Finite Group Databasebeta

← Group #13136720

Character table — Group #13136720

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122222244999912121212121212121212121218181818181818181818181818182424363636363636363636363636363636363636363636363636363672727272
order1222223666664444336666666666444444444412121212664444888812121212121212121212242424242424242412121212
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
χ51111-1-11111-1-1-1-1-1-1111111-1-1-111-111iiii−i−i−i−i-1-1-1-1-1-111-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ61111-1-11111-1-1-1-1-1-1111111-1-1-111-111iiii−i−i−i−i-1-1-1-1-1-1-1-111−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-111
χ71111-1-11111-1-1-1-1-1-1111111-1-1-111-111−i−i−i−iiiii-1-1-1-1-1-111-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ81111-1-11111-1-1-1-1-1-1111111-1-1-111-111−i−i−i−iiiii-1-1-1-1-1-1-1-111ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ911-1-11-11-1-111-1-1-1111111-1-111-1-1-1-11-1ii−i−iii−i−i-1-1111-1i−ii−i1-11-11-1ii−i−iii−i−i11-1-111-1-1i−ii−i
χ1011-1-11-11-1-111-1-1-1111111-1-111-1-1-1-11-1ii−i−iii−i−i-1-1111-1−ii−ii-11-111-1ii−i−iii−i−i-1-111-1-111−ii−ii
χ1111-1-11-11-1-111-1-1-1111111-1-111-1-1-1-11-1−i−iii−i−iii-1-1111-1i−ii−i-11-111-1−i−iii−i−iii-1-111-1-111i−ii−i
χ1211-1-11-11-1-111-1-1-1111111-1-111-1-1-1-11-1−i−iii−i−iii-1-1111-1−ii−ii1-11-11-1−i−iii−i−iii11-1-111-1-1−ii−ii
χ1311-1-1-111-1-11-1111-1-11111-1-1-1-11-1-111-111-1-1-1-11111-1-1-11i−i−ii−iii−i1-111-1-1-1-111−i−iiiii−i−ii−i−ii
χ1411-1-1-111-1-11-1111-1-11111-1-1-1-11-1-111-111-1-1-1-11111-1-1-11−iii−ii−i−ii1-111-1-1-1-111ii−i−i−i−iii−iii−i
χ1511-1-1-111-1-11-1111-1-11111-1-1-1-11-1-111-1-1-11111-1-111-1-1-11i−i−iii−i−ii1-1-1-11111-1-1ii−i−i−i−iiii−i−ii
χ1611-1-1-111-1-11-1111-1-11111-1-1-1-11-1-111-1-1-11111-1-111-1-1-11−iii−i−iii−i1-1-1-11111-1-1−i−iiiii−i−i−iii−i
χ17222222222222-2-2-2-2222222222222-2-200000000-2-2-2-22200000000-2-200000000000000000000
χ182222-2-22222-2-22222222222-2-2-222-2-2-2000000002222-2-200000000-2-200000000000000000000
χ1922-2-22-22-2-222-222-2-22222-2-222-2-2-2-2-220000000022-2-22-200000000-2200000000000000000000
χ2022-2-2-222-2-22-22-2-2222222-2-2-2-22-2-22-2200000000-2-222-2200000000-2200000000000000000000
χ212-22-20022-2-2002i−2i2i−2i22-2-22-20002-20001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i2i−2i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ222-22-20022-2-2002i−2i2i−2i22-2-22-20002-2000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i2i−2i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ232-22-20022-2-200−2i2i−2i2i22-2-22-20002-20001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i−2i2i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ242-22-20022-2-200−2i2i−2i2i22-2-22-20002-2000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i−2i2i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ252-2-22002-22-2002i−2i−2i2i22-2-2-22000-220001+i−1−i−1−i1+i−1+i1−i1−i−1+i2i−2i−2i2i0000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ262-2-22002-22-2002i−2i−2i2i22-2-2-22000-22000−1−i1+i1+i−1−i1−i−1+i−1+i1−i2i−2i−2i2i000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ272-2-22002-22-200−2i2i2i−2i22-2-2-22000-220001−i−1+i−1+i1−i−1−i1+i1+i−1−i−2i2i2i−2i0000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ282-2-22002-22-200−2i2i2i−2i22-2-2-22000-22000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−2i2i2i−2i000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ2944444444444400001-21-211111-2-2100222222220000-2-20000000000-1-1-1-1-1-1-1-1000000000000
χ3044444444444400001-21-211111-2-2100-2-2-2-2-2-2-2-20000-2-2000000000011111111000000000000
χ314444444444440000-21-21-2-2-2-2-211-2000000000000001122220000000000000000000000-1-1-1-1
χ324444444444440000-21-21-2-2-2-2-211-20000000000000011-2-2-2-200000000000000000000001111
χ334444-4-44444-4-400001-21-211-1-1-1-2-2-1002i2i2i2i−2i−2i−2i−2i0000220000000000−i−i−i−iiiii000000000000
χ344444-4-44444-4-400001-21-211-1-1-1-2-2-100−2i−2i−2i−2i2i2i2i2i0000220000000000iiii−i−i−i−i000000000000
χ354444-4-44444-4-40000-21-21-2-222211200000000000000-1-122-2-20000000000000000000000-1-111
χ364444-4-44444-4-40000-21-21-2-222211200000000000000-1-1-2-222000000000000000000000011-1-1
χ3744-4-44-44-4-444-400001-21-2-1-111-122-1002i2i−2i−2i2i2i−2i−2i0000-220000000000−i−iii−i−iii000000000000
χ3844-4-44-44-4-444-400001-21-2-1-111-122-100−2i−2i2i2i−2i−2i2i2i0000-220000000000ii−i−iii−i−i000000000000
χ3944-4-44-44-4-444-40000-21-2122-2-22-1-12000000000000001-12i−2i2i−2i0000000000000000000000−ii−ii
χ4044-4-44-44-4-444-40000-21-2122-2-22-1-12000000000000001-1−2i2i−2i2i0000000000000000000000i−ii−i
χ4144-4-4-444-4-44-4400001-21-2-1-1-1-112210022-2-2-2-22200002-20000000000-1-11111-1-1000000000000
χ4244-4-4-444-4-44-4400001-21-2-1-1-1-1122100-2-22222-2-200002-2000000000011-1-1-1-111000000000000
χ4344-4-4-444-4-44-440000-21-212222-2-1-1-200000000000000-112i−2i−2i2i0000000000000000000000−iii−i
χ4444-4-4-444-4-44-440000-21-212222-2-1-1-200000000000000-11−2i2i2i−2i0000000000000000000000i−i−ii
χ454-44-40044-4-40000001-2-121-13-33-22-3002-22-22-22-20000000000000000-11-11-11-11000000000000
χ464-44-40044-4-40000001-2-121-13-33-22-300-22-22-22-2200000000000000001-11-11-11-1000000000000
χ474-44-40044-4-40000001-2-121-1-33-3-223002i−2i2i−2i−2i2i−2i2i0000000000000000−ii−iii−ii−i000000000000
χ484-44-40044-4-40000001-2-121-1-33-3-22300−2i2i−2i2i2i−2i2i−2i0000000000000000i−ii−i−ii−ii000000000000
χ494-4-44004-44-40000001-2-12-113-3-32-23002i−2i−2i2i2i−2i−2i2i0000000000000000−iii−i−iii−i000000000000
χ504-4-44004-44-40000001-2-12-113-3-32-2300−2i2i2i−2i−2i2i2i−2i0000000000000000i−i−iii−i−ii000000000000
χ514-4-44004-44-40000001-2-12-11-3332-2-3002-2-22-222-20000000000000000-111-11-1-11000000000000
χ524-4-44004-44-40000001-2-12-11-3332-2-300-222-22-2-2200000000000000001-1-11-111-1000000000000
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
χ576666-6-6-3-3-3-3332222000000000000-2-200000000-1-1-1-10000002i2i−2i−2i1100000000−i−i−i−iiiii0000
χ586666-6-6-3-3-3-3332222000000000000-2-200000000-1-1-1-1000000−2i−2i2i2i1100000000iiii−i−i−i−i0000
χ596666-6-6-3-3-3-333-2-2-2-2000000000000220000000011110000000000-1-100000000−i3i3−i3i3i3−i3i3−i30000
χ606666-6-6-3-3-3-333-2-2-2-2000000000000220000000011110000000000-1-100000000i3−i3i3−i3−i3i3−i3i30000
χ6166-6-66-6-333-3-3322-2-2000000000000-2200000000-1-1110000002-22-21-100000000-1-111-1-1110000
χ6266-6-66-6-333-3-3322-2-2000000000000-2200000000-1-111000000-22-221-10000000011-1-111-1-10000
χ6366-6-66-6-333-3-33-2-2220000000000002-20000000011-1-10000000000-11000000003−3−333−3−330000
χ6466-6-66-6-333-3-33-2-2220000000000002-20000000011-1-10000000000-1100000000−333−3−333−30000
χ6566-6-6-66-333-33-322-2-20000000000002-200000000-1-1110000000000-1100000000−i3i3i3−i3i3−i3−i3i30000
χ6666-6-6-66-333-33-322-2-20000000000002-200000000-1-1110000000000-1100000000i3−i3−i3i3−i3i3i3−i30000
χ6766-6-6-66-333-33-3-2-222000000000000-220000000011-1-10000002i−2i−2i2i1-100000000−i−iiiii−i−i0000
χ6866-6-6-66-333-33-3-2-222000000000000-220000000011-1-1000000−2i2i2i−2i1-100000000ii−i−i−i−iii0000
χ698-88-80088-8-8000000-424-2-440002-200000000000000000000000000000000000000000000000
χ708-8-88008-88-8000000-424-24-4000-2200000000000000000000000000000000000000000000000
χ7112-1212-1200-6-666004i−4i4i−4i0000000000000000000000−2i2i−2i2i00000000000000000000000000000000
χ7212-1212-1200-6-66600−4i4i−4i4i00000000000000000000002i−2i2i−2i00000000000000000000000000000000
χ7312-12-121200-66-66004i−4i−4i4i0000000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ7412-12-121200-66-6600−4i4i4i−4i00000000000000000000002i−2i−2i2i00000000000000000000000000000000

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