Finite Group Databasebeta

← Group #69938

Character table — Group #69938

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
χ19222-2-2-2-2220000222-2-2-2-200000000002i−2i000022−2−2−i2−i2i2i22i2i−2i−2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000
χ20222-2-2-2-2220000222-2-2-2-200000000002i−2i0000−2−222i2i2−i2−i22i2i−2i−2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000
χ21222-2-2-2-2220000222-2-2-2-20000000000−2i2i000022−2−2i2i2−i2−i2−2i−2i2i2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000
χ22222-2-2-2-2220000222-2-2-2-20000000000−2i2i0000−2−222−i2−i2i2i2−2i−2i2i2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000
χ23222-2-2-2-22-10000-1-1-1111133−3−333−3−3002i−2i−i3−i3i3i322−2−2−i2−i2i2i2−i−iiiζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000
χ24222-2-2-2-22-10000-1-1-1111133−3−333−3−3002i−2i−i3−i3i3i3−2−222i2i2−i2−i2−i−iii−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000
χ25222-2-2-2-22-10000-1-1-1111133−3−333−3−300−2i2ii3i3−i3−i322−2−2i2i2−i2−i2ii−i−iζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000
χ26222-2-2-2-22-10000-1-1-1111133−3−333−3−300−2i2ii3i3−i3−i3−2−222−i2−i2i2i2ii−i−i−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000
χ27222-2-2-2-22-10000-1-1-11111−3−333−3−333002i−2ii3i3−i3−i322−2−2−i2−i2i2i2−i−iiiζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000
χ28222-2-2-2-22-10000-1-1-11111−3−333−3−333002i−2ii3i3−i3−i3−2−222i2i2−i2−i2−i−iii−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000
χ29222-2-2-2-22-10000-1-1-11111−3−333−3−33300−2i2i−i3−i3i3i322−2−2i2i2−i2−i2ii−i−iζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000
χ30222-2-2-2-22-10000-1-1-11111−3−333−3−33300−2i2i−i3−i3i3i3−2−222−i2−i2i2i2ii−i−i−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000
χ3122-2-222-2-222-22-22-2-22-2-222-22-22-22-20000000000000000000000000000000000000000002i−2i
χ3222-2-222-2-222-22-22-2-22-2-222-22-22-22-2000000000000000000000000000000000000000000−2i2i
χ3322-2-222-2-22-22-222-2-22-2-22-22-22-22-22000000000000000000000000000000000000002i−2i0000
χ3422-2-222-2-22-22-222-2-22-2-22-22-22-22-2200000000000000000000000000000000000000−2i2i0000
χ352-22-22-22-222-2-22-22-2-22-222-22-2-22-220000000000000000000000000000000000002i−2i000000
χ362-22-22-22-222-2-22-22-2-22-222-22-2-22-22000000000000000000000000000000000000−2i2i000000
χ372-22-22-22-22-222-2-22-2-22-22-22-222-22-200000000000000000000000000000000000000002i−2i00
χ382-22-22-22-22-222-2-22-2-22-22-22-222-22-20000000000000000000000000000000000000000−2i2i00
χ392-2-222-2-22222-2-2-2-22-2-2222222-2-2-2-20000000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i00000000
χ402-2-222-2-22222-2-2-2-22-2-2222222-2-2-2-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ412-2-222-2-222-2-222-2-22-2-222-2-2-2-22222000000002-22-2000000002-22-22-22-20000000000000000
χ422-2-222-2-222-2-222-2-22-2-222-2-2-2-2222200000000-22-2200000000-22-22-22-220000000000000000
χ432-2-222-2-22-122-2-211-111-1-1-1-1-1-111110000−i3i3−i3i300002i−2i2i−2i−i3i3−i3i33−33−3−33−33−ii−ii−ii−ii00000000
χ442-2-222-2-22-122-2-211-111-1-1-1-1-1-111110000−i3i3−i3i30000−2i2i−2i2i−i3i3−i3i3−33−333−33−3i−ii−ii−ii−i00000000
χ452-2-222-2-22-122-2-211-111-1-1-1-1-1-111110000i3−i3i3−i300002i−2i2i−2ii3−i3i3−i3−33−333−33−3−ii−ii−ii−ii00000000
χ462-2-222-2-22-122-2-211-111-1-1-1-1-1-111110000i3−i3i3−i30000−2i2i−2i2ii3−i3i3−i33−33−3−33−33i−ii−ii−ii−i00000000
χ472-2-222-2-22-1-2-22211-111-1-11111-1-1-1-10000−i3i3−i3i32-22-20000i3−i3i3−i3-11-11-11-11−i3i3−i3i3i3−i3i3−i300000000
χ482-2-222-2-22-1-2-22211-111-1-11111-1-1-1-10000−i3i3−i3i3-22-220000i3−i3i3−i31-11-11-11-1i3−i3i3−i3−i3i3−i3i300000000
χ492-2-222-2-22-1-2-22211-111-1-11111-1-1-1-10000i3−i3i3−i32-22-20000−i3i3−i3i3-11-11-11-11i3−i3i3−i3−i3i3−i3i300000000
χ502-2-222-2-22-1-2-22211-111-1-11111-1-1-1-10000i3−i3i3−i3-22-220000−i3i3−i3i31-11-11-11-1−i3i3−i3i3i3−i3i3−i300000000
χ512-2-2-2-222220000-2-2222-2-2000000002-2002-2-222−2−22−222−200002−2−222−2−22−222−2−222−200000000
χ522-2-2-2-222220000-2-2222-2-2000000002-2002-2-22−222−22−2−220000−222−2−222−22−2−222−2−2200000000
χ532-2-2-2-222220000-2-2222-2-200000000-2200-222-22−2−222−2−2200002−2−222−2−222−2−222−2−2200000000
χ542-2-2-2-222220000-2-2222-2-200000000-2200-222-2−222−2−222−20000−222−2−222−2−222−2−222−200000000
χ552-2-2-2-2222-1000011-1-1-11133−3−3−3−3332-200-111-12−2−22−222−23−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ562-2-2-2-2222-1000011-1-1-11133−3−3−3−3332-200-111-1−222−22−2−223−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ572-2-2-2-2222-1000011-1-1-11133−3−3−3−333-22001-1-112−2−222−2−22−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ582-2-2-2-2222-1000011-1-1-11133−3−3−3−333-22001-1-11−222−2−222−2−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ592-2-2-2-2222-1000011-1-1-111−3−33333−3−32-200-111-12−2−22−222−2−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ602-2-2-2-2222-1000011-1-1-111−3−33333−3−32-200-111-1−222−22−2−22−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ612-2-2-2-2222-1000011-1-1-111−3−33333−3−3-22001-1-112−2−222−2−223−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ622-2-2-2-2222-1000011-1-1-111−3−33333−3−3-22001-1-11−222−2−222−23−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ6344-44-4-44-4400004-4-4-444-40000000000000000000000000000000000000000000000000000
χ6444-44-4-44-4-20000-2222-2-2223−23−232323−23−232300000000000000000000000000000000000000000000
χ6544-44-4-44-4-20000-2222-2-22−232323−23−232323−2300000000000000000000000000000000000000000000
χ6644-4-444-4-4-24-44-4-222-222-2-22-22-22-2200000000000000000000000000000000000000000000
χ6744-4-444-4-4-2-44-44-222-222-22-22-22-22-200000000000000000000000000000000000000000000
χ684-444-44-4-440000-44-44-44-40000000000000000000000000000000000000000000000000000
χ694-444-44-4-4-200002-22-22-2223−23−2323−232323−2300000000000000000000000000000000000000000000
χ704-444-44-4-4-200002-22-22-22−232323−2323−23−232300000000000000000000000000000000000000000000
χ714-44-44-44-4-24-4-442-222-22-2-22-222-22-200000000000000000000000000000000000000000000
χ724-44-44-44-4-2-444-42-222-22-22-22-2-22-2200000000000000000000000000000000000000000000

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