Finite Group Databasebeta

← Group #10714420

Character table — Group #10714420

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222222222222222224444444444444448888888888888888888888888888888888884848484848484848
order122223444468812122424242466688812121224242424242424668812121616161616161616242424244848484848484848484848484848484824448888
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
χ31222-2-222-22-22222222222-2-2-22-22-2-2-2-22-22-2000000000000000000000000000000000000002i−2i0000
χ32222-2-222-22-22222222222-2-2-22-22-2-2-2-22-22-200000000000000000000000000000000000000−2i2i0000
χ33222-2-222-22-22-2-222-2-2-2-22-2-22-222-2-222-22-220000000000000000000000000000000000000000002i−2i
χ34222-2-222-22-22-2-222-2-2-2-22-2-22-222-2-222-22-22000000000000000000000000000000000000000000−2i2i
χ3522-22-22-2-222222222222-22-2-2-22-22-2-2-2-22-2200000000000000000000000000000000000000002-200
χ3622-22-22-2-222222222222-22-2-2-22-22-2-2-2-22-220000000000000000000000000000000000000000-2200
χ3722-22-22-2-2222-2-222-2-2-2-2-22-222-2-22-2222-22-20000000000000000000000000000000000002-2000000
χ3822-22-22-2-2222-2-222-2-2-2-2-22-222-2-22-2222-22-2000000000000000000000000000000000000-22000000
χ3922-2-2222-2-22200-2-20000-2-2200022-20000002-22200-2-22−22−22−22−200002−22−22−22−22−22−22−22−200000000
χ4022-2-2222-2-22200-2-20000-2-2200022-20000002-22200-2-2−22−22−22−220000−22−22−22−22−22−22−22−2200000000
χ4122-2-2222-2-22200-2-20000-2-2200022-2000000-22-2-200222−22−2−22−2200002−22−22−22−2−22−22−22−2200000000
χ4222-2-2222-2-22200-2-20000-2-2200022-2000000-22-2-20022−22−222−22−20000−22−22−22−222−22−22−22−200000000
χ4322-2-222-222-2222222222-2-222-2-2-2-2222-2-2-2-20000000000002i−2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i00000000
χ4422-2-222-222-2222222222-2-222-2-2-2-2222-2-2-2-2000000000000−2i2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ4522-2-222-222-22-2-222-2-2-2-2-2-22-222-2-22-2-22222000000002-2-22000000002-22-2-22-220000000000000000
χ4622-2-222-222-22-2-222-2-2-2-2-2-22-222-2-22-2-2222200000000-222-200000000-22-222-22-20000000000000000
χ4722-2-22-12-2-22-1001133−3−311-1000-1-113−3−3−3332-2-1-100112−22−22−22−23−33−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ4822-2-22-12-2-22-1001133−3−311-1000-1-113−3−3−3332-2-1-10011−22−22−22−223−33−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ4922-2-22-12-2-22-1001133−3−311-1000-1-113−3−3−333-221100-1-12−22−2−22−22−33−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ5022-2-22-12-2-22-1001133−3−311-1000-1-113−3−3−333-221100-1-1−22−222−22−2−33−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ5122-2-22-12-2-22-10011−3−33311-1000-1-11−3333−3−32-2-1-100112−22−22−22−2−33−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ5222-2-22-12-2-22-10011−3−33311-1000-1-11−3333−3−32-2-1-10011−22−22−22−22−33−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ5322-2-22-12-2-22-10011−3−33311-1000-1-11−3333−3−3-221100-1-12−22−2−22−223−33−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ5422-2-22-12-2-22-10011−3−33311-1000-1-11−3333−3−3-221100-1-1−22−222−22−23−33−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ5522-2-22-1-222-2-122-1-1-1-1-1-111-12-2-211-1-1-1111100−i3i300i3−i300002i−2i−2i2i−i3i3i3−i3−333−33−3−33−ii−iii−ii−i00000000
χ5622-2-22-1-222-2-122-1-1-1-1-1-111-12-2-211-1-1-1111100−i3i300i3−i30000−2i2i2i−2i−i3i3i3−i33−3−33−333−3i−ii−i−ii−ii00000000
χ5722-2-22-1-222-2-122-1-1-1-1-1-111-12-2-211-1-1-1111100i3−i300−i3i300002i−2i−2i2ii3−i3−i3i33−3−33−333−3−ii−iii−ii−i00000000
χ5822-2-22-1-222-2-122-1-1-1-1-1-111-12-2-211-1-1-1111100i3−i300−i3i30000−2i2i2i−2ii3−i3−i3i3−333−33−3−33i−ii−i−ii−ii00000000
χ5922-2-22-1-222-2-1-2-2-1-1111111-1-22211-111-1-1-1-100−i3i300i3−i32-2-220000i3−i3−i3i3-11-111-11-1i3−i3−i3i3−i3i3i3−i300000000
χ6022-2-22-1-222-2-1-2-2-1-1111111-1-22211-111-1-1-1-100−i3i300i3−i3-222-20000i3−i3−i3i31-11-1-11-11−i3i3i3−i3i3−i3−i3i300000000
χ6122-2-22-1-222-2-1-2-2-1-1111111-1-22211-111-1-1-1-100i3−i300−i3i32-2-220000−i3i3i3−i3-11-111-11-1−i3i3i3−i3i3−i3−i3i300000000
χ6222-2-22-1-222-2-1-2-2-1-1111111-1-22211-111-1-1-1-100i3−i300−i3i3-222-20000−i3i3i3−i31-11-1-11-11i3−i3−i3i3−i3i3i3−i300000000
χ63444-4-44-44-44400-4-400004-4-4000-44400000000000000000000000000000000000000000000000000
χ64444-4-4-24-44-4-244-2-2-2-2-2-2-222-44-4-22222-22-2200000000000000000000000000000000000000000000
χ65444-4-4-24-44-4-2-4-4-2-22222-2224-44-222-2-22-22-200000000000000000000000000000000000000000000
χ66444-4-4-2-44-44-200222323−23−23-2220002-2-2−232323−23−232300000000000000000000000000000000000000000000
χ67444-4-4-2-44-44-20022−23−232323-2220002-2-223−23−232323−2300000000000000000000000000000000000000000000
χ6844-44-4444-4-4400-4-40000-44-40004-4400000000000000000000000000000000000000000000000000
χ6944-44-4-244-4-4-200222323−23−232-22000-22-2−2323−232323−2300000000000000000000000000000000000000000000
χ7044-44-4-244-4-4-20022−23−2323232-22000-22-223−2323−23−232300000000000000000000000000000000000000000000
χ7144-44-4-2-4-444-244-2-2-2-2-2-22-22-4-442-22222-22-200000000000000000000000000000000000000000000
χ7244-44-4-2-4-444-2-4-4-2-222222-2244-42-22-2-2-22-2200000000000000000000000000000000000000000000
χ738-800080000-8−4i24i200−4i24i2−4i24i200000000000000000000000000000000000000000000000000000000000
χ748-800080000-84i2−4i2004i2−4i24i2−4i200000000000000000000000000000000000000000000000000000000000
χ758-8000-400004−4i24i243−434ζ5+4ζ7−4ζ5−4ζ74ζ13+4ζ23−4ζ13−4ζ2300000000000000000000000000000000000000000000000000000000000
χ768-8000-400004−4i24i2−43434ζ13+4ζ23−4ζ13−4ζ234ζ5+4ζ7−4ζ5−4ζ700000000000000000000000000000000000000000000000000000000000
χ778-8000-4000044i2−4i243−43−4ζ5−4ζ74ζ5+4ζ7−4ζ13−4ζ234ζ13+4ζ2300000000000000000000000000000000000000000000000000000000000
χ788-8000-4000044i2−4i2−4343−4ζ13−4ζ234ζ13+4ζ23−4ζ5−4ζ74ζ5+4ζ700000000000000000000000000000000000000000000000000000000000

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