Finite Group Databasebeta

← Group #72231632

Character table — Group #72231632

Order 9216.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122222661212121212121212121224242424242424242424242448484848484848484848484848484848727296969696969696969696128128144144144144144144192192192192192256256256256256288288288576576768768
order12236662222226666662222244466662444466666121212121212244444121212121212362444444121212123666644448612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111-1111-1111111111111111111111-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1
χ31111111111111111111-1-11111111111-111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1111111-1-1-1-111
χ41111111111111111111-1-1-1111-111111-111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111111-11111-1-1
χ522222222222222222220022222222220220020000222222220000000000-1-100220000000-1-1-1-1-120000-1-1
χ6222222222222222222200-2222-2222220220020000222222-2-20000000000-1-100-2-20000000-1-1-1-1-1-2000011
χ7222-1-1-1-1222222-1-1-1-1-1-122022202-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1002222-1-1-1-1-1-1220000002-1-1-1-1-12-1-1-10000000
χ8222-1-1-1-1222222-1-1-1-1-1-1-2-2022202-1-1-1-1-222-2-2-11111-1-1-1-1-1-100-2-2-2-211111122000000-21111-12-1-1-10000000
χ933333333333-1-1333333113-13-13-1-1-1-1-11-1-11131111-1-1-1-1-1-1-1-111-1-111111100113-111-1-1-1-1-100000-1-1-11-100
χ1033333333333-1-133333311-3-13-1-3-1-1-1-1-11-1-11131111-1-1-1-1-1-11111-1-111111100-1-1-31-1-1-1-1-1-1-100000111-1100
χ1133333333333-1-1333333-1-13-13-13-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-100-1-13-1-1-11111100000-111-1100
χ1233333333333-1-1333333-1-1-3-13-1-3-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-10011-311111111000001-1-11-100
χ13333333333-1-1333-1-13-1-1113-1-133-133-1-11-1-111-111113-1-1-1-1-133-1-11111-1-1-1-10011-1-111-111-1-100000-111-1-100
χ14333333333-1-1333-1-13-1-111-3-1-13-3-133-1-11-1-111-111113-1-1-1-1-1-3-3-1-11111-1-1-1-100-1-111-1-1-111-1-1000001-1-11100
χ15333333333-1-1333-1-13-1-1-1-13-1-133-133-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-13311-1-1-1-1111100-1-1-1-1-1-11-1-11100000-1-1-11100
χ16333333333-1-1333-1-13-1-1-1-1-3-1-13-3-133-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-3-311-1-1-1-11111001111111-1-11100000111-1-100
χ17333333333-1-1-1-13-1-13-1-11133-1-133-1-1331-1-111-11111-13-1-1-1-1-1-1-1-1-1-111-1-1-1-10011-13111-1-11100000-1-1-1-1100
χ18333333333-1-1-1-13-1-13-1-111-33-1-1-33-1-1331-1-111-11111-13-1-1-1-111-1-1-1-111-1-1-1-100-1-11-3-1-11-1-111000001111-100
χ19333333333-1-1-1-13-1-13-1-1-1-133-1-133-1-133-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-11111-1-1111100-1-1-13-1-1-111-1-100000-1111-100
χ20333333333-1-1-1-13-1-13-1-1-1-1-33-1-1-33-1-133-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1111111-1-1111100111-311-111-1-1000001-1-1-1100
χ21444-2-2-2-2444444-2-2-2-2-2-200044404-2-2-2-204400-20000-2-2-2-2-2-2000000000000-2-2000000000001-21110000000
χ2244-444-4-4-440000-400400224000-400000-2002-2022-2-20000000000002-20000112-2002-2000001-11-1-1000001-1
χ2344-444-4-4-440000-40040022-4000400000-2002-2022-2-20000000000002-2000011-2200-22000001-11-1-100000-11
χ2444-444-4-4-440000-400400-2-24000-400000200-220-2-222000000000000-22000011-2200-22000001-11-1-1000001-1
χ2544-444-4-4-440000-400400-2-2-4000400000200-220-2-222000000000000-220000112-2002-2000001-11-1-100000-11
χ26666666666-2-2-2-26-2-26-2-2006-2-2-26-2-2-2-2-202200-20000-2-22222-2-200000000000000-2-20000000000002000000
χ27666666666-2-2-2-26-2-26-2-200-6-2-2-2-6-2-2-2-2-202200-20000-2-22222220000000000000022000000000000-2000000
χ286666666-2-2226-2-222-2222202-2-20-26-22222-2-2-2-22222-2-222-2-200002-2-2-200000000000002-200000000000000
χ296666666-2-2226-2-222-222-2-202-2-20-26-222-22-222-2-2-2-2-2-2-222-2-20000-22220000000000000-2200000000000000
χ306666666-2-222-26-222-2222202-2-20-2-26222-22-2-2-22222-2-2-2-2220000-22-2-20000000000000-2200000000000000
χ316666666-2-222-26-222-222-2-202-2-20-2-2622-2-2222-2-2-2-2-2-2-2-2-22200002-22200000000000002-200000000000000
χ326666666-2-2-2-26-2-2-2-2-2-2-2000-22-2026-2-2-20-220020000-22-2-222000000000000002200-2-2000000000002-20000
χ336666666-2-2-2-26-2-2-2-2-2-2-2000-22-2026-2-2-20-220020000-22-2-22200000000000000-2-2002200000000000-220000
χ346666666-2-2-2-2-26-2-2-2-2-2-2000-22-202-26-2-202-20020000-2222-2-2000000000000002200-2-200000000000-220000
χ356666666-2-2-2-2-26-2-2-2-2-2-2000-22-202-26-2-202-20020000-2222-2-200000000000000-2-20022000000000002-20000
χ36666-3-3-3-36666-2-2-3-3-3-3-3-3220-26-20-211112-2-222-3-1-1-1-11111110022-2-2-1-1-1-1-1-100000000-21111000000000000
χ37666-3-3-3-36666-2-2-3-3-3-3-3-3-2-20-26-20-21111-2-2-2-2-2-3111111111100-2-222111111000000002-1-1-1-1000000000000
χ38666-3-3-3-366-2-266-311-311220-2-260-2-3-3112-2-2221-1-1-1-1-31111100-2-222-1-1111100000000-2-1-111000000000000
χ39666-3-3-3-366-2-266-311-311-2-20-2-260-2-3-311-2-2-2-2-211111-3111110022-2-211-1-1-1-100000000211-1-1000000000000
χ40666-3-3-3-366-2-2-2-2-311-3112206-2-20611-3-32-2-2221-1-1-1-11-3111100-2-2-2-2-1-1111100000000211-1-1000000000000
χ41666-3-3-3-366-2-2-2-2-311-311-2-206-2-20611-3-3-2-2-2-2-2111111-3111100222211-1-1-1-100000000-2-1-111000000000000
χ42666-3-3-3-3-2-2226-21−1+2i3−1−2i31−1+2i3−1−2i32202-2-20-2-31−1+2i3−1−2i322-2-2-21-1-1-1-111−1+2i3−1−2i31100002-211i3i3−i3−i3000000000-11i3−i3000000000000
χ43666-3-3-3-3-2-2226-21−1+2i3−1−2i31−1+2i3−1−2i3-2-202-2-20-2-31−1+2i3−1−2i3-22-2221111111−1+2i3−1−2i3110000-22-1-1−i3−i3i3i30000000001-1−i3i3000000000000
χ44666-3-3-3-3-2-2226-21−1−2i3−1+2i31−1−2i3−1+2i32202-2-20-2-31−1−2i3−1+2i322-2-2-21-1-1-1-111−1−2i3−1+2i31100002-211−i3−i3i3i3000000000-11−i3i3000000000000
χ45666-3-3-3-3-2-2226-21−1−2i3−1+2i31−1−2i3−1+2i3-2-202-2-20-2-31−1−2i3−1+2i3-22-2221111111−1−2i3−1+2i3110000-22-1-1i3i3−i3−i30000000001-1i3−i3000000000000
χ46666-3-3-3-3-2-222-261−1+2i3−1−2i31−1+2i3−1−2i32202-2-20-21-3−1−2i3−1+2i32-22-2-21-1-1-1-11111−1+2i3−1−2i30000-2211i3i3−i3−i30000000001-1−i3i3000000000000
χ47666-3-3-3-3-2-222-261−1+2i3−1−2i31−1+2i3−1−2i3-2-202-2-20-21-3−1−2i3−1+2i3-2-2222111111111−1+2i3−1−2i300002-2-1-1−i3−i3i3i3000000000-11i3−i3000000000000
χ48666-3-3-3-3-2-222-261−1−2i3−1+2i31−1−2i3−1+2i32202-2-20-21-3−1+2i3−1−2i32-22-2-21-1-1-1-11111−1−2i3−1+2i30000-2211−i3−i3i3i30000000001-1i3−i3000000000000
χ49666-3-3-3-3-2-222-261−1−2i3−1+2i31−1−2i3−1+2i3-2-202-2-20-21-3−1+2i3−1−2i3-2-2222111111111−1−2i3−1+2i300002-2-1-1i3i3−i3−i3000000000-11−i3i3000000000000
χ5088-888-8-8-880000-800800008000-8000000000000000000000000000000000-1-100000000000-11-11100000-11
χ5188-888-8-8-880000-80080000-80008000000000000000000000000000000000-1-100000000000-11-111000001-1
χ5288-8-4-444-880000400-400440000000000-4004-40-2-222000000000000-2200002200000000000-1-2-1110000000
χ5388-8-4-444-880000400-400-4-40000000000400-44022-2-20000000000002-200002200000000000-1-2-1110000000
χ548-808-80000-44000-4-40444-400000000000000004-400000000002-200002-22-22-20000000000020-2000000000
χ558-808-80000-44000-4-4044-440000000000000000-440000000000-220000-22-222-20000000000020-2000000000
χ568-80-444i3−4i300-440002−2i32+2i30−2+2i3−2−2i34-40000000000000000-222i3−2i3000000002-20000−1+i31−i3−1−i31+i32-200000000000-101i3−i30000000
χ578-80-444i3−4i300-440002−2i32+2i30−2+2i3−2−2i3-4400000000000000002-2−2i32i300000000-2200001−i3−1+i31+i3−1−i32-200000000000-101i3−i30000000
χ588-80-44−4i34i300-440002+2i32−2i30−2−2i3−2+2i34-40000000000000000-22−2i32i3000000002-20000−1−i31+i3−1+i31−i32-200000000000-101−i3i30000000
χ598-80-44−4i34i300-440002+2i32−2i30−2−2i3−2+2i3-4400000000000000002-22i3−2i300000000-2200001+i3−1−i31−i3−1+i32-200000000000-101−i3i30000000
χ6012121212121212-4-444-4-4-444-444000-4-4404-4-4-4-400000-400004400000000000000000000000000000000000000000
χ6112121212121212-4-4-4-4-4-4-4-4-4-4-4-40004440-4-4-44400000400004-400000000000000000000000000000000000000000
χ62121212-6-6-6-61212-4-4-4-4-622-622000-4-4-40-42222044002000022-2-2-2-20000000000000000000000000000000000000
χ63121212-6-6-6-6-4-444-4-42−2+4i3−2−4i32−2+4i3−2−4i3000-4-440422220000020000-2-2−2i32i3−2i32i30000000000000000000000000000000000000
χ64121212-6-6-6-6-4-444-4-42−2−4i3−2+4i32−2−4i3−2+4i3000-4-440422220000020000-2-22i3−2i32i3−2i30000000000000000000000000000000000000
χ65121212-6-6-6-6-4-4-4-412-4222222000-44-404-62220-4400-200002-222-2-20000000000000000000000000000000000000
χ66121212-6-6-6-6-4-4-4-4-412222222000-44-4042-62204-400-200002-2-2-2220000000000000000000000000000000000000
χ67121212-6-6-6-6-4-4-4-4-4-42222220004440-422−2+4i3−2−4i300000-20000-22−2i32i32i3−2i30000000000000000000000000000000000000
χ68121212-6-6-6-6-4-4-4-4-4-42222220004440-422−2−4i3−2+4i300000-20000-222i3−2i3−2i32i30000000000000000000000000000000000000
χ691212-121212-12-124-40000400-400220000000000-200-22022-2-20000004-40000-220000002-200-2200000000000000000
χ701212-121212-12-124-40000400-400220000000000-200-22022-2-2000000-440000-22000000-22002-200000000000000000
χ711212-121212-12-124-40000400-400-2-200000000002002-20-2-2220000004-400002-2000000-22002-200000000000000000
χ721212-121212-12-124-40000400-400-2-200000000002002-20-2-222000000-4400002-20000002-200-2200000000000000000
χ731616-16-8-888-16160000800-8000000000000000000000000000000000000000000-2-200000000000121-1-10000000
χ7416-16016-160000-88000-8-80880000000000000000000000000000000000000000-2200000000000-202000000000
χ7516-160-888i3−8i300-880004−4i34+4i30−4+4i3−4−4i30000000000000000000000000000000000000000-220000000000010-1−i3i30000000
χ7616-160-88−8i38i300-880004+4i34−4i30−4−4i3−4+4i30000000000000000000000000000000000000000-220000000000010-1i3−i30000000
χ772424-24-12-1212128-80000-400400440000000000-400-440-2-2220000000000002-200000000000000000000000000000
χ782424-24-12-1212128-80000-400400-4-400000000004004-4022-2-2000000000000-2200000000000000000000000000000
χ7924-24024-2400004-4000440-4-44-400000000000000004-40000000000-220000-22-220000000000000000000000000
χ8024-24024-2400004-4000440-4-4-440000000000000000-4400000000002-200002-22-20000000000000000000000000
χ8124-240-121212i3−12i3004-4000−2+2i3−2−2i302−2i32+2i34-40000000000000000-222i3−2i300000000-2200001−i3−1+i31+i3−1−i30000000000000000000000000
χ8224-240-121212i3−12i3004-4000−2+2i3−2−2i302−2i32+2i3-4400000000000000002-2−2i32i3000000002-20000−1+i31−i3−1−i31+i30000000000000000000000000
χ8324-240-1212−12i312i3004-4000−2−2i3−2+2i302+2i32−2i34-40000000000000000-22−2i32i300000000-2200001+i3−1−i31−i3−1+i30000000000000000000000000
χ8424-240-1212−12i312i3004-4000−2−2i3−2+2i302+2i32−2i3-4400000000000000002-22i3−2i3000000002-20000−1−i31+i3−1+i31−i30000000000000000000000000

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