Finite Group Databasebeta

← Group #11714102

Character table — Group #11714102

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222226666888888888888888888888888888888881212121212124848484848484848
order122244444488888888224436661212121212121212121212122424242424242424242424242424242444888822448888
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
χ51111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11-11-11-11-1
χ61111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-11-11-11-11
χ71111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-111-1-11
χ81111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-111-1-111-1
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
χ11222222-2-2-2-200000000-2-22222222222-2-2-2-2-2-2-2-200000000000000002-2000000000000
χ12222222-2-2-2-200000000-2-222-1-1-1-1-1-1-1-1111111113333−3−3−3−33333−3−3−3−32-2000000000000
χ13222222-2-2-2-200000000-2-222-1-1-1-1-1-1-1-111111111−3−3−3−33333−3−3−3−333332-2000000000000
χ142222-2-222-2-200000000-2-2222222-2-2-2-22222-2-2-2-20000000000000000-22000000000000
χ152222-2-222-2-200000000-2-222-1-1-1-11111-1-1-1-111113333−3−3−3−3−3−3−3−33333-22000000000000
χ162222-2-222-2-200000000-2-222-1-1-1-11111-1-1-1-11111−3−3−3−333333333−3−3−3−3-22000000000000
χ172222-2-2-2-2222222-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-2-222-2-200000000
χ182222-2-2-2-222-2-2-2-222222222-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-2-2-2-22200000000
χ192-2-2200002-2000022-2-22-2-2222-2-20000000022-2-20000000022-2-222-2-200002-200000000
χ202-2-2200002-2000022-2-22-2-22-1-11133−3−333−3−3-1-11133−3−333−3−3-1-111-1-11100002-200000000
χ212-2-2200002-2000022-2-22-2-22-1-111−3−333−3−333-1-111−3−333−3−333-1-111-1-11100002-200000000
χ222-2-2200002-20000-2-2222-2-2222-2-20000000022-2-200000000-2-222-2-2220000-2200000000
χ232-2-2200002-20000-2-2222-2-22-1-11133−3−333−3−3-1-111−3−333−3−33311-1-111-1-10000-2200000000
χ242-2-2200002-20000-2-2222-2-22-1-111−3−333−3−333-1-11133−3−333−3−311-1-111-1-10000-2200000000
χ252-2-220000-2222-2-20000-22-2222-2-200000000-2-22222-2-2-2-22200000000002-20000000000
χ262-2-220000-2222-2-20000-22-22-1-11133−3−3−3−33311-1-1-1-11111-1-1−3−33333−3−3002-20000000000
χ272-2-220000-2222-2-20000-22-22-1-111−3−33333−3−311-1-1-1-11111-1-133−3−3−3−333002-20000000000
χ282-2-220000-22-2-2220000-22-2222-2-200000000-2-222-2-22222-2-20000000000-220000000000
χ292-2-220000-22-2-2220000-22-22-1-11133−3−3−3−33311-1-111-1-1-1-11133−3−3−3−33300-220000000000
χ302-2-220000-22-2-2220000-22-22-1-111−3−33333−3−311-1-111-1-1-1-111−3−33333−3−300-220000000000
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
χ353333-3-3-3-3333333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-1111-11-1-11-11
χ363333-3-3-3-3333333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-111-11-111-11-1
χ373333-3-3-3-333-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-11-1-11-111-1
χ383333-3-3-3-333-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-1-111-11-1-11
χ3944-4-4004-400−2i22i2−2i22i2−2i22i2−2i22i200001-11-13−33−31-11-13−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000000000
χ4044-4-4004-400−2i22i2−2i22i2−2i22i2−2i22i200001-11-1−33−331-11-1−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000000000
χ4144-4-4004-400−2i22i2−2i22i2−2i22i2−2i22i20000-22-220000-22-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000000000
χ4244-4-4004-4002i2−2i22i2−2i22i2−2i22i2−2i200001-11-13−33−31-11-13−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000000000
χ4344-4-4004-4002i2−2i22i2−2i22i2−2i22i2−2i200001-11-1−33−331-11-1−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000000000
χ4444-4-4004-4002i2−2i22i2−2i22i2−2i22i2−2i20000-22-220000-22-220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000000000
χ4544-4-400-4400−2i22i2−2i22i22i2−2i22i2−2i200001-11-13−33−3-11-11−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000000000
χ4644-4-400-4400−2i22i2−2i22i22i2−2i22i2−2i200001-11-1−33−33-11-113−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000000000
χ4744-4-400-4400−2i22i2−2i22i22i2−2i22i2−2i20000-22-2200002-22-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000000000
χ4844-4-400-44002i2−2i22i2−2i2−2i22i2−2i22i200001-11-13−33−3-11-11−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000000000
χ4944-4-400-44002i2−2i22i2−2i2−2i22i2−2i22i200001-11-1−33−33-11-113−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000000000
χ5044-4-400-44002i2−2i22i2−2i2−2i22i2−2i22i20000-22-2200002-22-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000000000
χ514-44-44-40000−2i22i22i2−2i2−2i22i22i2−2i200001-1-111-1-113−3−33−333−3ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000000000
χ524-44-44-40000−2i22i22i2−2i2−2i22i22i2−2i200001-1-111-1-11−333−33−3−33ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000000000
χ534-44-44-40000−2i22i22i2−2i2−2i22i22i2−2i20000-222-2-222-200000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000000000
χ544-44-44-400002i2−2i2−2i22i22i2−2i2−2i22i200001-1-111-1-113−3−33−333−3−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000000000
χ554-44-44-400002i2−2i2−2i22i22i2−2i2−2i22i200001-1-111-1-11−333−33−3−33−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000000000
χ564-44-44-400002i2−2i2−2i22i22i2−2i2−2i22i20000-222-2-222-200000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000000000
χ574-44-4-440000−2i22i22i2−2i22i2−2i2−2i22i200001-1-11-111-13−3−333−3−33ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000000000
χ584-44-4-440000−2i22i22i2−2i22i2−2i2−2i22i200001-1-11-111-1−333−3−333−3ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000000000
χ594-44-4-440000−2i22i22i2−2i22i2−2i2−2i22i20000-222-22-2-2200000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000000
χ604-44-4-4400002i2−2i2−2i22i2−2i22i22i2−2i200001-1-11-111-13−3−333−3−33−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000000000
χ614-44-4-4400002i2−2i2−2i22i2−2i22i22i2−2i200001-1-11-111-1−333−3−333−3−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000000000
χ624-44-4-4400002i2−2i2−2i22i2−2i22i22i2−2i20000-222-22-2-2200000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000000
χ63666666-6-6-6-60000000022-2-200000000000000000000000000000000-22000000000000
χ646666-6-666-6-60000000022-2-2000000000000000000000000000000002-2000000000000
χ656-6-6600006-6000066-6-6-222-2000000000000000000000000000000000000-2200000000
χ666-6-6600006-60000-6-666-222-20000000000000000000000000000000000002-200000000
χ676-6-660000-6666-6-600002-22-20000000000000000000000000000000000-220000000000
χ686-6-660000-66-6-66600002-22-200000000000000000000000000000000002-20000000000

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