Finite Group Databasebeta

← Group #72271387

Character table — Group #72271387

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1111222222121212121616161624242424484848484848484848486464646464646464969696969696128128128128128128128128128128128128192192192192256256256256256256256256
order1222222222444424444444244444444433666666224444666666666666888866121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ311111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ411111111111111-1-1-1-11111-1-1-111-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ511111111111111-1-1-1-11111-1-1-111-11111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32
χ611111111111111-1-1-1-11111-1-1-111-11111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32
χ73333333333333333333333333333-1-1-1-100000000-1-1-1-1-1-1000000000000-1-1-1-100000000
χ833333333333333-3-3-3-33333-3-3-333-3-1-1-1-100000000-1-1-1-1-1-1000000000000111100000000
χ93333333333-1-1-1-13333-1-133-1-1-1-1-1-133-1-1000000003-1-1-1-1-10000000000003-1-1-100000000
χ103333333333-1-1-1-13333-1-133-1-1-1-1-1-1-1-13300000000-13-1-1-1-1000000000000-13-1-100000000
χ113333333333-1-1-1-13333-1-133-1-1-1-1-1-1-1-1-1-100000000-1-133-1-1000000000000-1-13-100000000
χ123333333333-1-1-1-13333-1-133-1-1-1-1-1-1-1-1-1-100000000-1-1-1-133000000000000-1-1-1300000000
χ133333333333-1-1-1-1-3-3-3-3-1-133111-1-1133-1-1000000003-1-1-1-1-1000000000000-311100000000
χ143333333333-1-1-1-1-3-3-3-3-1-133111-1-11-1-13300000000-13-1-1-1-10000000000001-31100000000
χ153333333333-1-1-1-1-3-3-3-3-1-133111-1-11-1-1-1-100000000-1-133-1-100000000000011-3100000000
χ163333333333-1-1-1-1-3-3-3-3-1-133111-1-11-1-1-1-100000000-1-1-1-133000000000000111-300000000
χ1744444-4-4-44-4004422-2-20-40022-200-200001111111100000011-1-1-1-111-1-1-1-10000-1-111-111-1
χ1844444-4-4-44-4004422-2-20-40022-200-20000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i3200001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ1944444-4-4-44-4004422-2-20-40022-200-20000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i3200001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ2044444-4-4-44-40044-2-2220-400-2-2200200001111111100000011-1-1-1-111-1-1-1-1000011-1-11-1-11
χ2144444-4-4-44-40044-2-2220-400-2-220020000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i320000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ2244444-4-4-44-40044-2-2220-400-2-220020000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i320000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ234444-44-4-4-4444002-22-2-40002-2200-2000011111111000000-1-111-1-1-1-111-1-10000-1-11-111-11
χ244444-44-4-4-4444002-22-2-40002-2200-20000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i320000001−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i3200001−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ254444-44-4-4-4444002-22-2-40002-2200-20000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i320000001+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i3200001+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ264444-44-4-4-444400-22-22-4000-22-2002000011111111000000-1-111-1-1-1-111-1-1000011-11-1-11-1
χ274444-44-4-4-444400-22-22-4000-22-20020000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i320000001−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i320000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ284444-44-4-4-444400-22-22-4000-22-20020000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i320000001+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i320000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ294444-4-444-4-400004-4-44004-4000000000011111111000000-1-1-1-111-1-1-1-1110000111-1-11-1-1
χ304444-4-444-4-400004-4-44004-40000000000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i320000001−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i320000−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ314444-4-444-4-400004-4-44004-40000000000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i320000001+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i320000−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ324444-4-444-4-40000-444-4004-4000000000011111111000000-1-1-1-111-1-1-1-1110000-1-1-111-111
χ334444-4-444-4-40000-444-4004-40000000000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i320000001−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i3200001−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ344444-4-444-4-40000-444-4004-40000000000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i320000001+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i3200001+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ35666666666666-2-200006-2-2-2000-2-20222200000000-2-22-22-2000000000000000000000000
χ36666666666666-2-200006-2-2-2000-2-20-2-2-2-20000000022-22-22000000000000000000000000
χ376666666666-2-2660000-26-2-2000-2-20222200000000-2-2-22-22000000000000000000000000
χ386666666666-2-2660000-26-2-2000-2-20-2-2-2-200000000222-22-2000000000000000000000000
χ396666666666-2-2-2-20000-2-2-2-20006-2022-2-200000000-222-2-22000000000000000000000000
χ406666666666-2-2-2-20000-2-2-2-20006-20-2-222000000002-2-222-2000000000000000000000000
χ416666666666-2-2-2-20000-2-2-2-2000-26022-2-200000000-22-222-2000000000000000000000000
χ426666666666-2-2-2-20000-2-2-2-2000-260-2-222000000002-22-2-22000000000000000000000000
χ4388-8-80-800088-800000000000000000000222-2-22-2-2000000002-200002-200000000000000
χ4488-8-80-800088-800000000000000000000−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i300000000−1+i31−i30000−1−i31+i300000000000000
χ4588-8-80-800088-800000000000000000000−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i300000000−1−i31+i30000−1+i31−i300000000000000
χ468-88-8-800080008-800000000000000000022-22-2-22-20000002-200002-20000000000000000
χ478-88-8-800080008-8000000000000000000−1+i3−1−i31−i3−1+i31−i31+i3−1−i31+i3000000−1+i31−i30000−1−i31+i30000000000000000
χ488-88-8-800080008-8000000000000000000−1−i3−1+i31+i3−1−i31+i31−i3−1+i31−i3000000−1−i31+i30000−1+i31−i30000000000000000
χ498-8-88008-800000000000000000000004-422-2-22-2-2200000000002-200002-2000000000000
χ508-8-88008-800000000000000000000004-4−1+i3−1−i31−i31−i3−1+i31+i31+i3−1−i30000000000−1+i31−i30000−1−i31+i3000000000000
χ518-8-88008-800000000000000000000004-4−1−i3−1+i31+i31+i3−1−i31−i31−i3−1+i30000000000−1−i31+i30000−1+i31−i3000000000000
χ528-8-8800-88000000000000000000004-40022-2-22-2-220000000000-220000-22000000000000
χ538-8-8800-88000000000000000000004-400−1+i3−1−i31−i31−i3−1+i31+i31+i3−1−i300000000001−i3−1+i300001+i3−1−i3000000000000
χ548-8-8800-88000000000000000000004-400−1−i3−1+i31+i31+i3−1−i31−i31−i3−1+i300000000001+i3−1−i300001−i3−1+i3000000000000
χ551212121212-12-12-1212-1200-4-466-6-60400-2-22002000000000000000000000000000000000000000000
χ561212121212-12-12-1212-1200-4-4-6-666040022-200-2000000000000000000000000000000000000000000
χ5712121212-1212-12-12-1212-4-4006-66-64000-22-2002000000000000000000000000000000000000000000
χ5812121212-1212-12-12-1212-4-400-66-6640002-2200-2000000000000000000000000000000000000000000
χ5912121212-12-121212-12-120000000000-444-4-4004000000000000000000000000000000000000000000
χ6012121212-12-121212-12-120000000000-44-44400-4000000000000000000000000000000000000000000
χ611616-16-16016000-160000000000000000000000-2-2-222-222000000002-200002-200000000000000
χ621616-16-16016000-1600000000000000000000001−i31+i31−i3−1+i3−1+i31+i3−1−i3−1−i300000000−1+i31−i30000−1−i31+i300000000000000
χ631616-16-16016000-1600000000000000000000001+i31−i31+i3−1−i3−1−i31−i3−1+i3−1+i300000000−1−i31+i30000−1+i31−i300000000000000
χ6416-1616-1616000-1600000000000000000000000-2-22-222-220000002-200002-20000000000000000
χ6516-1616-1616000-16000000000000000000000001−i31+i3−1+i31−i3−1+i3−1−i31+i3−1−i3000000−1+i31−i30000−1−i31+i30000000000000000
χ6616-1616-1616000-16000000000000000000000001+i31−i3−1−i31+i3−1−i3−1+i31−i3−1+i3000000−1−i31+i30000−1+i31−i30000000000000000
χ672424-24-240-2400024-880000000000000000000000000000000000000000000000000000000000
χ6824-2424-24-2400024000-8800000000000000000000000000000000000000000000000000000000
χ6924-24-24240024-240000000000000000000000-4400000000000000000000000000000000000000
χ7024-24-242400-242400000000000000000000-440000000000000000000000000000000000000000

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