Finite Group Databasebeta

← Group #68642

Character table — Group #68642

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111222222222222222222224444444444444444444444444444444444442424242424242424
order12222222344446666666121212121212121244448888888812121212121212122424242424242424242424242424242444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ9222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-2000000002222-2-2-2-2000000000000000000000000
χ10222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22200000000-2-2-2-22222000000000000000000000000
χ1122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000
χ1322222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000
χ1422222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000
χ1522222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−300000000
χ1622222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−3333300000000
χ1722222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−3333300000000
χ1822222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−300000000
χ1922-22-22-2-2222-2-222-2-22-2-22222-2-2-2-20000000000000000000000000000000000002-2000000
χ2022-22-22-2-2222-2-222-2-22-2-22222-2-2-2-2000000000000000000000000000000000000-22000000
χ2122-22-22-2-22-2-22222-2-22-2-2-2-2-2-22222000000000000000000000000000000000000002i−2i0000
χ2222-22-22-2-22-2-22222-2-22-2-2-2-2-2-2222200000000000000000000000000000000000000−2i2i0000
χ2322-2-22-2-22200002-22-2-22-2000000002-200−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ2422-2-22-2-22200002-22-2-22-2000000002-200i2i2−i2−i2i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ2522-2-22-2-22200002-22-2-22-200000000-2200−i2−i2i2i2i2i2−i2−i2-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ2622-2-22-2-22200002-22-2-22-200000000-2200i2i2−i2−i2−i2−i2i2i2-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ2722-2-22-2-22-10000-11-111-1133−3−333−3−32-200−i2−i2i2i2−i2−i2i2i2-1-11133−3−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000
χ2822-2-22-2-22-10000-11-111-1133−3−333−3−32-200i2i2−i2−i2i2i2−i2−i2-1-11133−3−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000
χ2922-2-22-2-22-10000-11-111-1133−3−333−3−3-2200−i2−i2i2i2i2i2−i2−i211-1-1−3−333ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000
χ3022-2-22-2-22-10000-11-111-1133−3−333−3−3-2200i2i2−i2−i2−i2−i2i2i211-1-1−3−333−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000
χ3122-2-22-2-22-10000-11-111-11−3−333−3−3332-200−i2−i2i2i2−i2−i2i2i2-1-111−3−333ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000
χ3222-2-22-2-22-10000-11-111-11−3−333−3−3332-200i2i2−i2−i2i2i2−i2−i2-1-111−3−333−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000
χ3322-2-22-2-22-10000-11-111-11−3−333−3−333-2200−i2−i2i2i2i2i2−i2−i211-1-133−3−3ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000
χ3422-2-22-2-22-10000-11-111-11−3−333−3−333-2200i2i2−i2−i2−i2−i2i2i211-1-133−3−3−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000
χ352-222-2-2-2222-22-2-2-2222-2-22-22-22-22-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ362-222-2-2-2222-22-2-2-2222-2-22-22-22-22-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ372-222-2-2-222-22-22-2-2222-2-2-22-22-22-2200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ382-222-2-2-222-22-22-2-2222-2-2-22-22-22-220000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ392-222-2-2-22-12-22-211-1-1-111-11-11-11-11000000002i−2i2i−2i3−33−33−33−3−i3i3−i3i3i3−i3i3−i3−ii−ii−ii−ii00000000
χ402-222-2-2-22-12-22-211-1-1-111-11-11-11-11000000002i−2i2i−2i−33−33−33−33i3−i3i3−i3−i3i3−i3i3−ii−ii−ii−ii00000000
χ412-222-2-2-22-12-22-211-1-1-111-11-11-11-1100000000−2i2i−2i2i3−33−33−33−3i3−i3i3−i3−i3i3−i3i3i−ii−ii−ii−i00000000
χ422-222-2-2-22-12-22-211-1-1-111-11-11-11-1100000000−2i2i−2i2i−33−33−33−33−i3i3−i3i3i3−i3i3−i3i−ii−ii−ii−i00000000
χ432-222-2-2-22-1-22-2211-1-1-1111-11-11-11-100002i−2i2i−2i00003−33−3−33−33−ii−ii−ii−iii3−i3i3−i3−i3i3−i3i300000000
χ442-222-2-2-22-1-22-2211-1-1-1111-11-11-11-100002i−2i2i−2i0000−33−333−33−3−ii−ii−ii−ii−i3i3−i3i3i3−i3i3−i300000000
χ452-222-2-2-22-1-22-2211-1-1-1111-11-11-11-10000−2i2i−2i2i00003−33−3−33−33i−ii−ii−ii−i−i3i3−i3i3i3−i3i3−i300000000
χ462-222-2-2-22-1-22-2211-1-1-1111-11-11-11-10000−2i2i−2i2i0000−33−333−33−3i−ii−ii−ii−ii3−i3i3−i3−i3i3−i3i300000000
χ472-2-222-22-222-2-22-2-2-2-22222-22-2-22-220000000000000000000000000000000000000000002i−2i
χ482-2-222-22-222-2-22-2-2-2-22222-22-2-22-22000000000000000000000000000000000000000000−2i2i
χ492-2-222-22-22-222-2-2-2-2-2222-22-222-22-200000000000000000000000000000000000000002i−2i00
χ502-2-222-22-22-222-2-2-2-2-2222-22-222-22-20000000000000000000000000000000000000000−2i2i00
χ512-2-2-2-222220000-222-2-2-2200000000002-22−2−222−2−2200002-2-222−2−222−2−222−2−222−2−2200000000
χ522-2-2-2-222220000-222-2-2-2200000000002-2−222−2−222−200002-2-22−222−2−222−2−222−2−222−200000000
χ532-2-2-2-222220000-222-2-2-220000000000-222−2−22−222−20000-222-22−2−222−2−22−222−2−222−200000000
χ542-2-2-2-222220000-222-2-2-220000000000-22−222−22−2−220000-222-2−222−2−222−22−2−222−2−2200000000
χ552-2-2-2-2222-100001-1-1111-13−3−333−3−33002-22−2−222−2−22−333−3-111-1ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ562-2-2-2-2222-100001-1-1111-13−3−333−3−33002-2−222−2−222−2−333−3-111-1−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ572-2-2-2-2222-100001-1-1111-13−3−333−3−3300-222−2−22−222−23−3−331-1-11ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ582-2-2-2-2222-100001-1-1111-13−3−333−3−3300-22−222−22−2−223−3−331-1-11−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ592-2-2-2-2222-100001-1-1111-1−333−3−333−3002-22−2−222−2−223−3−33-111-1ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ602-2-2-2-2222-100001-1-1111-1−333−3−333−3002-2−222−2−222−23−3−33-111-1−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ612-2-2-2-2222-100001-1-1111-1−333−3−333−300-222−2−22−222−2−333−31-1-11ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ622-2-2-2-2222-100001-1-1111-1−333−3−333−300-22−222−22−2−22−333−31-1-11−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ63444-4-4-44-4400004-4-44-4-440000000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-20000-222-222-22323−23−23−23−23232300000000000000000000000000000000000000000000
χ65444-4-4-44-4-20000-222-222-2−23−2323232323−23−2300000000000000000000000000000000000000000000
χ6644-44-44-4-4-244-4-4-2-222-222-2-2-2-2222200000000000000000000000000000000000000000000
χ6744-44-44-4-4-2-4-444-2-222-2222222-2-2-2-200000000000000000000000000000000000000000000
χ684-44-444-4-440000-44-44-44-40000000000000000000000000000000000000000000000000000
χ694-44-444-4-4-200002-22-22-2223−23−2323−232323−2300000000000000000000000000000000000000000000
χ704-44-444-4-4-200002-22-22-22−232323−2323−23−232300000000000000000000000000000000000000000000
χ714-4-444-44-4-24-4-442222-2-2-2-22-222-22-200000000000000000000000000000000000000000000
χ724-4-444-44-4-2-444-42222-2-2-22-22-2-22-2200000000000000000000000000000000000000000000

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