Finite Group Databasebeta

← Group #13180854

Character table — Group #13180854

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222244444466888899121212121616161616161616161616161616161618242436363636363636365454727272727272727272727272
order1223366366666443666441212121233336666666666664121222448888226612121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ31111111111111111111-1-111111111111111111111-1111-11-111-1-1-1-11-11-1-1-1-1-111-1-1
χ41111111111111111111-1-111111111111111111111-111-11-11-1-111-1-1-11-11-1-1-1-1-1-111
χ511-111111-1-1-1-11-111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11-11-1-1111-1-11-11-1
χ611-111111-1-1-1-11-111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-11-1-111-1-11-111-1-111-111-1-1-11-11
χ711-111111-1-1-1-11-111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-111-111-1-11-1-11-1111-1-1-1-1111-1-11
χ811-111111-1-1-1-11-111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-111-111-1-11-1-111-1-111-111-1
χ9222222222222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122200000000220000-1-1-1-10000
χ10222222222222222-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22200000000-2-2000011110000
χ112222-12-1-12-1-1-1-1222222002-12-12-1-1-12-1-1-122-1-1-1-1-1-10-1-102020022000-10-1000000-1-1
χ122222-12-1-12-1-1-1-1222222002-12-12-1-1-12-1-1-122-1-1-1-1-1-10-1-10-20-200-2-200010100000011
χ13222-12-12-1-12-1-1-122222200-12-12-12-1-1-12-1-1-1-122-1-1-1-10-1-12020220000-10-100000-1-100
χ14222-12-12-1-12-1-1-122222200-12-12-12-1-1-12-1-1-1-122-1-1-1-10-1-1-20-20-2-20000101000001100
χ1522-222222-2-2-2-22-22-111-122-2-222-1-1-1-1-1-1-1-111111111-22-2000000002-20000-1-1110000
χ1622-222222-2-2-2-22-22-111-1-2-2-2-222-1-1-1-1-1-1-1-11111111122-200000000-22000011-1-10000
χ1722-22-12-1-1-2111-1-222-2-2200-212-12-1-1-12-1-1-1-2-21111110-11020-200-22000-1010000001-1
χ1822-22-12-1-1-2111-1-222-2-2200-212-12-1-1-12-1-1-1-2-21111110-110-202002-200010-1000000-11
χ1922-2-12-12-11-211-1-222-2-22001-2-12-12-1-1-12-1-111-2-211110-1120-202-20000-10100000-1100
χ2022-2-12-12-11-211-1-222-2-22001-2-12-12-1-1-12-1-111-2-211110-11-2020-22000010-1000001-100
χ213333333333333-1-1000033-1-1-1-100000000000000003-1-11111-1-1-1-1-1-111110000-1-1-1-1
χ223333333333333-1-1000033-1-1-1-100000000000000003-1-1-1-1-1-11111-1-1-1-1-1-100001111
χ233333333333333-1-10000-3-3-1-1-1-10000000000000000-3-1-11-11-1-1-111111-11-10000-1-111
χ243333333333333-1-10000-3-3-1-1-1-10000000000000000-3-1-1-11-1111-1-111-11-11000011-1-1
χ2533-333333-3-3-3-331-100003311-1-10000000000000000-3-111-1-11-11-11-111-1-110000-11-11
χ2633-333333-3-3-3-331-100003311-1-10000000000000000-3-11-111-11-11-1-11-111-100001-11-1
χ2733-333333-3-3-3-331-10000-3-311-1-100000000000000003-1111-1-1-111-11-111-1-10000-111-1
χ2833-333333-3-3-3-331-10000-3-311-1-100000000000000003-11-1-1111-1-111-1-1-11100001-1-11
χ294444-24-2-24-2-2-2-244-2-2-2-2004-24-2-2111-2111-2-21111110-2-20000000000000000000000
χ30444-24-24-2-24-2-2-244-2-2-2-200-24-241-2111-21111-2-211110-2-20000000000000000000000
χ31444-2-2-2-21-2-211144444400-2-2-2-2-2-211-2-211-2-2-2-211110110000000000000000000000
χ32444-2-2-2-21-2-211144-2-2-2-200-2-2-2-211−1−3i32−1+3i3211−1−3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i320110000000000000000000000
χ33444-2-2-2-21-2-211144-2-2-2-200-2-2-2-211−1+3i32−1−3i3211−1+3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i320110000000000000000000000
χ3444-44-24-2-2-4222-2-44-222-200-424-2-2111-211122-1-1-1-1-1-10-220000000000000000000000
χ3544-4-24-24-22-422-2-44-222-2002-4-241-2111-211-1-122-1-1-1-10-220000000000000000000000
χ3644-4-2-2-2-2122-1-11-444-4-440022-2-2-2-211-2-2112222-1-1-1-101-10000000000000000000000
χ3744-4-2-2-2-2122-1-11-44-222-20022-2-211−1−3i32−1+3i3211−1−3i32−1+3i32-1-1-1-11+3i321+3i321−3i321−3i3201-10000000000000000000000
χ3844-4-2-2-2-2122-1-11-44-222-20022-2-211−1+3i32−1−3i3211−1+3i32−1−3i32-1-1-1-11−3i321−3i321+3i321+3i3201-10000000000000000000000
χ394-4044-4-440000-4001−i3i3-14i−4i00001111-1-1-1-1−i3i3−i3i3−i3i3−i3i300000000000000000i−i3−30000
χ404-4044-4-440000-4001−i3i3-1−4i4i00001111-1-1-1-1−i3i3−i3i3−i3i3−i3i300000000000000000−ii−330000
χ414-4044-4-440000-4001i3−i3-14i−4i00001111-1-1-1-1i3−i3i3−i3i3−i3i3−i300000000000000000i−i−330000
χ424-4044-4-440000-4001i3−i3-1−4i4i00001111-1-1-1-1i3−i3i3−i3i3−i3i3−i300000000000000000−ii3−30000
χ434-4044-4-440000-400-20024i−4i0000-2-2-2-222220000000000000000000000000−2i2i000000
χ444-4044-4-440000-400-2002−4i4i0000-2-2-2-2222200000000000000000000000002i−2i000000
χ456666-36-3-36-3-3-3-3-2-2000000-21-210000000000000000011020200-2-2000-10-100000011
χ466666-36-3-36-3-3-3-3-2-2000000-21-2100000000000000000110-20-20022000101000000-1-1
χ47666-36-36-3-36-3-3-3-2-20000001-21-200000000000000000112020-2-20000-10-1000001100
χ48666-36-36-3-36-3-3-3-2-20000001-21-20000000000000000011-20-2022000010100000-1-100
χ4966-66-36-3-3-6333-32-20000002-1-21000000000000000001-1020-2002-2000-101000000-11
χ5066-66-36-3-3-6333-32-20000002-1-21000000000000000001-10-20200-2200010-10000001-1
χ5166-6-36-36-33-633-32-2000000-121-2000000000000000001-120-20-220000-101000001-100
χ5266-6-36-36-33-633-32-2000000-121-2000000000000000001-1-20202-2000010-100000-1100
χ538-808-4-84-400004002−2i32i3-20000002-1-1-1-2111−2i32i3i3−i3i3−i3i3−i30000000000000000000000000
χ548-808-4-84-4000040022i3−2i3-20000002-1-1-1-21112i3−2i3−i3i3−i3i3−i3i30000000000000000000000000
χ558-808-4-84-40000400-4004000000-42224-2-2-2000000000000000000000000000000000
χ568-80-484-8-400004002−2i32i3-2000000-12-1-11-211i3−i3−2i32i3i3−i3i3−i30000000000000000000000000
χ578-80-484-8-4000040022i3−2i3-2000000-12-1-11-211−i3i32i3−2i3−i3i3−i3i30000000000000000000000000
χ588-80-484-8-40000400-40040000002-422-24-2-2000000000000000000000000000000000
χ598-80-4-4442006-6-2002−2i32i3-2000000-1-11−3i321+3i3211−1+3i32−1−3i32i3−i3i3−i33−i32−3+i32−3−i323+i320000000000000000000000000
χ608-80-4-4442006-6-20022i3−2i3-2000000-1-11+3i321−3i3211−1−3i32−1+3i32−i3i3−i3i33+i32−3−i32−3+i323−i320000000000000000000000000
χ618-80-4-4442006-6-200-400400000022-1-1-2-2110000-333-30000000000000000000000000
χ628-80-4-444200-66-2002−2i32i3-2000000-1-11+3i321−3i3211−1−3i32−1+3i32i3−i3i3−i3−3−i323+i323−i32−3+i320000000000000000000000000
χ638-80-4-444200-66-20022i3−2i3-2000000-1-11−3i321+3i3211−1+3i32−1−3i32−i3i3−i3i3−3+i323−i323+i32−3−i320000000000000000000000000
χ648-80-4-444200-66-200-400400000022-1-1-2-21100003-3-330000000000000000000000000
χ65121212-6-6-6-63-6-6333-4-4000000222200000000000000000-1-10000000000000000000000
χ661212-12-6-6-6-6366-3-334-4000000-2-22200000000000000000-110000000000000000000000

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