Finite Group Databasebeta

← Group #68690

Character table — Group #68690

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
χ19222-2-22-2-2222-2-222-2-22-2-22222-2-2-2-2000000000000000000000000000000000000002-20000
χ20222-2-22-2-2222-2-222-2-22-2-22222-2-2-2-200000000000000000000000000000000000000-220000
χ21222-2-22-2-22-2-22222-2-22-2-2-2-2-2-222220000000000000000000000000000000000002i−2i000000
χ22222-2-22-2-22-2-22222-2-22-2-2-2-2-2-22222000000000000000000000000000000000000−2i2i000000
χ2322-2-22-22-2200002-22-2-22-200000000002i−2i22−2−2−i2−i2i2i200002i2i−2i−2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000
χ2422-2-22-22-2200002-22-2-22-200000000002i−2i−2−222i2i2−i2−i200002i2i−2i−2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000
χ2522-2-22-22-2200002-22-2-22-20000000000−2i2i22−2−2i2i2−i2−i20000−2i−2i2i2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000
χ2622-2-22-22-2200002-22-2-22-20000000000−2i2i−2−222−i2−i2i2i20000−2i−2i2i2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000
χ2722-2-22-22-2-10000-11-111-1133−3−333−3−3002i−2i22−2−2−i2−i2i2i2−i3−i3i3i3−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
χ2822-2-22-22-2-10000-11-111-1133−3−333−3−3002i−2i−2−222i2i2−i2−i2−i3−i3i3i3−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
χ2922-2-22-22-2-10000-11-111-1133−3−333−3−300−2i2i22−2−2i2i2−i2−i2i3i3−i3−i3ii−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
χ3022-2-22-22-2-10000-11-111-1133−3−333−3−300−2i2i−2−222−i2−i2i2i2i3i3−i3−i3ii−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
χ3122-2-22-22-2-10000-11-111-11−3−333−3−333002i−2i22−2−2−i2−i2i2i2i3i3−i3−i3−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
χ3222-2-22-22-2-10000-11-111-11−3−333−3−333002i−2i−2−222i2i2−i2−i2i3i3−i3−i3−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
χ3322-2-22-22-2-10000-11-111-11−3−333−3−33300−2i2i22−2−2i2i2−i2−i2−i3−i3i3i3ii−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
χ3422-2-22-22-2-10000-11-111-11−3−333−3−33300−2i2i−2−222−i2−i2i2i2−i3−i3i3i3ii−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
χ352-22-22-2-2220000-222-2-2-22000000002i−2i00−i2i2−i2i22−22−22i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ362-22-22-2-2220000-222-2-2-22000000002i−2i00i2−i2i2−i2−22−222i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ372-22-22-2-2220000-222-2-2-2200000000−2i2i00−i2i2−i2i2−22−22−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ382-22-22-2-2220000-222-2-2-2200000000−2i2i00i2−i2i2−i22−22−2−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ392-22-22-2-22-100001-1-1111-13−33−33−33−32i−2i00−i2i2−i2i22−22−2−ii−ii−i3i3−i3i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000
χ402-22-22-2-22-100001-1-1111-13−33−33−33−32i−2i00i2−i2i2−i2−22−22−ii−ii−i3i3−i3i3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000
χ412-22-22-2-22-100001-1-1111-13−33−33−33−3−2i2i00−i2i2−i2i2−22−22i−ii−ii3−i3i3−i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000
χ422-22-22-2-22-100001-1-1111-13−33−33−33−3−2i2i00i2−i2i2−i22−22−2i−ii−ii3−i3i3−i3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000
χ432-22-22-2-22-100001-1-1111-1−33−33−33−332i−2i00−i2i2−i2i22−22−2−ii−iii3−i3i3−i3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000
χ442-22-22-2-22-100001-1-1111-1−33−33−33−332i−2i00i2−i2i2−i2−22−22−ii−iii3−i3i3−i3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
χ452-22-22-2-22-100001-1-1111-1−33−33−33−33−2i2i00−i2i2−i2i2−22−22i−ii−i−i3i3−i3i3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
χ462-22-22-2-22-100001-1-1111-1−33−33−33−33−2i2i00i2−i2i2−i22−22−2i−ii−i−i3i3−i3i3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000
χ472-2-2222-2-222-22-2-2-2222-2-22-2-222-2-22000000002i−2i−2i2i00000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ482-2-2222-2-222-22-2-2-2222-2-22-2-222-2-2200000000−2i2i2i−2i0000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ492-2-2222-2-22-22-22-2-2222-2-2-222-2-222-200002i−2i−2i2i0000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ502-2-2222-2-22-22-22-2-2222-2-2-222-2-222-20000−2i2i2i−2i000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ512-2-2222-2-2-12-22-211-1-1-111-111-1-111-1000000002i−2i−2i2i3−3−33−333−3i3−i3−i3i3−i3i3i3−i3−iii−i−iii−i00000000
χ522-2-2222-2-2-12-22-211-1-1-111-111-1-111-1000000002i−2i−2i2i−333−33−3−33−i3i3i3−i3i3−i3−i3i3−iii−i−iii−i00000000
χ532-2-2222-2-2-12-22-211-1-1-111-111-1-111-100000000−2i2i2i−2i3−3−33−333−3−i3i3i3−i3i3−i3−i3i3i−i−iii−i−ii00000000
χ542-2-2222-2-2-12-22-211-1-1-111-111-1-111-100000000−2i2i2i−2i−333−33−3−33i3−i3−i3i3−i3i3i3−i3i−i−iii−i−ii00000000
χ552-2-2222-2-2-1-22-2211-1-1-1111-1-111-1-1100002i−2i−2i2i00003−3−333−3−33−iii−i−iii−i−i3i3i3−i3i3−i3−i3i300000000
χ562-2-2222-2-2-1-22-2211-1-1-1111-1-111-1-1100002i−2i−2i2i0000−333−3−333−3−iii−i−iii−ii3−i3−i3i3−i3i3i3−i300000000
χ572-2-2222-2-2-1-22-2211-1-1-1111-1-111-1-110000−2i2i2i−2i00003−3−333−3−33i−i−iii−i−iii3−i3−i3i3−i3i3i3−i300000000
χ582-2-2222-2-2-1-22-2211-1-1-1111-1-111-1-110000−2i2i2i−2i0000−333−3−333−3i−i−iii−i−ii−i3i3i3−i3i3−i3−i3i300000000
χ592-2-2-2-222222-2-22-2-2-2-22222-2-22-222-200000000000000000000000000000000000000002-200
χ602-2-2-2-222222-2-22-2-2-2-22222-2-22-222-20000000000000000000000000000000000000000-2200
χ612-2-2-2-22222-222-2-2-2-2-2222-222-22-2-220000000000000000000000000000000000000000002-2
χ622-2-2-2-22222-222-2-2-2-2-2222-222-22-2-22000000000000000000000000000000000000000000-22
χ63444-4-44-4-4-244-4-4-2-222-222-2-2-2-2222200000000000000000000000000000000000000000000
χ64444-4-44-4-4-2-4-444-2-222-2222222-2-2-2-200000000000000000000000000000000000000000000
χ6544-44-4-4-44400004-4-44-4-440000000000000000000000000000000000000000000000000000
χ6644-44-4-4-44-20000-222-222-22323−23−23−23−23232300000000000000000000000000000000000000000000
χ6744-44-4-4-44-20000-222-222-2−23−2323232323−23−2300000000000000000000000000000000000000000000
χ684-444-4-44-440000-44-44-44-40000000000000000000000000000000000000000000000000000
χ694-444-4-44-4-200002-22-22-2223−2323−23−2323−232300000000000000000000000000000000000000000000
χ704-444-4-44-4-200002-22-22-22−2323−232323−2323−2300000000000000000000000000000000000000000000
χ714-4-4-4-4444-24-4-442222-2-2-2-222-22-2-2200000000000000000000000000000000000000000000
χ724-4-4-4-4444-2-444-42222-2-2-22-2-22-222-200000000000000000000000000000000000000000000

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