Finite Group Databasebeta

← Group #69964

Character table — Group #69964

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111222222222222222222224444444444444444444444444444444444442424242424242424
order1222222234444666666612121212121212122244666688888888121212122424242424242424242424242424242444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ9222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-2222200000000-2-2-2-2000000000000000000000000
χ10222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2000000002222000000000000000000000000
χ1122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000
χ1322222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000
χ1422222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000
χ1522222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-1-1-1-10000000011113333−3−3−3−33333−3−3−3−300000000
χ1622222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-1-1-1-1000000001111−3−3−3−33333−3−3−3−3333300000000
χ1722222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222111100000000-1-1-1-13333−3−3−3−3−3−3−3−3333300000000
χ1822222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222111100000000-1-1-1-1−3−3−3−333333333−3−3−3−300000000
χ192222-2-2-2-220000222-2-2-2-2000000002-20022-2-222−2−222−2−2000022−2−222−2−222−2−222−2−200000000
χ202222-2-2-2-220000222-2-2-2-2000000002-20022-2-2−2−222−2−2220000−2−222−2−222−2−222−2−22200000000
χ212222-2-2-2-220000222-2-2-2-200000000-2200-2-22222−2−2−2−222000022−2−222−2−2−2−222−2−22200000000
χ222222-2-2-2-220000222-2-2-2-200000000-2200-2-222−2−22222−2−20000−2−222−2−22222−2−222−2−200000000
χ232222-2-2-2-2-10000-1-1-1111133−3−333−3−32-200-1-11122−2−222−2−233−3−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000
χ242222-2-2-2-2-10000-1-1-1111133−3−333−3−32-200-1-111−2−222−2−22233−3−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000
χ252222-2-2-2-2-10000-1-1-1111133−3−333−3−3-220011-1-122−2−2−2−222−3−333ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000
χ262222-2-2-2-2-10000-1-1-1111133−3−333−3−3-220011-1-1−2−22222−2−2−3−333−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000
χ272222-2-2-2-2-10000-1-1-11111−3−333−3−3332-200-1-11122−2−222−2−2−3−333ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000
χ282222-2-2-2-2-10000-1-1-11111−3−333−3−3332-200-1-111−2−222−2−222−3−333−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000
χ292222-2-2-2-2-10000-1-1-11111−3−333−3−333-220011-1-122−2−2−2−22233−3−3ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000
χ302222-2-2-2-2-10000-1-1-11111−3−333−3−333-220011-1-1−2−22222−2−233−3−3−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000
χ3122-2-22-2-22222-2-22-2-22-2-222222-2-2-2-20000000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i00000000
χ3222-2-22-2-22222-2-22-2-22-2-222222-2-2-2-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ3322-2-22-2-222-2-2222-2-22-2-22-2-2-2-22222000000002-22-2000000002-22-22-22-20000000000000000
χ3422-2-22-2-222-2-2222-2-22-2-22-2-2-2-2222200000000-22-2200000000-22-22-22-220000000000000000
χ3522-2-22-2-22-122-2-2-111-111-1-1-1-1-111110000−i3i3−i3i300002i−2i2i−2i−i3i3−i3i33−33−3−33−33−ii−ii−ii−ii00000000
χ3622-2-22-2-22-122-2-2-111-111-1-1-1-1-111110000−i3i3−i3i30000−2i2i−2i2i−i3i3−i3i3−33−333−33−3i−ii−ii−ii−i00000000
χ3722-2-22-2-22-122-2-2-111-111-1-1-1-1-111110000i3−i3i3−i300002i−2i2i−2ii3−i3i3−i3−33−333−33−3−ii−ii−ii−ii00000000
χ3822-2-22-2-22-122-2-2-111-111-1-1-1-1-111110000i3−i3i3−i30000−2i2i−2i2ii3−i3i3−i33−33−3−33−33i−ii−ii−ii−i00000000
χ3922-2-22-2-22-1-2-222-111-111-11111-1-1-1-10000−i3i3−i3i32-22-20000i3−i3i3−i3-11-11-11-11−i3i3−i3i3i3−i3i3−i300000000
χ4022-2-22-2-22-1-2-222-111-111-11111-1-1-1-10000−i3i3−i3i3-22-220000i3−i3i3−i31-11-11-11-1i3−i3i3−i3−i3i3−i3i300000000
χ4122-2-22-2-22-1-2-222-111-111-11111-1-1-1-10000i3−i3i3−i32-22-20000−i3i3−i3i3-11-11-11-11i3−i3i3−i3−i3i3−i3i300000000
χ4222-2-22-2-22-1-2-222-111-111-11111-1-1-1-10000i3−i3i3−i3-22-220000−i3i3−i3i31-11-11-11-1−i3i3−i3i3i3−i3i3−i300000000
χ4322-2-2-222-2200002-2-2-222-200000000002i−2i00002−2−22−i2i2i2−i22i−2i−2i2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i200000000
χ4422-2-2-222-2200002-2-2-222-200000000002i−2i0000−222−2i2−i2−i2i22i−2i−2i2i−222−2−222−2i2−i2−i2i2i2−i2−i2i200000000
χ4522-2-2-222-2200002-2-2-222-20000000000−2i2i00002−2−22i2−i2−i2i2−2i2i2i−2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i200000000
χ4622-2-2-222-2200002-2-2-222-20000000000−2i2i0000−222−2−i2i2i2−i2−2i2i2i−2i−222−2−222−2−i2i2i2−i2−i2i2i2−i200000000
χ4722-2-2-222-2-10000-1111-1-1133−3−3−3−333002i−2i−i3i3i3−i32−2−22−i2i2i2−i2−iii−iζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000
χ4822-2-2-222-2-10000-1111-1-1133−3−3−3−333002i−2i−i3i3i3−i3−222−2i2−i2−i2i2−iii−i−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000
χ4922-2-2-222-2-10000-1111-1-1133−3−3−3−33300−2i2ii3−i3−i3i32−2−22i2−i2−i2i2i−i−iiζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000
χ5022-2-2-222-2-10000-1111-1-1133−3−3−3−33300−2i2ii3−i3−i3i3−222−2−i2i2i2−i2i−i−ii−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000
χ5122-2-2-222-2-10000-1111-1-11−3−33333−3−3002i−2ii3−i3−i3i32−2−22−i2i2i2−i2−iii−iζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000
χ5222-2-2-222-2-10000-1111-1-11−3−33333−3−3002i−2ii3−i3−i3i3−222−2i2−i2−i2i2−iii−i−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000
χ5322-2-2-222-2-10000-1111-1-11−3−33333−3−300−2i2i−i3i3i3−i32−2−22i2−i2−i2i2i−i−iiζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000
χ5422-2-2-222-2-10000-1111-1-11−3−33333−3−300−2i2i−i3i3i3−i3−222−2−i2i2i2−i2i−i−ii−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000
χ552-22-2-22-2222-22-2-22-2-22-222-22-22-22-200000000000000000000000000000000000000002-200
χ562-22-2-22-2222-22-2-22-2-22-222-22-22-22-20000000000000000000000000000000000000000-2200
χ572-22-2-22-222-22-22-22-2-22-22-22-22-22-220000000000000000000000000000000000002-2000000
χ582-22-2-22-222-22-22-22-2-22-22-22-22-22-22000000000000000000000000000000000000-22000000
χ592-2-22-2-22222-2-22-2-22-2-2222-22-2-22-22000000000000000000000000000000000000002-20000
χ602-2-22-2-22222-2-22-2-22-2-2222-22-2-22-2200000000000000000000000000000000000000-220000
χ612-2-22-2-2222-222-2-2-22-2-222-22-222-22-20000000000000000000000000000000000000000002-2
χ622-2-22-2-2222-222-2-2-22-2-222-22-222-22-2000000000000000000000000000000000000000000-22
χ634-44-44-44-440000-44-44-44-40000000000000000000000000000000000000000000000000000
χ644-44-44-44-4-200002-22-22-2223−23−232323−23−232300000000000000000000000000000000000000000000
χ654-44-44-44-4-200002-22-22-22−232323−23−232323−2300000000000000000000000000000000000000000000
χ664-44-4-44-44-24-44-42-222-22-2-22-22-22-2200000000000000000000000000000000000000000000
χ674-44-4-44-44-2-44-442-222-22-22-22-22-22-200000000000000000000000000000000000000000000
χ684-4-4444-4-440000-4-4444-4-40000000000000000000000000000000000000000000000000000
χ694-4-4444-4-4-2000022-2-2-22223−23−2323−232323−2300000000000000000000000000000000000000000000
χ704-4-4444-4-4-2000022-2-2-222−232323−2323−23−232300000000000000000000000000000000000000000000
χ714-4-44-4-444-24-4-4422-222-2-2-22-222-22-200000000000000000000000000000000000000000000
χ724-4-44-4-444-2-444-422-222-2-22-22-2-22-2200000000000000000000000000000000000000000000

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