Finite Group Databasebeta

← Group #13166515

Character table — Group #13166515

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222244444444448888888888888888888899991212181818181818242424242424242436363636363636363636363636365454545454545454108108
order12223446663366666612123366666612121212121212121212121244442444121212126666121212128888121224242424242424248888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111ii−i−i-1-1iiii−i−i−i−iii−i−iii−i−i-1-1
χ61111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111−i−iii-1-1−i−i−i−iiiii−i−iii−i−iii-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i−i−iii−i−iii11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiiiii−i−iii−i−i11
χ911111-1-111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1-1-1-11-11-1-1-111-1-111-1-11111-1-1-1-1-11
χ1011111-1-111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1-1-1-1-11-11-1-1-1-111-1-111-1-1-1-11111-11
χ1111111-1-111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-1-1-111111-11-1-1-111-1-111-1-1-1-1-1-111111-1
χ1211111-1-111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-1-1-11111-11-11-1-1-1-111-1-1111111-1-1-1-11-1
χ1311111-1-111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-1-1-1i−i−ii11ii−i−i−i−iiiii−i−i−i−iii1-1
χ1411111-1-111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-1-1-1−iii−i11−i−iiiii−i−i−i−iiiii−i−i1-1
χ1511111-1-111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111i−i−ii11ii−i−i−i−iii−i−iiiii−i−i-11
χ1611111-1-111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111−iii−i11−i−iiiii−i−iii−i−i−i−iii-11
χ172222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220022-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-10000000000
χ182222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220022-1-1-1-100000000-2-2-2-2-1-1111111110000000000
χ192222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200-2-21111000000002i2i−2i−2i11−i−i−i−iiiii0000000000
χ202222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200-2-2111100000000−2i−2i2i2i11iiii−i−i−i−i0000000000
χ212222-1-2-2-1-1-12222222211-1-1-1-1-1-1-1-1-2-2-2-211111111222200-2-2-1-1-1-1000000002-22-211-1-111-1-1110000000000
χ222222-1-2-2-1-1-12222222211-1-1-1-1-1-1-1-1-2-2-2-211111111222200-2-2-1-1-1-100000000-22-221111-1-111-1-10000000000
χ232222-1-2-2-1-1-12222222211-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-200221111000000002i−2i−2i2i-1-1−i−iiiii−i−i0000000000
χ242222-1-2-2-1-1-12222222211-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-20022111100000000−2i2i2i−2i-1-1ii−i−i−i−iii0000000000
χ2522-2-22002-2-222-2-222-2-20022-2-2-2-2220000000000002i−2i2i−2i00002i−2i2i−2i00000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ2622-2-22002-2-222-2-222-2-20022-2-2-2-2220000000000002i−2i2i−2i00002i−2i2i−2i0000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ2722-2-22002-2-222-2-222-2-20022-2-2-2-222000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ2822-2-22002-2-222-2-222-2-20022-2-2-2-222000000000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ292-22-222i−2i-22-22222-2-2-2-22i−2i2222-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i−2i−2i2i002-22i−2i−2i2i0000000000002-2000000000000000000
χ302-22-222i−2i-22-22222-2-2-2-22i−2i2222-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i−2i2i2i−2i00-22−2i2i2i−2i000000000000-22000000000000000000
χ312-22-22−2i2i-22-22222-2-2-2-2−2i2i2222-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i2i−2i−2i2i00-222i−2i−2i2i000000000000-22000000000000000000
χ322-22-22−2i2i-22-22222-2-2-2-2−2i2i2222-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i−2i2i2i−2i002-2−2i2i2i−2i0000000000002-2000000000000000000
χ332-22-2-12i−2i1-112222-2-2-2-2−ii-1-1-1-111112i2i−2i−2i−i−i−i−iiiii2i−2i−2i2i002-2−iii−i000000000000-11ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ342-22-2-12i−2i1-112222-2-2-2-2−ii-1-1-1-111112i2i−2i−2i−i−i−i−iiiii2i−2i−2i2i002-2−iii−i000000000000-11−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ352-22-2-12i−2i1-112222-2-2-2-2−ii-1-1-1-111112i2i−2i−2i−i−i−i−iiiii−2i2i2i−2i00-22i−i−ii0000000000001-1−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000
χ362-22-2-12i−2i1-112222-2-2-2-2−ii-1-1-1-111112i2i−2i−2i−i−i−i−iiiii−2i2i2i−2i00-22i−i−ii0000000000001-1ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000
χ372-22-2-1−2i2i1-112222-2-2-2-2i−i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i2i−2i−2i2i00-22−iii−i0000000000001-1ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000
χ382-22-2-1−2i2i1-112222-2-2-2-2i−i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i2i−2i−2i2i00-22−iii−i0000000000001-1−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000
χ392-22-2-1−2i2i1-112222-2-2-2-2i−i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i−2i2i2i−2i002-2i−i−ii000000000000-11−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ402-22-2-1−2i2i1-112222-2-2-2-2i−i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i−2i2i2i−2i002-2i−i−ii000000000000-11ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ412-2-22200-2-2222-2-2-2-2220022-2-222-2-200000000000022-2-2000022-2-2000000000000000000000000002i−2i2i−2i00
χ422-2-22200-2-2222-2-2-2-2220022-2-222-2-200000000000022-2-2000022-2-200000000000000000000000000−2i2i−2i2i00
χ432-2-22200-2-2222-2-2-2-2220022-2-222-2-2000000000000-2-2220000-2-222000000000000000000000000002-2-2200
χ442-2-22200-2-2222-2-2-2-2220022-2-222-2-2000000000000-2-2220000-2-22200000000000000000000000000-222-200
χ4544444444441-21-21-21-2441-21-21-21-21-21-211-2-211-2-200004400000011-2-211-2-2000000000000000000000000
χ4644444444441-21-21-21-2441-21-21-21-21-21-211-2-211-2-20000-4-4000000-1-122-1-122000000000000000000000000
χ474444444444-21-21-21-2144-21-21-21-21-21-21-2-211-2-211000044000000-2-211-2-211000000000000000000000000
χ484444444444-21-21-21-2144-21-21-21-21-21-21-2-211-2-2110000-4-400000022-1-122-1-1000000000000000000000000
χ4944444-4-44441-21-21-21-2-4-41-21-21-21-2-12-12-1-122-1-12200004-400000011-2-2-1-122000000000000000000000000
χ5044444-4-44441-21-21-21-2-4-41-21-21-21-2-12-12-1-122-1-1220000-44000000-1-12211-2-2000000000000000000000000
χ5144444-4-4444-21-21-21-21-4-4-21-21-21-212-12-122-1-122-1-100004-4000000-2-21122-1-1000000000000000000000000
χ5244444-4-4444-21-21-21-21-4-4-21-21-21-212-12-122-1-122-1-10000-4400000022-1-1-2-211000000000000000000000000
χ5344-4-4-200-22244-4-444-4-400-2-22222-2-20000000000004i−4i4i−4i0000−2i2i−2i2i00000000000000000000000000000000
χ5444-4-4-200-22244-4-444-4-400-2-22222-2-2000000000000−4i4i−4i4i00002i−2i2i−2i00000000000000000000000000000000
χ554-44-444i−4i-44-41-21-2-12-124i−4i1-21-2-12-12i−2i−i2iii−2i−2i−i−i2i2i0000000000003-3003i−3i00000000000000000000000000
χ564-44-444i−4i-44-41-21-2-12-124i−4i1-21-2-12-12i−2i−i2iii−2i−2i−i−i2i2i000000000000-3300−3i3i00000000000000000000000000
χ574-44-444i−4i-44-4-21-212-12-14i−4i-21-212-12-1−2ii2i−i−2i−2iii2i2i−i−i000000000000003-3003i−3i000000000000000000000000
χ584-44-444i−4i-44-4-21-212-12-14i−4i-21-212-12-1−2ii2i−i−2i−2iii2i2i−i−i00000000000000-3300−3i3i000000000000000000000000
χ594-44-44−4i4i-44-41-21-2-12-12−4i4i1-21-2-12-12−i2ii−2i−i−i2i2iii−2i−2i0000000000003-300−3i3i00000000000000000000000000
χ604-44-44−4i4i-44-41-21-2-12-12−4i4i1-21-2-12-12−i2ii−2i−i−i2i2iii−2i−2i000000000000-33003i−3i00000000000000000000000000
χ614-44-44−4i4i-44-4-21-212-12-1−4i4i-21-212-12-12i−i−2ii2i2i−i−i−2i−2iii000000000000003-300−3i3i000000000000000000000000
χ624-44-44−4i4i-44-4-21-212-12-1−4i4i-21-212-12-12i−i−2ii2i2i−i−i−2i−2iii00000000000000-33003i−3i000000000000000000000000
χ634-4-44-20022-244-4-4-4-44400-2-222-2-22200000000000044-4-40000-2-22200000000000000000000000000000000
χ644-4-44-20022-244-4-4-4-44400-2-222-2-222000000000000-4-444000022-2-200000000000000000000000000000000
χ658888-488-4-4-42-42-42-42-4-4-4-12-12-12-122-42-4-1-122-1-12200000000000000000000000000000000000000000000
χ668888-488-4-4-4-42-42-42-42-4-42-12-12-12-1-42-4222-1-122-1-100000000000000000000000000000000000000000000
χ678888-4-8-8-4-4-42-42-42-42-444-12-12-12-12-24-2411-2-211-2-200000000000000000000000000000000000000000000
χ688888-4-8-8-4-4-4-42-42-42-42442-12-12-12-14-24-2-2-211-2-21100000000000000000000000000000000000000000000
χ6988-8-88008-8-82-4-242-4-24002-4-24-242-400000000000000000000000000000000000000000000000000000000
χ7088-8-88008-8-8-424-2-424-200-424-24-2-4200000000000000000000000000000000000000000000000000000000
χ7188-8-8-400-4442-4-242-4-2400-121-21-2-120000−3i33i300−3i33i30000000000000000000000000000000000000000000000
χ7288-8-8-400-4442-4-242-4-2400-121-21-2-1200003i3−3i3003i3−3i30000000000000000000000000000000000000000000000
χ7388-8-8-400-444-424-2-424-2002-1-21-212-1000000−3i33i300−3i33i300000000000000000000000000000000000000000000
χ7488-8-8-400-444-424-2-424-2002-1-21-212-10000003i3−3i3003i3−3i300000000000000000000000000000000000000000000
χ758-88-8-48i−8i4-442-42-4-24-24−4i4i-12-121-21-22i−4i−2i4i−i−i2i2iii−2i−2i00000000000000000000000000000000000000000000
χ768-88-8-48i−8i4-44-42-424-24-2−4i4i2-12-1-21-21−4i2i4i−2i2i2i−i−i−2i−2iii00000000000000000000000000000000000000000000
χ778-88-8-4−8i8i4-442-42-4-24-244i−4i-12-121-21-2−2i4i2i−4iii−2i−2i−i−i2i2i00000000000000000000000000000000000000000000
χ788-88-8-4−8i8i4-44-42-424-24-24i−4i2-12-1-21-214i−2i−4i2i−2i−2iii2i2i−i−i00000000000000000000000000000000000000000000
χ798-8-88800-8-882-4-24-242-4002-4-242-4-2400000000000000000000000000000000000000000000000000000000
χ808-8-88800-8-88-424-24-2-4200-424-2-424-200000000000000000000000000000000000000000000000000000000
χ818-8-88-40044-42-4-24-242-400-121-2-121-2000033−3300−33330000000000000000000000000000000000000000000000
χ828-8-88-40044-42-4-24-242-400-121-2-121-20000−33330033−330000000000000000000000000000000000000000000000
χ838-8-88-40044-4-424-24-2-42002-1-212-1-2100000033−3300−333300000000000000000000000000000000000000000000
χ848-8-88-40044-4-424-24-2-42002-1-212-1-21000000−33330033−3300000000000000000000000000000000000000000000

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