Finite Group Databasebeta

← Group #13146615

Character table — Group #13146615

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122222244999912121212121212121212121218181818181818181818181818182424363636363636363636363636363636363636363636363636363672727272
order12223446661212222233666666121212124444444444666612124444444412121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111-1-1111-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111-1-1111-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111-1-1111-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ811111-1-1111-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ911-1-111-1-1-111-11-1-1111-111-1-1-111-1-11-1ii−i−iii−i−i1-1-111-1i−ii−i1-11-11-1ii−i−iii−i−i11-1-111-1-1i−ii−i
χ1011-1-111-1-1-111-11-1-1111-111-1-1-111-1-11-1ii−i−iii−i−i1-1-111-1−ii−ii-11-111-1ii−i−iii−i−i-1-111-1-111−ii−ii
χ1111-1-111-1-1-111-11-1-1111-111-1-1-111-1-11-1−i−iii−i−iii1-1-111-1i−ii−i-11-111-1−i−iii−i−iii-1-111-1-111i−ii−i
χ1211-1-111-1-1-111-11-1-1111-111-1-1-111-1-11-1−i−iii−i−iii1-1-111-1−ii−ii1-11-11-1−i−iii−i−iii11-1-111-1-1−ii−ii
χ1311-1-11-11-1-11-111-1-1111-111-1-1-1-1-111-11ii−i−i−i−iii1-1-11-11i−i−ii1-1-11-11ii−i−i−i−iii11-1-1-1-111i−i−ii
χ1411-1-11-11-1-11-111-1-1111-111-1-1-1-1-111-11ii−i−i−i−iii1-1-11-11−iii−i-111-1-11ii−i−i−i−iii-1-11111-1-1−iii−i
χ1511-1-11-11-1-11-111-1-1111-111-1-1-1-1-111-11−i−iiiii−i−i1-1-11-11i−i−ii-111-1-11−i−iiiii−i−i-1-11111-1-1i−i−ii
χ1611-1-11-11-1-11-111-1-1111-111-1-1-1-1-111-11−i−iiiii−i−i1-1-11-11−iii−i1-1-11-11−i−iiiii−i−i11-1-1-1-111−iii−i
χ17222222222222-2-2-2-2222222222222-2-200000000-2-2-2-22200000000-2-200000000000000000000
χ1822222-2-2222-2-2-2-2-2-222222222-2-2-2-22200000000-2-2-2-2-2-2000000002200000000000000000000
χ1922-2-222-2-2-222-2-222-222-222-2-2-222-2-2-2200000000-222-22-200000000-2200000000000000000000
χ2022-2-22-22-2-22-22-222-222-222-2-2-2-2-2222-200000000-222-2-22000000002-200000000000000000000
χ212-22-22002-2-20022-2-2222-2-22-2-20000002-22-2000022-2-20000000000002-22-20000000000000000
χ222-22-22002-2-20022-2-2222-2-22-2-2000000-22-22000022-2-2000000000000-22-220000000000000000
χ232-22-22002-2-200-2-222222-2-22-2-200000000002i−2i2i−2i-2-22200000000000000002i−2i2i−2i000000000000
χ242-22-22002-2-200-2-222222-2-22-2-20000000000−2i2i−2i2i-2-2220000000000000000−2i2i−2i2i000000000000
χ252-2-22200-22-2002-22-222-2-2-2-2220000002i−2i−2i2i00002-22-20000000000002i−2i−2i2i0000000000000000
χ262-2-22200-22-2002-22-222-2-2-2-222000000−2i2i2i−2i00002-22-2000000000000−2i2i2i−2i0000000000000000
χ272-2-22200-22-200-22-2222-2-2-2-22200000000002-2-22-22-2200000000000000002-2-22000000000000
χ282-2-22200-22-200-22-2222-2-2-2-2220000000000-222-2-22-220000000000000000-222-2000000000000
χ2944444444444400001-211-2-2-21-2-2-2-2000000000000001122220000000000000000000000-1-1-1-1
χ3044444444444400001-211-2-2-21-2-2-2-20000000000000011-2-2-2-200000000000000000000001111
χ314444444444440000-21-2-2111-2111100222222220000-2-20000000000-1-1-1-1-1-1-1-1000000000000
χ324444444444440000-21-2-2111-2111100-2-2-2-2-2-2-2-20000-2-2000000000011111111000000000000
χ3344444-4-4444-4-400001-211-2-2-21222200000000000000-1-122-2-20000000000000000000000-1-111
χ3444444-4-4444-4-400001-211-2-2-21222200000000000000-1-1-2-222000000000000000000000011-1-1
χ3544444-4-4444-4-40000-21-2-2111-2-1-1-1-1002222-2-2-2-20000220000000000-1-1-1-11111000000000000
χ3644444-4-4444-4-40000-21-2-2111-2-1-1-1-100-2-2-2-2222200002200000000001111-1-1-1-1000000000000
χ3744-4-444-4-4-444-400001-2-11-222-1-2-222000000000000001-12i−2i2i−2i0000000000000000000000−ii−ii
χ3844-4-444-4-4-444-400001-2-11-222-1-2-222000000000000001-1−2i2i−2i2i0000000000000000000000i−ii−i
χ3944-4-444-4-4-444-40000-212-21-1-1211-1-1002i2i−2i−2i2i2i−2i−2i0000-220000000000−i−iii−i−iii000000000000
χ4044-4-444-4-4-444-40000-212-21-1-1211-1-100−2i−2i2i2i−2i−2i2i2i0000-220000000000ii−i−iii−i−i000000000000
χ4144-4-44-44-4-44-4400001-2-11-222-122-2-200000000000000-112i−2i−2i2i0000000000000000000000−iii−i
χ4244-4-44-44-4-44-4400001-2-11-222-122-2-200000000000000-11−2i2i2i−2i0000000000000000000000i−i−ii
χ4344-4-44-44-4-44-440000-212-21-1-12-1-111002i2i−2i−2i−2i−2i2i2i00002-20000000000−i−iiiii−i−i000000000000
χ4444-4-44-44-4-44-440000-212-21-1-12-1-11100−2i−2i2i2i2i2i−2i−2i00002-20000000000ii−i−i−i−iii000000000000
χ454-44-44004-4-4000000-21-22-11-123i−3i3i−3i002-22-22i−2i2i−2i0000000000000000-11-11−ii−ii000000000000
χ464-44-44004-4-4000000-21-22-11-123i−3i3i−3i00-22-22−2i2i−2i2i00000000000000001-11-1i−ii−i000000000000
χ474-44-44004-4-4000000-21-22-11-12−3i3i−3i3i002-22-2−2i2i−2i2i0000000000000000-11-11i−ii−i000000000000
χ484-44-44004-4-4000000-21-22-11-12−3i3i−3i3i00-22-222i−2i2i−2i00000000000000001-11-1−ii−ii000000000000
χ494-4-44400-44-4000000-2122-1-11-23i−3i−3i3i002i−2i−2i2i-222-20000000000000000−iii−i1-1-11000000000000
χ504-4-44400-44-4000000-2122-1-11-23i−3i−3i3i00−2i2i2i−2i2-2-220000000000000000i−i−ii-111-1000000000000
χ514-4-44400-44-4000000-2122-1-11-2−3i3i3i−3i002i−2i−2i2i2-2-220000000000000000−iii−i-111-1000000000000
χ524-4-44400-44-4000000-2122-1-11-2−3i3i3i−3i00−2i2i2i−2i-222-20000000000000000i−i−ii1-1-11000000000000
χ536666-366-3-3-3-3-322220000000000002200000000-1-1-1-10000000000-1-1000000003−33−33−33−30000
χ546666-366-3-3-3-3-322220000000000002200000000-1-1-1-10000000000-1-100000000−33−33−33−330000
χ556666-366-3-3-3-3-3-2-2-2-2000000000000-2-200000000111100000022221100000000-1-1-1-1-1-1-1-10000
χ566666-366-3-3-3-3-3-2-2-2-2000000000000-2-2000000001111000000-2-2-2-21100000000111111110000
χ576666-3-6-6-3-3-3332222000000000000-2-200000000-1-1-1-1000000000011000000003−33−3−33−330000
χ586666-3-6-6-3-3-3332222000000000000-2-200000000-1-1-1-100000000001100000000−33−333−33−30000
χ596666-3-6-6-3-3-333-2-2-2-20000000000002200000000111100000022-2-2-1-100000000-1-1-1-111110000
χ606666-3-6-6-3-3-333-2-2-2-200000000000022000000001111000000-2-222-1-1000000001111-1-1-1-10000
χ6166-6-6-36-633-3-332-2-220000000000002-200000000-111-10000000000-11000000003−3−333−3−330000
χ6266-6-6-36-633-3-332-2-220000000000002-200000000-111-10000000000-1100000000−333−3−333−30000
χ6366-6-6-36-633-3-33-222-2000000000000-22000000001-1-110000002-22-21-100000000-1-111-1-1110000
χ6466-6-6-36-633-3-33-222-2000000000000-22000000001-1-11000000-22-221-10000000011-1-111-1-10000
χ6566-6-6-3-6633-33-32-2-22000000000000-2200000000-111-100000000001-1000000003−3−33−333−30000
χ6666-6-6-3-6633-33-32-2-22000000000000-2200000000-111-100000000001-100000000−333−33−3−330000
χ6766-6-6-3-6633-33-3-222-20000000000002-2000000001-1-110000002-2-22-1100000000-1-11111-1-10000
χ6866-6-6-3-6633-33-3-222-20000000000002-2000000001-1-11000000-222-2-110000000011-1-1-1-1110000
χ698-88-88008-8-80000002-42-24-44-200000000000000000000000000000000000000000000000000
χ708-8-88800-88-80000002-4-2-244-4200000000000000000000000000000000000000000000000000
χ7112-1212-12-600-6660044-4-40000000000000000000000-2-22200000000000000000000000000000000
χ7212-1212-12-600-66600-4-444000000000000000000000022-2-200000000000000000000000000000000
χ7312-12-1212-6006-66004-44-40000000000000000000000-22-2200000000000000000000000000000000
χ7412-12-1212-6006-6600-44-4400000000000000000000002-22-200000000000000000000000000000000

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