Finite Group Databasebeta

← Group #11713997

Character table — Group #11713997

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222226666888888888888888888888888888888881212121212124848484848484848
order12222244448888888822443666666612121212121212122424242424242424242424242424242424888824448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1
χ41111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111
χ51111-1-11-1-111111-1-1-1-11111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11-11-11-11-1
χ61111-1-11-1-111111-1-1-1-11111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-11-11-11-11
χ71111-1-11-1-11-1-1-1-111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-111-1-11
χ81111-1-11-1-11-1-1-1-111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-111-1-111-1
χ92222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222200000000
χ102222222222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-2-200000000
χ11222222-2-2-2-200000000-2-22222222222-2-2-2-2-2-2-2-20000000000000000-22000000000000
χ12222222-2-2-2-200000000-2-222-1-1-1-1-1-1-1-1111111113333−3−3−3−33333−3−3−3−3-22000000000000
χ13222222-2-2-2-200000000-2-222-1-1-1-1-1-1-1-111111111−3−3−3−33333−3−3−3−33333-22000000000000
χ142222-2-22-2-222222-2-2-2-22222-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-222-2-200000000
χ152222-2-22-2-22-2-2-2-222222222-1-1-11111-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-2-2-22200000000
χ162222-2-2-222-200000000-2-222222-2-2-2-22-2-22222-2-200000000000000002-2000000000000
χ172222-2-2-222-200000000-2-222-1-1-11111-111-1-1-1-1113333−3−3−3−3−3−3−3−333332-2000000000000
χ182222-2-2-222-200000000-2-222-1-1-11111-111-1-1-1-111−3−3−3−333333333−3−3−3−32-2000000000000
χ192-2-2200200-22i2i−2i−2i00002-22-22-2-200002220000-2-22i2i−2i−2i2i2i−2i−2i00000000002i−2i0000000000
χ202-2-2200200-22i2i−2i−2i00002-22-2-111−i3−i3i3i3-1-1-1−i3−i3i3i311−i−iii−i−iii33−3−333−3−3002i−2i0000000000
χ212-2-2200200-22i2i−2i−2i00002-22-2-111i3i3−i3−i3-1-1-1i3i3−i3−i311−i−iii−i−iii−3−333−3−333002i−2i0000000000
χ222-2-2200200-2−2i−2i2i2i00002-22-22-2-200002220000-2-2−2i−2i2i2i−2i−2i2i2i0000000000−2i2i0000000000
χ232-2-2200200-2−2i−2i2i2i00002-22-2-111−i3−i3i3i3-1-1-1−i3−i3i3i311ii−i−iii−i−i−3−333−3−33300−2i2i0000000000
χ242-2-2200200-2−2i−2i2i2i00002-22-2-111i3i3−i3−i3-1-1-1i3i3−i3−i311ii−i−iii−i−i33−3−333−3−300−2i2i0000000000
χ252-2-2200-2002000022-2-2-222-22-2-200002-2-20000220000000022-2-2-2-22200002-200000000
χ262-2-2200-2002000022-2-2-222-2-111−i3−i3i3i3-111i3i3−i3−i3-1-1−i3−i3i3i3i3i3−i3−i3-1-11111-1-100002-200000000
χ272-2-2200-2002000022-2-2-222-2-111i3i3−i3−i3-111−i3−i3i3i3-1-1i3i3−i3−i3−i3−i3i3i3-1-11111-1-100002-200000000
χ282-2-2200-20020000-2-222-222-22-2-200002-2-200002200000000-2-22222-2-20000-2200000000
χ292-2-2200-20020000-2-222-222-2-111−i3−i3i3i3-111i3i3−i3−i3-1-1i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000-2200000000
χ302-2-2200-20020000-2-222-222-2-111i3i3−i3−i3-111−i3−i3i3i3-1-1−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000-2200000000
χ31333333333333333333-1-1-1-100000000000000000000000000000000-1-1-1-1-1-11111-1-1-1-1
χ32333333333333333333-1-1-1-100000000000000000000000000000000-1-1-1-1-1-1-1-1-1-11111
χ333333333333-3-3-3-3-3-3-3-3-1-1-1-100000000000000000000000000000000-1-1111111-1-1-1-111
χ343333333333-3-3-3-3-3-3-3-3-1-1-1-100000000000000000000000000000000-1-11111-1-11111-1-1
χ353333-3-33-3-333333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-1111-11-1-11-11
χ363333-3-33-3-333333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-111-11-111-11-1
χ373333-3-33-3-33-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-11-1-11-111-1
χ383333-3-33-3-33-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-1-111-11-1-11
χ3944-4-40004i−4i022−2222−22−2i22i2−2i22i2000011-1−i3i3−i3i3-13−3i−ii−i3−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000000000
χ4044-4-40004i−4i022−2222−22−2i22i2−2i22i2000011-1i3−i3i3−i3-1−33i−ii−i−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000000000
χ4144-4-40004i−4i022−2222−22−2i22i2−2i22i20000-2-220000200−2i2i−2i2i002−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000000000
χ4244-4-40004i−4i0−2222−22222i2−2i22i2−2i2000011-1−i3i3−i3i3-13−3i−ii−i3−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000000000
χ4344-4-40004i−4i0−2222−22222i2−2i22i2−2i2000011-1i3−i3i3−i3-1−33i−ii−i−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000000000
χ4444-4-40004i−4i0−2222−22222i2−2i22i2−2i20000-2-220000200−2i2i−2i2i00−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000000000
χ4544-4-4000−4i4i022−2222−222i2−2i22i2−2i2000011-1−i3i3−i3i3-1−33−ii−ii−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000000000
χ4644-4-4000−4i4i022−2222−222i2−2i22i2−2i2000011-1i3−i3i3−i3-13−3−ii−ii3−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000000000
χ4744-4-4000−4i4i022−2222−222i2−2i22i2−2i20000-2-2200002002i−2i2i−2i002−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000000000
χ4844-4-4000−4i4i0−2222−2222−2i22i2−2i22i2000011-1−i3i3−i3i3-1−33−ii−ii−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000000000
χ4944-4-4000−4i4i0−2222−2222−2i22i2−2i22i2000011-1i3−i3i3−i3-13−3−ii−ii3−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000000000
χ5044-4-4000−4i4i0−2222−2222−2i22i2−2i22i20000-2-2200002002i−2i2i−2i00−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000000000
χ514-44-44-40000−2i22i22i2−2i2−2i22i22i2−2i200001-111-1-11-13−33−3−33−33ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000000000
χ524-44-44-40000−2i22i22i2−2i2−2i22i22i2−2i200001-111-1-11-1−33−333−33−3ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000000000
χ534-44-44-40000−2i22i22i2−2i2−2i22i22i2−2i20000-22-2-222-2200000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000000000
χ544-44-44-400002i2−2i2−2i22i22i2−2i2−2i22i200001-111-1-11-13−33−3−33−33−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000000000
χ554-44-44-400002i2−2i2−2i22i22i2−2i2−2i22i200001-111-1-11-1−33−333−33−3−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000000000
χ564-44-44-400002i2−2i2−2i22i22i2−2i2−2i22i20000-22-2-222-2200000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000000000
χ574-44-4-440000−2i22i22i2−2i22i2−2i2−2i22i200001-11-111-1-13−3−333−3−33ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000000000
χ584-44-4-440000−2i22i22i2−2i22i2−2i2−2i22i200001-11-111-1-1−333−3−333−3ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000000000
χ594-44-4-440000−2i22i22i2−2i22i2−2i2−2i22i20000-22-22-2-22200000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000
χ604-44-4-4400002i2−2i2−2i22i2−2i22i22i2−2i200001-11-111-1-13−3−333−3−33−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000000000
χ614-44-4-4400002i2−2i2−2i22i2−2i22i22i2−2i200001-11-111-1-1−333−3−333−3−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000000000
χ624-44-4-4400002i2−2i2−2i22i2−2i22i22i2−2i20000-22-22-2-22200000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000
χ63666666-6-6-6-60000000022-2-2000000000000000000000000000000002-2000000000000
χ646666-6-6-666-60000000022-2-200000000000000000000000000000000-22000000000000
χ656-6-6600600-66i6i−6i−6i0000-22-220000000000000000000000000000000000−2i2i0000000000
χ666-6-6600600-6−6i−6i6i6i0000-22-2200000000000000000000000000000000002i−2i0000000000
χ676-6-6600-6006000066-6-62-2-22000000000000000000000000000000000000-2200000000
χ686-6-6600-60060000-6-6662-2-220000000000000000000000000000000000002-200000000

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