Finite Group Databasebeta

← Group #13146704

Character table — Group #13146704

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122222244999912121212121212121212121218181818181818181818181818182424363636363636363636363636363636363636363636363636363672727272
order12222236666622223366666666662222222222666666444444446666666666121212121212121212121212
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
χ51111-1-11111-1-11111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111-1-11111-1-11111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111-1-11111-1-11111111111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ81111-1-11111-1-11111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ911-1-11-111-1-11-111-1-11111-1-111-1-1-1-11-111-1-111-1-111-1-11-1i−ii−ii−ii−i1-111-1-111-1-1ii−i−iii−i−ii−ii−i
χ1011-1-11-111-1-11-111-1-11111-1-111-1-1-1-11-111-1-111-1-111-1-11-1−ii−ii−ii−ii1-111-1-111-1-1−i−iii−i−iii−ii−ii
χ1111-1-11-111-1-11-111-1-11111-1-111-1-1-1-11-1-1-111-1-11111-1-11-1i−ii−i−ii−ii1-1-1-111-1-111−i−iii−i−iiii−ii−i
χ1211-1-11-111-1-11-111-1-11111-1-111-1-1-1-11-1-1-111-1-11111-1-11-1−ii−iii−ii−i1-1-1-111-1-111ii−i−iii−i−i−ii−ii
χ1311-1-1-1111-1-1-1111-1-11111-1-1-1-111-1-1-1111-1-1-1-11111-1-1-11i−i−iii−i−ii-1111-1-1-1-111ii−i−i−i−iiii−i−ii
χ1411-1-1-1111-1-1-1111-1-11111-1-1-1-111-1-1-1111-1-1-1-11111-1-1-11−iii−i−iii−i-1111-1-1-1-111−i−iiiii−i−i−iii−i
χ1511-1-1-1111-1-1-1111-1-11111-1-1-1-111-1-1-11-1-11111-1-111-1-1-11i−i−ii−iii−i-11-1-11111-1-1−i−iiiii−i−ii−i−ii
χ1611-1-1-1111-1-1-1111-1-11111-1-1-1-111-1-1-11-1-11111-1-111-1-1-11−iii−ii−i−ii-11-1-11111-1-1ii−i−i−i−iii−iii−i
χ17222222222222-2-2-2-2222222222222-2-200000000-2-2-2-22200000000-2-200000000000000000000
χ182222-2-22222-2-2-2-2-2-2222222-2-2-2-2222200000000-2-2-2-2-2-2000000002200000000000000000000
χ1922-2-22-222-2-22-2-2-2222222-2-222-2-2-2-2-2200000000-2-2222-200000000-2200000000000000000000
χ2022-2-2-2222-2-2-22-2-2222222-2-2-2-222-2-22-200000000-2-222-22000000002-200000000000000000000
χ212-22-2002-22-2002-22-222-2-22-200002-20000002-22-22-22-200000000000000002-22-2000000000000
χ222-22-2002-22-2002-22-222-2-22-200002-2000000-22-222-22-20000000000000000-22-22000000000000
χ232-22-2002-22-200-22-2222-2-22-200002-2002-22-20000-22-220000000000002-22-20000000000000000
χ242-22-2002-22-200-22-2222-2-22-200002-200-22-220000-22-22000000000000-22-220000000000000000
χ252-2-22002-2-22002-2-2222-2-2-220000-220000002-2-222-2-2200000000000000002-2-22000000000000
χ262-2-22002-2-22002-2-2222-2-2-220000-22000000-222-22-2-220000000000000000-222-2000000000000
χ272-2-22002-2-2200-222-222-2-2-220000-22002-2-220000-222-20000000000002-2-220000000000000000
χ282-2-22002-2-2200-222-222-2-2-220000-2200-222-20000-222-2000000000000-222-20000000000000000
χ2944444444444400001-21-2-2-2-2-2-2-211000000000000001122220000000000000000000000-1-1-1-1
χ3044444444444400001-21-2-2-2-2-2-2-2110000000000000011-2-2-2-200000000000000000000001111
χ314444444444440000-21-21111111-2-200222222220000-2-20000000000-1-1-1-1-1-1-1-1000000000000
χ324444444444440000-21-21111111-2-200-2-2-2-2-2-2-2-20000-2-2000000000011111111000000000000
χ334444-4-44444-4-400001-21-2-2-222221100000000000000-1-122-2-20000000000000000000000-1-111
χ344444-4-44444-4-400001-21-2-2-222221100000000000000-1-1-2-222000000000000000000000011-1-1
χ354444-4-44444-4-40000-21-2111-1-1-1-1-2-2002222-2-2-2-20000220000000000-1-1-1-11111000000000000
χ364444-4-44444-4-40000-21-2111-1-1-1-1-2-200-2-2-2-2222200002200000000001111-1-1-1-1000000000000
χ3744-4-44-444-4-44-400001-21-222-2-222-1-1000000000000001-12i−2i2i−2i0000000000000000000000−ii−ii
χ3844-4-44-444-4-44-400001-21-222-2-222-1-1000000000000001-1−2i2i−2i2i0000000000000000000000i−ii−i
χ3944-4-44-444-4-44-40000-21-21-1-111-1-1220022-2-222-2-20000-220000000000-1-111-1-111000000000000
χ4044-4-44-444-4-44-40000-21-21-1-111-1-12200-2-222-2-2220000-22000000000011-1-111-1-1000000000000
χ4144-4-4-4444-4-4-4400001-21-22222-2-2-1-100000000000000-112i−2i−2i2i0000000000000000000000−iii−i
χ4244-4-4-4444-4-4-4400001-21-22222-2-2-1-100000000000000-11−2i2i2i−2i0000000000000000000000i−i−ii
χ4344-4-4-4444-4-4-440000-21-21-1-1-1-111220022-2-2-2-22200002-20000000000-1-11111-1-1000000000000
χ4444-4-4-4444-4-4-440000-21-21-1-1-1-1112200-2-22222-2-200002-2000000000011-1-1-1-111000000000000
χ454-44-4004-44-4000000-212-11-13-33-3-22002-22-22-22-20000000000000000-11-11-11-11000000000000
χ464-44-4004-44-4000000-212-11-13-33-3-2200-22-22-22-2200000000000000001-11-11-11-1000000000000
χ474-44-4004-44-4000000-212-11-1-33-33-22002-22-2-22-220000000000000000-11-111-11-1000000000000
χ484-44-4004-44-4000000-212-11-1-33-33-2200-22-222-22-200000000000000001-11-1-11-11000000000000
χ494-4-44004-4-44000000-212-1-113-3-332-2002-2-222-2-220000000000000000-111-1-111-1000000000000
χ504-4-44004-4-44000000-212-1-113-3-332-200-222-2-222-200000000000000001-1-111-1-11000000000000
χ514-4-44004-4-44000000-212-1-11-333-32-2002-2-22-222-20000000000000000-111-11-1-11000000000000
χ524-4-44004-4-44000000-212-1-11-333-32-200-222-22-2-2200000000000000001-1-11-111-1000000000000
χ53666666-3-3-3-3-3-322220000000000002200000000-1-1-1-10000000000-1-1000000003−33−33−33−30000
χ54666666-3-3-3-3-3-322220000000000002200000000-1-1-1-10000000000-1-100000000−33−33−33−330000
χ55666666-3-3-3-3-3-3-2-2-2-2000000000000-2-200000000111100000022221100000000-1-1-1-1-1-1-1-10000
χ56666666-3-3-3-3-3-3-2-2-2-2000000000000-2-2000000001111000000-2-2-2-21100000000111111110000
χ576666-6-6-3-3-3-3332222000000000000-2-200000000-1-1-1-1000000000011000000003−33−3−33−330000
χ586666-6-6-3-3-3-3332222000000000000-2-200000000-1-1-1-100000000001100000000−33−333−33−30000
χ596666-6-6-3-3-3-333-2-2-2-20000000000002200000000111100000022-2-2-1-100000000-1-1-1-111110000
χ606666-6-6-3-3-3-333-2-2-2-200000000000022000000001111000000-2-222-1-1000000001111-1-1-1-10000
χ6166-6-66-6-3-333-3322-2-20000000000002-200000000-1-1110000000000-1100000000−i3i3i3−i3−i3i3i3−i30000
χ6266-6-66-6-3-333-3322-2-20000000000002-200000000-1-1110000000000-1100000000i3−i3−i3i3i3−i3−i3i30000
χ6366-6-66-6-3-333-33-2-222000000000000-220000000011-1-10000002i−2i2i−2i1-100000000−i−iii−i−iii0000
χ6466-6-66-6-3-333-33-2-222000000000000-220000000011-1-1000000−2i2i−2i2i1-100000000ii−i−iii−i−i0000
χ6566-6-6-66-3-3333-322-2-2000000000000-2200000000-1-11100000000001-100000000−i3i3i3−i3i3−i3−i3i30000
χ6666-6-6-66-3-3333-322-2-2000000000000-2200000000-1-11100000000001-100000000i3−i3−i3i3−i3i3i3−i30000
χ6766-6-6-66-3-3333-3-2-2220000000000002-20000000011-1-10000002i−2i−2i2i-1100000000−i−iiiii−i−i0000
χ6866-6-6-66-3-3333-3-2-2220000000000002-20000000011-1-1000000−2i2i2i−2i-1100000000ii−i−i−i−iii0000
χ698-88-8008-88-80000002-4-24-4400002-20000000000000000000000000000000000000000000000
χ708-8-88008-8-880000002-4-244-40000-220000000000000000000000000000000000000000000000
χ7112-1212-1200-66-66004-44-40000000000000000000000-22-2200000000000000000000000000000000
χ7212-1212-1200-66-6600-44-4400000000000000000000002-22-200000000000000000000000000000000
χ7312-12-121200-666-6004-4-440000000000000000000000-222-200000000000000000000000000000000
χ7412-12-121200-666-600-444-400000000000000000000002-2-2200000000000000000000000000000000

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