Finite Group Databasebeta

← Group #71821

Character table — Group #71821

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order1222444434444444466612121212246612121212121212121212444412121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1111111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1111111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1111111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1111111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-11-1-1-1-11111111-1-1-1-1-11-1-111-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111-1-1-1-11-1-1-1-11111111-1-1-1-1-11-1-111-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-11-1-1-1-11111111-1-1-1-1-11-1-111-1-1-1-11111-111-1-1-11111-1-111-1-1-1-111-1-11111-1-1
χ161111-1-1-1-11-1-1-1-11111111-1-1-1-1-11-1-111-1-1-1-11111-111-1-1-11111-1-1-1-11111-1-111-1-1-1-111
χ1722222222222-2-222-2-22222222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000
χ18222222222-2-222-2-2222222222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000
χ1922222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2022222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2122222222-122-2-222-2-2-1-1-1-1-1-1-1-2-21111-1-111-1-1110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2222222222-122-2-222-2-2-1-1-1-1-1-1-1-2-21111-1-111-1-1110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2322222222-1-2-222-2-222-1-1-1-1-1-1-1-2-2111111-1-111-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2422222222-1-2-222-2-222-1-1-1-1-1-1-1-2-2111111-1-111-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ272222-2-2-2-2222-2-2-2-222222-2-2-2-22-222-2-222-2-2-2-2220000000000000000000000000000
χ282222-2-2-2-22-2-22222-2-2222-2-2-2-22-222-2-2-2-22222-2-20000000000000000000000000000
χ292222-2-2-2-2-12222-2-2-2-2-1-1-11111-2211-1-1-1-1-1-111112-22-2-1-111-1-1110000000000000000
χ302222-2-2-2-2-12222-2-2-2-2-1-1-11111-2211-1-1-1-1-1-11111-22-2211-1-111-1-10000000000000000
χ312222-2-2-2-2-122-2-2-2-222-1-1-111112-2-1-111-1-11111-1-10000−i3i3i3−i3−i3i3i3−i30000000000000000
χ322222-2-2-2-2-122-2-2-2-222-1-1-111112-2-1-111-1-11111-1-10000i3−i3−i3i3i3−i3−i3i30000000000000000
χ332222-2-2-2-2-1-2-22222-2-2-1-1-111112-2-1-11111-1-1-1-1110000−i3i3i3−i3i3−i3−i3i30000000000000000
χ342222-2-2-2-2-1-2-22222-2-2-1-1-111112-2-1-11111-1-1-1-1110000i3−i3−i3i3−i3i3i3−i30000000000000000
χ352222-2-2-2-2-1-2-2-2-22222-1-1-11111-2211-1-11111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ362222-2-2-2-2-1-2-2-2-22222-1-1-11111-2211-1-11111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ372-22-22i2i−2i−2i2002-2002i−2i-22-22i2i−2i−2i000000002-2002i−2i0000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ382-22-22i2i−2i−2i2002-2002i−2i-22-22i2i−2i−2i000000002-2002i−2i000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ392-22-22i2i−2i−2i200-2200−2i2i-22-22i2i−2i−2i00000000-2200−2i2i0000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i00000000
χ402-22-22i2i−2i−2i200-2200−2i2i-22-22i2i−2i−2i00000000-2200−2i2i000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i00000000
χ412-22-2−2i−2i2i2i2002-200−2i2i-22-2−2i−2i2i2i000000002-200−2i2i0000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ422-22-2−2i−2i2i2i2002-200−2i2i-22-2−2i−2i2i2i000000002-200−2i2i000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ432-22-2−2i−2i2i2i200-22002i−2i-22-2−2i−2i2i2i00000000-22002i−2i0000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i00000000
χ442-22-2−2i−2i2i2i200-22002i−2i-22-2−2i−2i2i2i00000000-22002i−2i000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00000000
χ452-2-222i−2i2i−2i22-2002i−2i00-2-222i−2i2i−2i0000002-2002i−2i00000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ462-2-222i−2i2i−2i22-2002i−2i00-2-222i−2i2i−2i0000002-2002i−2i0000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ472-2-222i−2i2i−2i2-2200−2i2i00-2-222i−2i2i−2i000000-2200−2i2i00000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ482-2-222i−2i2i−2i2-2200−2i2i00-2-222i−2i2i−2i000000-2200−2i2i0000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ492-2-22−2i2i−2i2i22-200−2i2i00-2-22−2i2i−2i2i0000002-200−2i2i00000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ502-2-22−2i2i−2i2i22-200−2i2i00-2-22−2i2i−2i2i0000002-200−2i2i0000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ512-2-22−2i2i−2i2i2-22002i−2i00-2-22−2i2i−2i2i000000-22002i−2i00000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i
χ522-2-22−2i2i−2i2i2-22002i−2i00-2-22−2i2i−2i2i000000-22002i−2i0000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i
χ5344-4-44-4-444000000004-4-44-4-44000000000000000000000000000000000000000000
χ5444-4-44-4-44-200000000-222-222-200−2i32i3−2i32i3000000000000000000000000000000000000
χ5544-4-44-4-44-200000000-222-222-2002i3−2i32i3−2i3000000000000000000000000000000000000
χ5644-4-4-444-44000000004-4-4-444-4000000000000000000000000000000000000000000
χ5744-4-4-444-4-200000000-2222-2-2200−2i32i32i3−2i3000000000000000000000000000000000000
χ5844-4-4-444-4-200000000-2222-2-22002i3−2i3−2i32i3000000000000000000000000000000000000
χ594-44-44i4i−4i−4i-2004-4004i−4i2-22−2i−2i2i2i00000000-2200−2i2i0000000000000000000000000000
χ604-44-44i4i−4i−4i-200-4400−4i4i2-22−2i−2i2i2i000000002-2002i−2i0000000000000000000000000000
χ614-44-4−4i−4i4i4i-2004-400−4i4i2-222i2i−2i−2i00000000-22002i−2i0000000000000000000000000000
χ624-44-4−4i−4i4i4i-200-44004i−4i2-222i2i−2i−2i000000002-200−2i2i0000000000000000000000000000
χ634-4-444i−4i4i−4i-24-4004i−4i0022-2−2i2i−2i2i000000-2200−2i2i000000000000000000000000000000
χ644-4-444i−4i4i−4i-2-4400−4i4i0022-2−2i2i−2i2i0000002-2002i−2i000000000000000000000000000000
χ654-4-44−4i4i−4i4i-24-400−4i4i0022-22i−2i2i−2i000000-22002i−2i000000000000000000000000000000
χ664-4-44−4i4i−4i4i-2-44004i−4i0022-22i−2i2i−2i0000002-200−2i2i000000000000000000000000000000

Here i is the imaginary unit (i² = −1).