Finite Group Databasebeta

← Group #13166578

Character table — Group #13166578

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122224444444444466888888888888888888889999121818181818181818242424242424242436363636363636363636363636545454545454108108108
order1222366623366666666443366666666666666666644444888812121212121212121212121248812122424242424242424448888488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-11-1-1
χ311111111111111111111111111111111111111111-1-1-1-11ii−i−i-1-1-1-111111111-1i−i-1-1iiii−i−i−i−i-1-1ii−i−i-1i−i
χ411111111111111111111111111111111111111111-1-1-1-11−i−iii-1-1-1-111111111-1−ii-1-1−i−i−i−iiiii-1-1−i−iii-1−ii
χ51111111111111111111-1-1111111111111111111111111-111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1
χ61111111111111111111-1-1111111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-11111-111
χ71111111111111111111-1-111111111111111111111-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1i−i-1-1iiii−i−i−i−i11−i−iii1−ii
χ81111111111111111111-1-111111111111111111111-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-1−ii-1-1−i−i−i−iiiii11ii−i−i1i−i
χ911111111-111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111111111111-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1
χ1011111111-111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-111
χ1111111111-111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11111-1-1-1-11−ii11ii−i−i−i−iii-1-1ii−i−i1−ii
χ1211111111-111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-11111-1-1-1-11i−i11−i−iiiii−i−i-1-1−i−iii1i−i
χ1311111111-111-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111
χ1411111111-111-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11111-111-1-1-1-111-1-111-1-111111-1-1
χ1511111111-111-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11ii−i−i-1-1-1-1-1-1-1-111111−ii11ii−i−i−i−iii11−i−iii-1i−i
χ1611111111-111-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11−i−iii-1-1-1-1-1-1-1-111111i−i11−i−iiiii−i−i11ii−i−i-1−ii
χ172222-1-1-1-1222-1-122222200-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222202222-1-1-1-100000000222-1-1-1-1-1-1-1-1-1-1000000000
χ182222-1-1-1-1222-1-122222200-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122220-2-2-2-2-1-1-1-1000000002-2-2-1-111111111000000000
χ192222-1-1-1-1222-1-122222200-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-202i2i−2i−2i111100000000-22i−2i11−i−i−i−iiiii000000000
χ202222-1-1-1-1222-1-122222200-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20−2i−2i2i2i111100000000-2−2i2i11iiii−i−i−i−i000000000
χ212222-1-1-1-1-2221122222200-1-1-2-2-2-2-1-1-1-1-1-111111111222202222-1-1-1-100000000-2-2-211-1-111-1-111000000000
χ222222-1-1-1-1-2221122222200-1-1-2-2-2-2-1-1-1-1-1-11111111122220-2-2-2-2-1-1-1-100000000-2221111-1-111-1-1000000000
χ232222-1-1-1-1-2221122222200-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2-2-202i2i−2i−2i1111000000002−2i2i-1-1−i−iiiii−i−i000000000
χ242222-1-1-1-1-2221122222200-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2-2-20−2i−2i2i2i11110000000022i−2i-1-1ii−i−i−i−iii000000000
χ2522-2-22-2-220220022-2-2-2-22i−2i22000022-2-2-2-20000000022-2-20000022-2-22i2i−2i−2i000000000000000002i−2i0000000
χ2622-2-22-2-220220022-2-2-2-22i−2i22000022-2-2-2-200000000-2-22200000-2-2222i2i−2i−2i00000000000000000−2i2i0000000
χ2722-2-22-2-220220022-2-2-2-2−2i2i22000022-2-2-2-20000000022-2-20000022-2-2−2i−2i2i2i00000000000000000−2i2i0000000
χ2822-2-22-2-220220022-2-2-2-2−2i2i22000022-2-2-2-200000000-2-22200000-2-222−2i−2i2i2i000000000000000002i−2i0000000
χ292-22-222-2-202200-2-222-2-200220000-2-222-2-2000000002i−2i2i−2i000002i−2i2i−2i000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000
χ302-22-222-2-202200-2-222-2-200220000-2-222-2-2000000002i−2i2i−2i000002i−2i2i−2i00000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000
χ312-22-222-2-202200-2-222-2-200220000-2-222-2-200000000−2i2i−2i2i00000−2i2i−2i2i00000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000
χ322-22-222-2-202200-2-222-2-200220000-2-222-2-200000000−2i2i−2i2i00000−2i2i−2i2i000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000
χ332-2-222-22-202200-2-2-2-22200220000-2-2-2-222000000002i−2i−2i2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i−2i2i00000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000000
χ342-2-222-22-202200-2-2-2-22200220000-2-2-2-222000000002i−2i−2i2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i−2i2i0000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000000
χ352-2-222-22-202200-2-2-2-22200220000-2-2-2-22200000000−2i2i2i−2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i2i2i−2i0000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000000
χ362-2-222-22-202200-2-2-2-22200220000-2-2-2-22200000000−2i2i2i−2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i2i2i−2i00000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000000
χ372-2-22-11-11022−i3i3-2-2-2-22200-1-100001111-1-1−i3−i3−i3−i3i3i3i3i32i−2i−2i2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−iii−i000000000003−3−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000
χ382-2-22-11-11022−i3i3-2-2-2-22200-1-100001111-1-1−i3−i3−i3−i3i3i3i3i32i−2i−2i2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−iii−i000000000003−3ζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000
χ392-2-22-11-11022−i3i3-2-2-2-22200-1-100001111-1-1−i3−i3−i3−i3i3i3i3i3−2i2i2i−2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23i−i−ii00000000000−33ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000
χ402-2-22-11-11022−i3i3-2-2-2-22200-1-100001111-1-1−i3−i3−i3−i3i3i3i3i3−2i2i2i−2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23i−i−ii00000000000−33−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000
χ412-2-22-11-11022i3−i3-2-2-2-22200-1-100001111-1-1i3i3i3i3−i3−i3−i3−i32i−2i−2i2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−iii−i00000000000−33−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000
χ422-2-22-11-11022i3−i3-2-2-2-22200-1-100001111-1-1i3i3i3i3−i3−i3−i3−i32i−2i−2i2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−iii−i00000000000−33ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000
χ432-2-22-11-11022i3−i3-2-2-2-22200-1-100001111-1-1i3i3i3i3−i3−i3−i3−i3−2i2i2i−2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23i−i−ii000000000003−3ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000
χ442-2-22-11-11022i3−i3-2-2-2-22200-1-100001111-1-1i3i3i3i3−i3−i3−i3−i3−2i2i2i−2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23i−i−ii000000000003−3−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000
χ454444444441-2441-21-21-2441-211-2-21-21-21-211-2-211-2-200004000000001-21-211-2-20000000000000000000000
χ464444444441-2441-21-21-2-4-41-211-2-21-21-21-211-2-211-2-20000-400000000-12-12-1-1220000000000000000000000
χ47444444444-2144-21-21-2144-21-2-211-21-21-21-2-211-2-2110000400000000-21-21-2-2110000000000000000000000
χ48444444444-2144-21-21-21-4-4-21-2-211-21-21-21-2-211-2-2110000-4000000002-12-122-1-10000000000000000000000
χ4944444444-41-2-4-41-21-21-2441-2-1-1221-21-21-2-1-122-1-1220000-4000000001-21-2-1-1220000000000000000000000
χ5044444444-41-2-4-41-21-21-2-4-41-2-1-1221-21-21-2-1-122-1-1220000400000000-12-1211-2-20000000000000000000000
χ5144444444-4-21-4-4-21-21-2144-2122-1-1-21-21-2122-1-122-1-10000-400000000-21-2122-1-10000000000000000000000
χ5244444444-4-21-4-4-21-21-21-4-4-2122-1-1-21-21-2122-1-122-1-100004000000002-12-1-2-2110000000000000000000000
χ5344-4-44-4-4401-2001-2-12-124i−4i1-23-3001-2-12-123-3003-3000000000000000i−2i−i2i3i−3i000000000000000000000000
χ5444-4-44-4-4401-2001-2-12-124i−4i1-2-33001-2-12-12-3300-33000000000000000i−2i−i2i−3i3i000000000000000000000000
χ5544-4-44-4-4401-2001-2-12-12−4i4i1-23-3001-2-12-123-3003-3000000000000000−i2ii−2i−3i3i000000000000000000000000
χ5644-4-44-4-4401-2001-2-12-12−4i4i1-2-33001-2-12-12-3300-33000000000000000−i2ii−2i3i−3i000000000000000000000000
χ5744-4-44-4-440-2100-212-12-14i−4i-21003-3-212-12-1003-3003-30000000000000−2ii2i−i003i−3i0000000000000000000000
χ5844-4-44-4-440-2100-212-12-14i−4i-2100-33-212-12-100-3300-330000000000000−2ii2i−i00−3i3i0000000000000000000000
χ5944-4-44-4-440-2100-212-12-1−4i4i-21003-3-212-12-1003-3003-300000000000002i−i−2ii00−3i3i0000000000000000000000
χ6044-4-44-4-440-2100-212-12-1−4i4i-2100-33-212-12-100-3300-3300000000000002i−i−2ii003i−3i0000000000000000000000
χ6144-4-4-222-20440044-4-4-4-400-2-20000-2-222220000000044-4-400000-2-222000000000000000000000000000000
χ6244-4-4-222-20440044-4-4-4-400-2-20000-2-2222200000000-4-4440000022-2-2000000000000000000000000000000
χ634-44-4-2-22204400-4-444-4-400-2-2000022-2-222000000004i−4i4i−4i00000−2i2i−2i2i000000000000000000000000000000
χ644-44-4-2-22204400-4-444-4-400-2-2000022-2-22200000000−4i4i−4i4i000002i−2i2i−2i000000000000000000000000000000
χ658888-4-4-4-482-4-4-42-42-42-400-1222-4-4-12-12-12-1-122-1-1220000000000000000000000000000000000000000000
χ668888-4-4-4-48-42-4-4-42-42-42002-1-4-4222-12-12-122-1-122-1-10000000000000000000000000000000000000000000
χ678888-4-4-4-4-82-4442-42-42-400-12-2-244-12-12-1211-2-211-2-20000000000000000000000000000000000000000000
χ688888-4-4-4-4-8-4244-42-42-42002-144-2-22-12-12-1-2-211-2-2110000000000000000000000000000000000000000000
χ6988-8-8-444-402-4002-4-24-2400-126-600-121-21-2-3300-33000000000000000000000000000000000000000000000
χ7088-8-8-444-402-4002-4-24-2400-12-6600-121-21-23-3003-3000000000000000000000000000000000000000000000
χ7188-8-8-444-40-4200-424-24-2002-1006-62-1-21-2100-3300-330000000000000000000000000000000000000000000
χ7288-8-8-444-40-4200-424-24-2002-100-662-1-21-21003-3003-30000000000000000000000000000000000000000000
χ738-88-888-8-802-400-242-4-24002-40000-242-4-24000000000000000000000000000000000000000000000000000
χ748-88-888-8-80-42004-2-424-200-4200004-2-424-2000000000000000000000000000000000000000000000000000
χ758-88-8-4-44402-400-242-4-2400-1200001-2-121-2−3i33i3003i3−3i3000000000000000000000000000000000000000000000
χ768-88-8-4-44402-400-242-4-2400-1200001-2-121-23i3−3i300−3i33i3000000000000000000000000000000000000000000000
χ778-88-8-4-4440-42004-2-424-2002-10000-212-1-2100−3i33i3003i3−3i30000000000000000000000000000000000000000000
χ788-88-8-4-4440-42004-2-424-2002-10000-212-1-21003i3−3i300−3i33i30000000000000000000000000000000000000000000
χ798-8-888-88-802-400-24-242-4002-40000-24-242-4000000000000000000000000000000000000000000000000000
χ808-8-888-88-80-42004-24-2-4200-4200004-24-2-42000000000000000000000000000000000000000000000000000
χ818-8-88-44-4402-4−4i34i3-24-242-400-1200001-21-2-12−i3−i32i32i3i3i3−2i3−2i30000000000000000000000000000000000000000000
χ828-8-88-44-4402-44i3−4i3-24-242-400-1200001-21-2-12i3i3−2i3−2i3−i3−i32i32i30000000000000000000000000000000000000000000
χ838-8-88-44-440-42−4i34i34-24-2-42002-10000-21-212-12i32i3−i3−i3−2i3−2i3i3i30000000000000000000000000000000000000000000
χ848-8-88-44-440-424i3−4i34-24-2-42002-10000-21-212-1−2i3−2i3i3i32i32i3−i3−i30000000000000000000000000000000000000000000

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