Finite Group Databasebeta

← Group #70482

Character table — Group #70482

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111222222222222222222224444444444444444444444444444444444442424242424242424
order12222222344446666666121212121212121244448888888812121212121212122424242424242424242424242424242422444444
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
χ1922-22-22-2-22000022-2-22-2-200000000002i−2i22−2−2−i2−i2i2i200002i2i−2i−2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000
χ2022-22-22-2-22000022-2-22-2-200000000002i−2i−2−222i2i2−i2−i200002i2i−2i−2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000
χ2122-22-22-2-22000022-2-22-2-20000000000−2i2i22−2−2i2i2−i2−i20000−2i−2i2i2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000
χ2222-22-22-2-22000022-2-22-2-20000000000−2i2i−2−222−i2−i2i2i20000−2i−2i2i2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000
χ2322-22-22-2-2-10000-1-111-111333−3−3−33−3002i−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
χ2422-22-22-2-2-10000-1-111-111333−3−3−33−3002i−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
χ2522-22-22-2-2-10000-1-111-111333−3−3−33−300−2i2i22−2−2i2i2−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
χ2622-22-22-2-2-10000-1-111-111333−3−3−33−300−2i2i−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
χ2722-22-22-2-2-10000-1-111-111−3−3−3333−33002i−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
χ2822-22-22-2-2-10000-1-111-111−3−3−3333−33002i−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
χ2922-22-22-2-2-10000-1-111-111−3−3−3333−3300−2i2i22−2−2i2i2−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
χ3022-22-22-2-2-10000-1-111-111−3−3−3333−3300−2i2i−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
χ3122-2-2-2-222222-2-22-22-2-22-222-222-2-2-200000000000000000000000000000000000000002i−2i00
χ3222-2-2-2-222222-2-22-22-2-22-222-222-2-2-20000000000000000000000000000000000000000−2i2i00
χ3322-2-2-2-2222-2-2222-22-2-22-2-2-22-2-22220000000000000000000000000000000000000000002-2
χ3422-2-2-2-2222-2-2222-22-2-22-2-2-22-2-2222000000000000000000000000000000000000000000-22
χ352-222-2-22-220000-2-2222-2-2000000002-200−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ362-222-2-22-220000-2-2222-2-2000000002-200i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ372-222-2-22-220000-2-2222-2-200000000-2200−i2i2−i2i2i2−i2i2−i2-22-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ382-222-2-22-220000-2-2222-2-200000000-2200i2−i2i2−i2−i2i2−i2i2-22-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ392-222-2-22-2-1000011-1-1-1113−333−3−3−332-200−i2i2−i2i2−i2i2−i2i2-11-113−33−3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ402-222-2-22-2-1000011-1-1-1113−333−3−3−332-200i2−i2i2−i2i2−i2i2−i2-11-113−33−3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ412-222-2-22-2-1000011-1-1-1113−333−3−3−33-2200−i2i2−i2i2i2−i2i2−i21-11-1−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ422-222-2-22-2-1000011-1-1-1113−333−3−3−33-2200i2−i2i2−i2−i2i2−i2i21-11-1−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ432-222-2-22-2-1000011-1-1-111−33−3−3333−32-200−i2i2−i2i2−i2i2−i2i2-11-11−33−33ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ442-222-2-22-2-1000011-1-1-111−33−3−3333−32-200i2−i2i2−i2i2−i2i2−i2-11-11−33−33−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ452-222-2-22-2-1000011-1-1-111−33−3−3333−3-2200−i2i2−i2i2i2−i2i2−i21-11-13−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ462-222-2-22-2-1000011-1-1-111−33−3−3333−3-2200i2−i2i2−i2−i2i2−i2i21-11-13−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ472-22-2-22-2222-22-2-22-22-22-2-2222-22-2-2000000000000000000000000000000000000002i−2i0000
χ482-22-2-22-2222-22-2-22-22-22-2-2222-22-2-200000000000000000000000000000000000000−2i2i0000
χ492-22-2-22-222-22-22-22-22-22-22-2-2-22-2220000000000000000000000000000000000002-2000000
χ502-22-2-22-222-22-22-22-22-22-22-2-2-22-222000000000000000000000000000000000000-22000000
χ512-2-222-2-2222-2-22-2-2-2-2222-22-22-2-222000000002-2-2200000000000000002-2-222-2-2200000000
χ522-2-222-2-2222-2-22-2-2-2-2222-22-22-2-22200000000-222-20000000000000000-222-2-222-200000000
χ532-2-222-2-222-222-2-2-2-2-22222-22-222-2-200002i−2i−2i2i0000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ542-2-222-2-222-222-2-2-2-2-22222-22-222-2-20000−2i2i2i−2i000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ552-2-222-2-22-12-2-221111-1-1-11-11-111-1-1000000002-2-22−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3-111-1-111-100000000
χ562-2-222-2-22-12-2-221111-1-1-11-11-111-1-1000000002-2-22i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3-111-1-111-100000000
χ572-2-222-2-22-12-2-221111-1-1-11-11-111-1-100000000-222-2−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i31-1-111-1-1100000000
χ582-2-222-2-22-12-2-221111-1-1-11-11-111-1-100000000-222-2i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i31-1-111-1-1100000000
χ592-2-222-2-22-1-222-21111-1-1-1-11-11-1-11100002i−2i−2i2i0000−i3i3i3−i3−i3i3i3−i3−iii−i−iii−i−333−33−3−3300000000
χ602-2-222-2-22-1-222-21111-1-1-1-11-11-1-11100002i−2i−2i2i0000i3−i3−i3i3i3−i3−i3i3−iii−i−iii−i3−3−33−333−300000000
χ612-2-222-2-22-1-222-21111-1-1-1-11-11-1-1110000−2i2i2i−2i0000−i3i3i3−i3−i3i3i3−i3i−i−iii−i−ii3−3−33−333−300000000
χ622-2-222-2-22-1-222-21111-1-1-1-11-11-1-1110000−2i2i2i−2i0000i3−i3−i3i3i3−i3−i3i3i−i−iii−i−ii−333−33−3−3300000000
χ63444-44-4-4-4400004-4-44-4-440000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-20000-222-222-22323−23−23−2323−232300000000000000000000000000000000000000000000
χ65444-44-4-4-4-20000-222-222-2−23−23232323−2323−2300000000000000000000000000000000000000000000
χ6644-4-4-4-444-244-4-4-22-222-22-2-22-2-222200000000000000000000000000000000000000000000
χ6744-4-4-4-444-2-4-444-22-222-2222-222-2-2-200000000000000000000000000000000000000000000
χ684-44-4-44-44-24-44-42-22-22-222-2-2-22-22200000000000000000000000000000000000000000000
χ694-44-4-44-44-2-44-442-22-22-22-2222-22-2-200000000000000000000000000000000000000000000
χ704-4-4-4444-440000-444-4-4-440000000000000000000000000000000000000000000000000000
χ714-4-4-4444-4-200002-2-2222-223−23−2323−232323−2300000000000000000000000000000000000000000000
χ724-4-4-4444-4-200002-2-2222-2−232323−2323−23−232300000000000000000000000000000000000000000000

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