Finite Group Databasebeta

← Group #72343979

Character table — Group #72343979

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size111122446666881212121212121212161616242424242432323232323232324848484848484848484864646464646464646464646496969696969696969696969696
order122244882244222222444448888888366612121212222244444466121224242424242424242444444488888
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ3111111111111-1-111111111-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-11111
χ4111111111111-1-111111111-1-1-11111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1-1
χ5111111-1-1111111111111111-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1
χ6111111-1-1111111111111111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-111
χ7111111-1-11111-1-111111111-111-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111-1-1-111111-1-1
χ8111111-1-11111-1-111111111-111-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1111-1-11-1-111
χ9222222222222222222222222222222-1-1-1-1-1-1-1-10000220000-1-1-1-1-1-1-1-1-1-1-1-10000000020000
χ10222222222222-2-222222222-2-2-222222-1-1-1-1-1-1-1-10000-2-200001111-1-1-1-1111100000000-20000
χ11222222-2-2222222222222222-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000220000-1-1-1-11111111100000000-20000
χ12222222-2-22222-2-222222222-222-2-2-2-2-2-1-1-1-1-1-1-1-10000-2-2000011111111-1-1-1-10000000020000
χ132222-2-20022-2-222-2-2222-2-22-200000002222-2-2-2-200002-2000022-2-2000000000000000000000
χ142222-2-20022-2-222-2-2222-2-22-20000000-1-1-1-1111100002-20000-1-11133−3−333−3−30000000000000
χ152222-2-20022-2-222-2-2222-2-22-20000000-1-1-1-1111100002-20000-1-111−3−333−3−3330000000000000
χ162222-2-20022-2-2-2-2-2-2222-2-22200000002222-2-2-2-20000-220000-2-222000000000000000000000
χ172222-2-20022-2-2-2-2-2-2222-2-2220000000-1-1-1-111110000-22000011-1-133−3−3−3−3330000000000000
χ182222-2-20022-2-2-2-2-2-2222-2-2220000000-1-1-1-111110000-22000011-1-1−3−33333−3−30000000000000
χ192-22-22-200-22-22002-22-2-22-22000000002-2-2222-2-2002-200002-200000000000000002-20000000
χ202-22-22-200-22-22002-22-2-22-22000000002-2-2222-2-200-220000-220000000000000000-220000000
χ212-22-2-2200-222-200-222-2-2-222000000002-2-22-2-2222-200002-2000000000000000000000002-200
χ222-22-2-2200-222-200-222-2-2-222000000002-2-22-2-222-220000-2200000000000000000000000-2200
χ2333333333333333-1-1-1-1-1-1-1-13333-1-1-1-1000000001111-1-111110000000000001111-1-1-1-1-1-1-1-1-1
χ2433333333333333-1-1-1-1-1-1-1-13333-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-11111-11111
χ25333333333333-3-3-1-1-1-1-1-1-1-1-3-3-33-1-1-1-10000000011-1-11111-1-10000000000001-1-1111111-1-1-1-1
χ26333333333333-3-3-1-1-1-1-1-1-1-1-3-3-33-1-1-1-100000000-1-11111-1-111000000000000-111-1-1-1-1-111111
χ27333333-3-3333333-1-1-1-1-1-1-1-13-3-3-31111000000001111-1-11111000000000000-1-1-1-1-1-1111-1-111
χ28333333-3-3333333-1-1-1-1-1-1-1-13-3-3-3111100000000-1-1-1-1-1-1-1-1-1-1000000000000111111-1-1111-1-1
χ29333333-3-33333-3-3-1-1-1-1-1-1-1-1-333-311110000000011-1-11111-1-1000000000000-111-111-1-1-1-1-111
χ30333333-3-33333-3-3-1-1-1-1-1-1-1-1-333-3111100000000-1-11111-1-1110000000000001-1-11-1-111-111-1-1
χ314-44-44-400-44-44004-44-4-44-4400000000-222-2-2-22200000000000000000000000000000000000
χ324-44-4-4400-444-400-444-4-4-44400000000-222-222-2-200000000000000000000000000000000000
χ3366666666-2-2-2-20022-2-22-2-22000-222-2-200000000220000-2-200000000000000200-2000000000
χ3466666666-2-2-2-20022-2-22-2-22000-222-2-200000000-2-200002200000000000000-2002000000000
χ3566666666-2-2-2-200-2-222-222-2000-2-2-2220000000000220000-2-200000000000002-20000000000
χ3666666666-2-2-2-200-2-222-222-2000-2-2-2220000000000-2-20000220000000000000-220000000000
χ37666666-6-6-2-2-2-20022-2-22-2-220002-2-22200000000220000-2-200000000000000-2002000000000
χ38666666-6-6-2-2-2-20022-2-22-2-220002-2-22200000000-2-200002200000000000000200-2000000000
χ39666666-6-6-2-2-2-200-2-222-222-2000222-2-20000000000220000-2-20000000000000-220000000000
χ40666666-6-6-2-2-2-200-2-222-222-2000222-2-20000000000-2-200002200000000000002-20000000000
χ416666-6-60066-6-66622-2-2-222-2-60000000000000000000-2200000000000000000000000000000
χ426666-6-60066-6-6-6-622-2-2-222-2600000000000000000002-200000000000000000000000000000
χ436-66-66-6002-22-200-222-222-2-20000004i−4i00000000002-20000-220000000000000000002i−2i00000
χ446-66-66-6002-22-200-222-222-2-20000004i−4i0000000000-2200002-2000000000000000000−2i2i00000
χ456-66-66-6002-22-200-222-222-2-2000000−4i4i00000000002-20000-22000000000000000000−2i2i00000
χ466-66-66-6002-22-200-222-222-2-2000000−4i4i0000000000-2200002-20000000000000000002i−2i00000
χ476-66-66-600-66-6600-22-222-22-20000000000000000002-200002-20000000000000000-220000000
χ486-66-66-600-66-6600-22-222-22-2000000000000000000-220000-2200000000000000002-20000000
χ496-66-6-66002-2-2200-22-22-22-2200004-400000000002-20000-2200000000000000000000000002-2
χ506-66-6-66002-2-2200-22-22-22-2200004-40000000000-2200002-20000000000000000000000000-22
χ516-66-6-66002-2-2200-22-22-22-220000-4400000000002-20000-220000000000000000000000000-22
χ526-66-6-66002-2-2200-22-22-22-220000-440000000000-2200002-200000000000000000000000002-2
χ536-66-6-6600-666-6002-2-2222-2-200000000000000002-200002-200000000000000000000000-2200
χ546-66-6-6600-666-6002-2-2222-2-20000000000000000-220000-22000000000000000000000002-200
χ558-8-880042−4200004-400000000022−220000022-2-2000000000000002-2002−22−22−22−20000000000000
χ568-8-880042−4200004-400000000022−2200000-1-1113−33−30000000000-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000
χ578-8-880042−4200004-400000000022−2200000-1-111−33−330000000000-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000
χ588-8-880042−420000-44000000000−22220000022-2-200000000000000-22002−22−2−22−220000000000000
χ598-8-880042−420000-44000000000−222200000-1-1113−33−300000000001-1−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000
χ608-8-880042−420000-44000000000−222200000-1-111−33−3300000000001-13−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000
χ618-8-8800−424200004-4000000000−22220000022-2-2000000000000002-200−22−22−22−220000000000000
χ628-8-8800−424200004-4000000000−222200000-1-1113−33−30000000000-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000
χ638-8-8800−424200004-4000000000−222200000-1-111−33−330000000000-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000
χ648-8-8800−42420000-4400000000022−220000022-2-200000000000000-2200−22−222−22−20000000000000
χ658-8-8800−42420000-4400000000022−2200000-1-1113−33−300000000001-1−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000
χ668-8-8800−42420000-4400000000022−2200000-1-111−33−3300000000001-13−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000
χ6712121212-12-1200-4-444004444-4-4-4-4000000000000000000000000000000000000000000000000000
χ6812121212-12-1200-4-44400-4-4-4-44444000000000000000000000000000000000000000000000000000
χ6912-1212-1212-12004-44-4004-4-44-4-444000000000000000000000000000000000000000000000000000
χ7012-1212-12-1212004-4-44004-44-44-44-4000000000000000000000000000000000000000000000000000
χ711616-16-16000000000000000000000000004-44-4000000000000000000000000000000000000000
χ721616-16-1600000000000000000000000000-22-2223−23−232300000000000000000000000000000000000
χ731616-16-1600000000000000000000000000-22-22−232323−2300000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.