000000
χ263-3-333-33-33-3-1-1311-1-111-3-1-111−3i3i-11i−ii−i-11-1-111ii−i−ii−i11-1-1−i−iii00000000
χ27666666-2-2-2-222-2-2-2-2-222-22-22-200002222000000-2-2-2-2000000000000000000
χ28666666-2-2-2-222-2-2-2-2-222-22-22-20000-2-2-2-20000002222000000000000000000
χ29666666-2-2-2-2-2-2-22222-2-2-2-22-220022000022-2-2-2-20000000000000000000000
χ30666666-2-2-2-2-2-2-22222-2-2-2-22-2200-2-20000-2-222220000000000000000000000
χ316666-6-66666-2-2-6-2-2-2-2-2-2-62222000000000000000000000000000000000000
χ326666-6-6-2-2-2-2222-2-2-2-2222-22-220000000000000000000000002-22-200000000
χ336666-6-6-2-2-2-2222-2-2-2-2222-22-22000000000000000000000000-22-2200000000
χ346666-6-6-2-2-2-2-2-222222-2-222-22-2000000000000000000002-22-2000000000000
χ356666-6-6-2-2-2-2-2-222222-2-222-22-200000000000000000000-22-22000000000000
χ366-6-666-6-22-2222-222-2-2-2-222-2-2200002i−2i2i−2i000000−2i−2i2i2i000000000000000000
χ376-6-666-6-22-2222-222-2-2-2-222-2-220000−2i2i−2i2i0000002i2i−2i−2i000000000000000000
χ386-6-666-6-22-22-2-2-2-2-222222-222-2002-200002-2-2-2220000000000000000000000
χ396-6-666-6-22-22-2-2-2-2-222222-222-200-220000-2222-2-20000000000000000000000
χ406-6-66-666-66-6-2-2-622-2-222622-2-2000000000000000000000000000000000000
χ416-6-66-66-22-2222222-2-2-2-2-2-222-20000000000000000000000002i−2i−2i2i00000000
χ426-6-66-66-22-2222222-2-2-2-2-2-222-2000000000000000000000000−2i2i2i−2i00000000
χ436-6-66-66-22-22-2-22-2-22222-22-2-22000000000000000000002-2-22000000000000
χ446-6-66-66-22-22-2-22-2-22222-22-2-2200000000000000000000-222-2000000000000
χ451212-4-4004-4-440004-44-40000000000022-2-20000002-22-2000000000000000000
χ461212-4-4004-4-440004-44-400000000000-2-222000000-22-22000000000000000000
χ471212-4-4004-4-44000-44-440000000000022-2-2000000-22-22000000000000000000
χ481212-4-4004-4-44000-44-4400000000000-2-2220000002-22-2000000000000000000
χ491212-4-400-444-44-4000004-40000000220000-2-22-22-20000000000000000000000
χ501212-4-400-444-44-4000004-40000000-2-2000022-22-220000000000000000000000
χ511212-4-400-444-4-4400000-440000000220000-2-2-22-220000000000000000000000
χ521212-4-400-444-4-4400000-440000000-2-20000222-22-20000000000000000000000
χ5312-124-40044-4-40004-4-44000000000002i−2i−2i2i000000−2i2i2i−2i000000000000000000
χ5412-124-40044-4-40004-4-4400000000000−2i2i2i−2i0000002i−2i−2i2i000000000000000000
χ5512-124-40044-4-4000-444-4000000000002i−2i−2i2i0000002i−2i−2i2i000000000000000000
χ5612-124-40044-4-4000-444-400000000000−2i2i2i−2i000000−2i2i2i−2i000000000000000000
χ5712-124-400-4-4444-400000-4400000002-20000-222-2-220000000000000000000000
χ5812-124-400-4-4444-400000-440000000-2200002-2-222-20000000000000000000000
χ5912-124-400-4-444-44000004-400000002-20000-22-222-20000000000000000000000
χ6012-124-400-4-444-44000004-40000000-2200002-22-2-220000000000000000000000

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