Finite Group Databasebeta

← Group #13140586

Character table — Group #13140586

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11222222244444444666699121212121212121212121818181818181824242424242424242424363636363636363636363636363636367272727272727272
order122223666246666121233664436666666664441212121266666612121212244444444466121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-11111111111-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111-1-11111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-111-1-1-1-111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-1
χ6111111111-1-111-1-1-1-111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111
χ7111111111-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111
χ8111111111-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-111-1-111-1-11111-1-1
χ9111-1-111111-1-1-111-1-1111111111111-1-1-1-11-1-1111111-1-111-1-1-1-1-11i−ii−ii−ii−i-1-1-1-111i−ii−ii−ii−i
χ10111-1-111111-1-1-111-1-1111111111111-1-1-1-11-1-1111111-1-111-1-1-1-1-11−ii−ii−ii−ii-1-1-1-111−ii−ii−ii−ii
χ11111-1-111111-1-1-111-1-11111-1-1111111-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11-1i−ii−i−ii−ii1111-1-1i−ii−i−ii−ii
χ12111-1-111111-1-1-111-1-11111-1-1111111-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11-1−ii−iii−ii−i1111-1-1−ii−iii−ii−i
χ13111-1-11111-11-1-1-1-111111111111111-1-1-1-11-1-11111-1-1-1-1-1-111111-1i−i−iii−i−ii11-1-1-1-1i−i−iii−i−ii
χ14111-1-11111-11-1-1-1-111111111111111-1-1-1-11-1-11111-1-1-1-1-1-111111-1−iii−i−iii−i11-1-1-1-1−iii−i−iii−i
χ15111-1-11111-11-1-1-1-1111111-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11i−i−ii−iii−i-1-11111i−i−ii−iii−i
χ16111-1-11111-11-1-1-1-1111111-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11−iii−ii−i−ii-1-11111−iii−ii−i−ii
χ17222222222222222222-12-100-12-1-1-1-122-1-100000002-1-1-1-1-12-1-1-100000022220000000000-1-1-1-1
χ18222222222222222222-12-100-12-1-1-1-122-1-100000002-1-1-1-1-12-1-1-1000000-2-2-2-200000000001111
χ1922222222222222222-12-1200-1-12-1-1-1-1-1220000000-12-1-1-1-1-12-1-10022220000000000-1-1-1-10000
χ2022222222222222222-12-1200-1-12-1-1-1-1-1220000000-12-1-1-1-1-12-1-100-2-2-2-2000000000011110000
χ21222222222-2-222-2-2-2-22-12-100-12-1-1-1-122-1-10000000-21-1-111-211100000022-2-20000000000-1-111
χ22222222222-2-222-2-2-2-22-12-100-12-1-1-1-122-1-10000000-21-1-111-2111000000-2-222000000000011-1-1
χ23222222222-2-222-2-2-2-2-12-1200-1-12-1-1-1-1-12200000001-2-1-1111-2110022-2-20000000000-1-1110000
χ24222222222-2-222-2-2-2-2-12-1200-1-12-1-1-1-1-12200000001-2-1-1111-21100-2-222000000000011-1-10000
χ25222-2-222222-2-2-222-2-22-12-100-12-1-1-1-1-2-21100000002-111-1-1-21110000002i−2i2i−2i0000000000−ii−ii
χ26222-2-222222-2-2-222-2-22-12-100-12-1-1-1-1-2-21100000002-111-1-1-2111000000−2i2i−2i2i0000000000i−ii−i
χ27222-2-222222-2-2-222-2-2-12-1200-1-12-1-1-111-2-20000000-1211-1-11-211002i−2i2i−2i0000000000−ii−ii0000
χ28222-2-222222-2-2-222-2-2-12-1200-1-12-1-1-111-2-20000000-1211-1-11-21100−2i2i−2i2i0000000000i−ii−i0000
χ29222-2-22222-22-2-2-2-2222-12-100-12-1-1-1-1-2-2110000000-2111112-1-1-10000002i−2i−2i2i0000000000−iii−i
χ30222-2-22222-22-2-2-2-2222-12-100-12-1-1-1-1-2-2110000000-2111112-1-1-1000000−2i2i2i−2i0000000000i−i−ii
χ31222-2-22222-22-2-2-2-222-12-1200-1-12-1-1-111-2-200000001-21111-12-1-1002i−2i−2i2i0000000000−iii−i0000
χ32222-2-22222-22-2-2-2-222-12-1200-1-12-1-1-111-2-200000001-21111-12-1-100−2i2i2i−2i0000000000i−i−ii0000
χ3322-22-22-2-22002-200002222222-2-2-2-222-22-2-22-222-2-2002-20000000000000000002-20000000000
χ3422-22-22-2-22002-200002222-2-22-2-2-2-222-22-22-22-2-222002-2000000000000000000-220000000000
χ3522-2-222-2-2200-2200002222222-2-2-2-22-22-22-2-2222-2-200-22000000000000000000-220000000000
χ3622-2-222-2-2200-2200002222-2-22-2-2-2-22-22-2222-2-2-22200-220000000000000000002-20000000000
χ3744444444444444444-2-2-2-2001-2-2111-2-2-2-20000000-2-21111-2-211000000000000000000000000
χ38444444444-4-444-4-4-4-4-2-2-2-2001-2-2111-2-2-2-200000002211-1-122-1-1000000000000000000000000
χ39444-4-444444-4-4-444-4-4-2-2-2-2001-2-211122220000000-2-2-1-11122-1-1000000000000000000000000
χ40444-4-44444-44-4-4-4-444-2-2-2-2001-2-21112222000000022-1-1-1-1-2-211000000000000000000000000
χ4144-44-44-4-44004-400004-24-200-2-4222-24-4-22000000000-22000000000000000000000000000000
χ4244-44-44-4-44004-40000-24-2400-22-422-2-224-4000000000-22000000000000000000000000000000
χ4344-44-44-4-44004-40000-2-2-2-200122-1-11-22-220000000001-13-3003-3000000000000000000000000
χ4444-44-44-4-44004-40000-2-2-2-200122-1-11-22-220000000001-1-3300-33000000000000000000000000
χ4544-4-444-4-4400-4400004-24-200-2-4222-2-442-20000000002-2000000000000000000000000000000
χ4644-4-444-4-4400-440000-24-2400-22-422-22-2-440000000002-2000000000000000000000000000000
χ4744-4-444-4-4400-440000-2-2-2-200122-1-112-22-2000000000-113-300-33000000000000000000000000
χ4844-4-444-4-4400-440000-2-2-2-200122-1-112-22-2000000000-11-33003-3000000000000000000000000
χ494-4000400-40000000044-4-44i−4i40000-400000004i−4i000000000000000000000000000000000000
χ504-4000400-40000000044-4-4−4i4i40000-40000000−4i4i000000000000000000000000000000000000
χ5166666-3-3-3-366-3-3-3-3-3-30000220000000000222-1-1-1-100000000002200000000-1-1-1-1-1-100000000
χ5266666-3-3-3-366-3-3-3-3-3-30000-2-20000000000-2-2-211110000000000-2-20000000011111100000000
χ5366666-3-3-3-3-6-6-3-333330000220000000000222-1-1-1-10000000000-2-20000000011-1-11100000000
χ5466666-3-3-3-3-6-6-3-333330000-2-20000000000-2-2-2111100000000002200000000-1-111-1-100000000
χ55666-6-6-3-3-3-36-633-3-33300002200000000002-2-2-1-1-1-10000000000-22000000001111-1-100000000
χ56666-6-6-3-3-3-36-633-3-3330000-2-20000000000-222111100000000002-200000000-1-1-1-11100000000
χ57666-6-6-3-3-3-3-663333-3-300002200000000002-2-2-1-1-1-100000000002-200000000-1-1111100000000
χ58666-6-6-3-3-3-3-663333-3-30000-2-20000000000-22211110000000000-220000000011-1-1-1-100000000
χ5966-66-6-333-300-33−3i33i3−3i33i30000220000000000-22-2-1-11100000000000000000000−i3i3-11−i3i300000000
χ6066-66-6-333-300-33−3i33i3−3i33i30000-2-200000000002-2211-1-100000000000000000000i3−i31-1i3−i300000000
χ6166-66-6-333-300-333i3−3i33i3−3i30000220000000000-22-2-1-11100000000000000000000i3−i3-11i3−i300000000
χ6266-66-6-333-300-333i3−3i33i3−3i30000-2-200000000002-2211-1-100000000000000000000−i3i31-1−i3i300000000
χ6366-6-66-333-3003-3−3i33i33i3−3i30000220000000000-2-22-1-11100000000000000000000i3−i31-1−i3i300000000
χ6466-6-66-333-3003-3−3i33i33i3−3i30000-2-2000000000022-211-1-100000000000000000000−i3i3-11i3−i300000000
χ6566-6-66-333-3003-33i3−3i3−3i33i30000220000000000-2-22-1-11100000000000000000000−i3i31-1i3−i300000000
χ6666-6-66-333-3003-33i3−3i3−3i33i30000-2-2000000000022-211-1-100000000000000000000i3−i3-11−i3i300000000
χ678-8000800-8000000008-4-8400-400004000000000000000000000000000000000000000000000
χ688-8000800-800000000-484-800-400004000000000000000000000000000000000000000000000
χ698-8000800-800000000-4-444002006-6-2000000000000000000000000000000000000000000000
χ708-8000800-800000000-4-44400200-66-2000000000000000000000000000000000000000000000
χ7112-12000-6−6i36i360000000000004i−4i0000000000000−2i2i23−230000000000000000000000000000000000
χ7212-12000-6−6i36i36000000000000−4i4i00000000000002i−2i−23230000000000000000000000000000000000
χ7312-12000-66i3−6i360000000000004i−4i0000000000000−2i2i−23230000000000000000000000000000000000
χ7412-12000-66i3−6i36000000000000−4i4i00000000000002i−2i23−230000000000000000000000000000000000

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