Finite Group Databasebeta

← Group #72271289

Character table — Group #72271289

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111122222212121616161624242424244848484848484848484848484848646464646464646496969696128128128128128128128128128128128128192192192192256256256256256256256256
order12222222222224442444422222444444444336666664444666666666666888866121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ311111111111111111111111111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ4111111111111-1-1-1-1111111111-1-111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ5111111111111-1-1-1-1111111111-1-111-1-11111−1+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−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32
χ6111111111111-1-1-1-1111111111-1-111-1-11111−1−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+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32
χ7333333333333333333333-1-1-1-1333333-1-1-1-100000000-1-1-1-1000000000000-1-1-1-100000000
χ8333333333333-3-3-3-333333-1-1-1-1-3-333-3-3-1-1-1-100000000-1-1-1-1000000000000111100000000
χ93333333333-1-13333-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1000000003-1-1-10000000000003-1-1-100000000
χ103333333333-1-13333-1-1-133-1-133-1-1-1-1-1-1-1-1-1-100000000-13-1-1000000000000-13-1-100000000
χ113333333333-1-13333-1-1-133-1-1-1-1-1-1-1-1-1-133-1-100000000-1-13-1000000000000-1-13-100000000
χ123333333333-1-13333-1-1-133-1-1-1-1-1-1-1-1-1-1-1-13300000000-1-1-13000000000000-1-1-1300000000
χ133333333333-1-1-3-3-3-3-1-1-13333-1-111-1-111-1-1-1-1000000003-1-1-1000000000000-311100000000
χ143333333333-1-1-3-3-3-3-1-1-133-1-13311-1-111-1-1-1-100000000-13-1-10000000000001-31100000000
χ153333333333-1-1-3-3-3-3-1-1-133-1-1-1-111-1-11133-1-100000000-1-13-100000000000011-3100000000
χ163333333333-1-1-3-3-3-3-1-1-133-1-1-1-111-1-111-1-13300000000-1-1-13000000000000111-300000000
χ1744444-4-4-4-444422-2-2-4000000002200-2-2000011111111000011-1-1-1-111-1-1-1-10000-1-111-111-1
χ1844444-4-4-4-444422-2-2-4000000002200-2-20000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i320000−1+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
χ1944444-4-4-4-444422-2-2-4000000002200-2-20000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i320000−1−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
χ2044444-4-4-4-4444-2-222-400000000-2-20022000011111111000011-1-1-1-111-1-1-1-1000011-1-11-1-11
χ2144444-4-4-4-4444-2-222-400000000-2-200220000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i320000−1+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
χ2244444-4-4-4-4444-2-222-400000000-2-200220000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i320000−1−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
χ234444-444-4-4-4002-22-204-4000000-22002-20000111111110000-1-111-1-1-1-111-1-10000-1-11-111-11
χ244444-444-4-4-4002-22-204-4000000-22002-20000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200001−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
χ254444-444-4-4-4002-22-204-4000000-22002-20000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200001+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
χ264444-444-4-4-400-22-2204-40000002-200-220000111111110000-1-111-1-1-1-111-1-1000011-11-1-11-1
χ274444-444-4-4-400-22-2204-40000002-200-220000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200001−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
χ284444-444-4-4-400-22-2204-40000002-200-220000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200001+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
χ294444-4-4-444-4004-4-440004-400000000000000111111110000-1-1-1-111-1-1-1-1110000111-1-11-1-1
χ304444-4-4-444-4004-4-440004-400000000000000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200001−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
χ314444-4-4-444-4004-4-440004-400000000000000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200001+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
χ324444-4-4-444-400-444-40004-400000000000000111111110000-1-1-1-111-1-1-1-1110000-1-1-111-111
χ334444-4-4-444-400-444-40004-400000000000000−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200001−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
χ344444-4-4-444-400-444-40004-400000000000000−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200001+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
χ3566666666666600006-2-2-2-2222200-2-200222200000000-2-2-2-2000000000000000000000000
χ3666666666666600006-2-2-2-2-2-2-2-200-2-200-2-2-2-2000000002222000000000000000000000000
χ376666666666-2-20000-266-2-2222200-2-200-2-2-2-200000000-2-222000000000000000000000000
χ386666666666-2-20000-266-2-2-2-2-2-200-2-20022220000000022-2-2000000000000000000000000
χ396666666666-2-20000-2-2-2-2-222-2-2006-20022-2-200000000-22-22000000000000000000000000
χ406666666666-2-20000-2-2-2-2-222-2-200-2600-2-22200000000-222-2000000000000000000000000
χ416666666666-2-20000-2-2-2-2-2-2-222006-200-2-222000000002-22-2000000000000000000000000
χ426666666666-2-20000-2-2-2-2-2-2-22200-260022-2-2000000002-2-22000000000000000000000000
χ4388-8-8-8000088-800000000000000000000000222-2-22-2-200002-200002-20000000000000000
χ4488-8-8-8000088-800000000000000000000000−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i30000−1+i31−i30000−1−i31+i30000000000000000
χ4588-8-8-8000088-800000000000000000000000−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i30000−1−i31+i30000−1+i31−i30000000000000000
χ468-88-80008-8000000000000004-4000000000022-22-2-22-2000000002-200002-2000000000000
χ478-88-80008-8000000000000004-40000000000−1+i3−1−i31−i3−1+i31−i31+i3−1−i31+i300000000−1+i31−i30000−1−i31+i3000000000000
χ488-88-80008-8000000000000004-40000000000−1−i3−1+i31+i3−1−i31+i31−i3−1+i31−i300000000−1−i31+i30000−1+i31−i3000000000000
χ498-88-8000-880000000000004-400000000000022-22-2-22-200000000-220000-22000000000000
χ508-88-8000-880000000000004-4000000000000−1+i3−1−i31−i3−1+i31−i31+i3−1−i31+i3000000001−i3−1+i300001+i3−1−i3000000000000
χ518-88-8000-880000000000004-4000000000000−1−i3−1+i31+i3−1−i31+i31−i3−1+i31−i3000000001+i3−1−i300001−i3−1+i3000000000000
χ528-8-8808-8000000000000000000000000004-422-2-22-2-220000002-200002-200000000000000
χ538-8-8808-8000000000000000000000000004-4−1+i3−1−i31−i31−i3−1+i31+i31+i3−1−i3000000−1+i31−i30000−1−i31+i300000000000000
χ548-8-8808-8000000000000000000000000004-4−1−i3−1+i31+i31+i3−1−i31−i31−i3−1+i3000000−1−i31+i30000−1+i31−i300000000000000
χ558-8-880-880000000000000000000000004-40022-2-22-2-22000000-220000-2200000000000000
χ568-8-880-880000000000000000000000004-400−1+i3−1−i31−i31−i3−1+i31+i31+i3−1−i30000001−i3−1+i300001+i3−1−i300000000000000
χ578-8-880-880000000000000000000000004-400−1−i3−1+i31+i31+i3−1−i31−i31−i3−1+i30000001+i3−1−i300001−i3−1+i300000000000000
χ581212121212-12-12-12-1212-4-466-6-6400000000-2-200220000000000000000000000000000000000000000
χ591212121212-12-12-12-1212-4-4-6-6664000000002200-2-20000000000000000000000000000000000000000
χ6012121212-121212-12-12-12006-66-60-440000002-200-220000000000000000000000000000000000000000
χ6112121212-121212-12-12-1200-66-660-44000000-22002-20000000000000000000000000000000000000000
χ6212121212-12-12-121212-12000000000-4400004-4004-40000000000000000000000000000000000000000
χ6312121212-12-12-121212-12000000000-440000-4400-440000000000000000000000000000000000000000
χ641616-16-16160000-160000000000000000000000000-2-2-222-22200002-200002-20000000000000000
χ651616-16-16160000-1600000000000000000000000001−i31+i31−i3−1+i3−1+i31+i3−1−i3−1−i30000−1+i31−i30000−1−i31+i30000000000000000
χ661616-16-16160000-1600000000000000000000000001+i31−i31+i3−1−i3−1−i31−i3−1+i3−1+i30000−1−i31+i30000−1+i31−i30000000000000000
χ672424-24-24-24000024-8800000000000000000000000000000000000000000000000000000000000
χ6824-2424-2400024-2400000000000000-440000000000000000000000000000000000000000000000
χ6924-2424-24000-2424000000000000-44000000000000000000000000000000000000000000000000
χ7024-24-2424024-2400000000000000000000000000-44000000000000000000000000000000000000
χ7124-24-24240-2424000000000000000000000000-4400000000000000000000000000000000000000

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