Finite Group Databasebeta

← Group #10714497

Character table — Group #10714497

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222222222222222224444444444444448888888888888888888888888888888888884848484848484848
order122223444468812122424242466688812121224242424242424668812121616161616161616242424244848484848484848484848484848484822448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ922222222222-2-222-2-2-2-2222-2-2-2222-2-2-2-2-2-22222-2-22200000000-2-2-2-2000000000000000000000000
χ1022222222222-2-222-2-2-2-2222-2-2-2222-2-2-2-2-2-2-2-2-2-222-2-2000000002222000000000000000000000000
χ11222222-2-2-2-2200-2-20000222000-2-2-200000000002i−2i0022−2−2−i2−i2i2i22i2i−2i−2i2222−2−2−2−2−i2−i2−i2−i2i2i2i2i200000000
χ12222222-2-2-2-2200-2-20000222000-2-2-200000000002i−2i00−2−222i2i2−i2−i22i2i−2i−2i−2−2−2−22222i2i2i2i2−i2−i2−i2−i200000000
χ13222222-2-2-2-2200-2-20000222000-2-2-20000000000−2i2i0022−2−2i2i2−i2−i2−2i−2i2i2i2222−2−2−2−2i2i2i2i2−i2−i2−i2−i200000000
χ14222222-2-2-2-2200-2-20000222000-2-2-20000000000−2i2i00−2−222−i2−i2i2i2−2i−2i2i2i−2−2−2−22222−i2−i2−i2−i2i2i2i2i200000000
χ1522222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-122-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1622222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-122-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000
χ1722222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-211-2-2112222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000
χ1822222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-211-2-211-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000
χ1922222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-111111122-1-1-2-2-1-100000000111133−3−333−3−333−3−333−3−300000000
χ2022222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-111111122-1-1-2-2-1-1000000001111−3−333−3−333−3−333−3−33300000000
χ2122222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-1111111-2-211221100000000-1-1-1-133−3−333−3−3−3−333−3−33300000000
χ2222222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-1111111-2-211221100000000-1-1-1-1−3−333−3−33333−3−333−3−300000000
χ2322222-1-2-2-2-2-1001133−3−3-1-1-10001113−333−3−300−i3i32i−2i−i3i322−2−2−i2−i2i2i2−i−iiiζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ2300000000
χ2422222-1-2-2-2-2-1001133−3−3-1-1-10001113−333−3−300−i3i32i−2i−i3i3−2−222i2i2−i2−i2−i−iii−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ2300000000
χ2522222-1-2-2-2-2-1001133−3−3-1-1-10001113−333−3−300i3−i3−2i2ii3−i322−2−2i2i2−i2−i2ii−i−iζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ2300000000
χ2622222-1-2-2-2-2-1001133−3−3-1-1-10001113−333−3−300i3−i3−2i2ii3−i3−2−222−i2−i2i2i2ii−i−i−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ2300000000
χ2722222-1-2-2-2-2-10011−3−333-1-1-1000111−33−3−33300−i3i3−2i2i−i3i322−2−2i2i2−i2−i2ii−i−iζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ700000000
χ2822222-1-2-2-2-2-10011−3−333-1-1-1000111−33−3−33300−i3i3−2i2i−i3i3−2−222−i2−i2i2i2ii−i−i−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ700000000
χ2922222-1-2-2-2-2-10011−3−333-1-1-1000111−33−3−33300i3−i32i−2ii3−i322−2−2−i2−i2i2i2−i−iiiζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ700000000
χ3022222-1-2-2-2-2-10011−3−333-1-1-1000111−33−3−33300i3−i32i−2ii3−i3−2−222i2i2−i2−i2−i−iii−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ700000000
χ31222-2-2222-2-22222222222-2-2-22-22-2-2-2-22-22-2000000000000000000000000000000000000002i−2i0000
χ32222-2-2222-2-22222222222-2-2-22-22-2-2-2-22-22-200000000000000000000000000000000000000−2i2i0000
χ33222-2-2222-2-22-2-222-2-2-2-22-2-22-222-2-222-22-220000000000000000000000000000000000000000002i−2i
χ34222-2-2222-2-22-2-222-2-2-2-22-2-22-222-2-222-22-22000000000000000000000000000000000000000000−2i2i
χ3522-22-222-22-2200-2-20000-22-200022-20000002-22200-2-2−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ3622-22-222-22-2200-2-20000-22-200022-20000002-22200-2-2i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ3722-22-222-22-2200-2-20000-22-200022-2000000-22-2-20022−i2i2−i2i2i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ3822-22-222-22-2200-2-20000-22-200022-2000000-22-2-20022i2−i2i2−i2−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ3922-22-22-22-22222222222-22-22-2-2-2-2222-2-2-2-2000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ4022-22-22-22-22222222222-22-22-2-2-2-2222-2-2-2-200000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ4122-22-22-22-222-2-222-2-2-2-2-22-2-222-2-22-2-222220000000000002-2-220000000000002-22-2-22-2200000000
χ4222-22-22-22-222-2-222-2-2-2-2-22-2-222-2-22-2-22222000000000000-222-2000000000000-22-222-22-200000000
χ4322-22-2-12-22-2-1001133−3−31-11000-1-113−3−3−3332-2-1-10011−i2i2−i2i2−i2i2−i2i23−33−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ4422-22-2-12-22-2-1001133−3−31-11000-1-113−3−3−3332-2-1-10011i2−i2i2−i2i2−i2i2−i23−33−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ4522-22-2-12-22-2-1001133−3−31-11000-1-113−3−3−333-221100-1-1−i2i2−i2i2i2−i2i2−i2−33−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ4622-22-2-12-22-2-1001133−3−31-11000-1-113−3−3−333-221100-1-1i2−i2i2−i2−i2i2−i2i2−33−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ4722-22-2-12-22-2-10011−3−3331-11000-1-11−3333−3−32-2-1-10011−i2i2−i2i2−i2i2−i2i2−33−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ4822-22-2-12-22-2-10011−3−3331-11000-1-11−3333−3−32-2-1-10011i2−i2i2−i2i2−i2i2−i2−33−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ4922-22-2-12-22-2-10011−3−3331-11000-1-11−3333−3−3-221100-1-1−i2i2−i2i2i2−i2i2−i23−33−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ5022-22-2-12-22-2-10011−3−3331-11000-1-11−3333−3−3-221100-1-1i2−i2i2−i2−i2i2−i2i23−33−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ5122-22-2-1-22-22-122-1-1-1-1-1-11-112-2-211-1-1-1111100−i3i300i3−i32i−2i−2i2i0000−i3i3i3−i3−ii−iii−ii−i−333−33−3−3300000000
χ5222-22-2-1-22-22-122-1-1-1-1-1-11-112-2-211-1-1-1111100−i3i300i3−i3−2i2i2i−2i0000−i3i3i3−i3i−ii−i−ii−ii3−3−33−333−300000000
χ5322-22-2-1-22-22-122-1-1-1-1-1-11-112-2-211-1-1-1111100i3−i300−i3i32i−2i−2i2i0000i3−i3−i3i3−ii−iii−ii−i3−3−33−333−300000000
χ5422-22-2-1-22-22-122-1-1-1-1-1-11-112-2-211-1-1-1111100i3−i300−i3i3−2i2i2i−2i0000i3−i3−i3i3i−ii−i−ii−ii−333−33−3−3300000000
χ5522-22-2-1-22-22-1-2-2-1-111111-11-22211-111-1-1-1-100−i3i300i3−i300002-2-22i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3-11-111-11-100000000
χ5622-22-2-1-22-22-1-2-2-1-111111-11-22211-111-1-1-1-100−i3i300i3−i30000-222-2i3−i3−i3i3−i3i3i3−i3i3−i3−i3i31-11-1-11-1100000000
χ5722-22-2-1-22-22-1-2-2-1-111111-11-22211-111-1-1-1-100i3−i300−i3i300002-2-22−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3-11-111-11-100000000
χ5822-22-2-1-22-22-1-2-2-1-111111-11-22211-111-1-1-1-100i3−i300−i3i30000-222-2−i3i3i3−i3i3−i3−i3i3−i3i3i3−i31-11-1-11-1100000000
χ5922-2-222-222-2222222222-2-22-2-22-22-2-2-2-22-220000000000000000000000000000000000002-2000000
χ6022-2-222-222-2222222222-2-22-2-22-22-2-2-2-22-22000000000000000000000000000000000000-22000000
χ6122-2-222-222-22-2-222-2-2-2-2-2-2222-2-22-2222-22-200000000000000000000000000000000000000002-200
χ6222-2-222-222-22-2-222-2-2-2-2-2-2222-2-22-2222-22-20000000000000000000000000000000000000000-2200
χ63444-4-44-4-444400-4-400004-4-4000-44400000000000000000000000000000000000000000000000000
χ64444-4-4-244-4-4-244-2-2-2-2-2-2-222-44-4-22222-22-2200000000000000000000000000000000000000000000
χ65444-4-4-244-4-4-2-4-4-2-22222-2224-44-222-2-22-22-200000000000000000000000000000000000000000000
χ66444-4-4-2-4-444-200222323−23−23-2220002-2-2−232323−23−232300000000000000000000000000000000000000000000
χ67444-4-4-2-4-444-20022−23−232323-2220002-2-223−23−232323−2300000000000000000000000000000000000000000000
χ6844-4-4444-4-44400-4-40000-4-440004-4400000000000000000000000000000000000000000000000000
χ6944-4-44-24-4-44-200222323−23−2322-2000-22-2−2323−232323−2300000000000000000000000000000000000000000000
χ7044-4-44-24-4-44-20022−23−23232322-2000-22-223−2323−23−232300000000000000000000000000000000000000000000
χ7144-4-44-2-444-4-244-2-2-2-2-2-222-2-4-442-22222-22-200000000000000000000000000000000000000000000
χ7244-4-44-2-444-4-2-4-4-2-2222222-244-42-22-2-2-22-2200000000000000000000000000000000000000000000
χ738-800080000-842−420042−4242−4200000000000000000000000000000000000000000000000000000000000
χ748-800080000-8−424200−4242−424200000000000000000000000000000000000000000000000000000000000
χ758-8000-40000442−4243−434ζ5−4ζ7−4ζ5+4ζ74ζ13−4ζ23−4ζ13+4ζ2300000000000000000000000000000000000000000000000000000000000
χ768-8000-40000442−42−43434ζ13−4ζ23−4ζ13+4ζ234ζ5−4ζ7−4ζ5+4ζ700000000000000000000000000000000000000000000000000000000000
χ778-8000-400004−424243−43−4ζ5+4ζ74ζ5−4ζ7−4ζ13+4ζ234ζ13−4ζ2300000000000000000000000000000000000000000000000000000000000
χ788-8000-400004−4242−4343−4ζ13+4ζ234ζ13−4ζ23−4ζ5+4ζ74ζ5−4ζ700000000000000000000000000000000000000000000000000000000000

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