Finite Group Databasebeta

← Group #13180542

Character table — Group #13180542

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1122244444666688888888991212121212121212121618181818182424242424242424242424242436363636363636364848545454547272727272108
order1223633666244433666666222441212121212126244666666121212121212121212244446121261224446121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-11-111111111-1-111-11-11-1111-1111111-1-1-11-1-1-1-111-1-111-1-1-1-1
χ3111111111111-1-111111111111-11-1-1-1-1-1-1111111111111-111-1-1-1-1-1-11-1-11111111-1-1-1-11-1-1-1
χ4111111111111-1-11111111111-1-1-1-1-1-1-1-1-111-1-111-11-11-11-11-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1111
χ51111111111-1-111111111111111111111111-1-1111-11-11-11-111111-1-1-1111-1-111-1-1-1-1-1-1-111-1
χ61111111111-1-1111111111111-11-1111111111111-1-1-1-1-1-11-1-11111-1-11-1-1111-1-1-1-111-1-11-1-11
χ71111111111-1-1-1-111111111111-11-1-1-1-1-1-111-1-1111-11-11-1-1-11-1-1-1-111-1-1-11-1-111-1-11111-1-1-11
χ81111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-1
χ911-11111-1111-11111-1-1-1-111111-1-111-1-111-1-1-1-1111111-1-1-1-1-111-1-1-1111-1-1-1-11-11-1-1-1-1111-11
χ1011-11111-1111-11111-1-1-1-11111-1-1111-1-111-1-11111-11-111-1-1-1111-1-1-11-1-11-111-111-111-11-1-11-1
χ1111-11111-1111-1-1-111-1-1-1-1111111-1-1-111-1-1-1-1-1-1111111-1-11-1-1-1-1111-11-11-1-1-11-11-1111-11-11-1
χ1211-11111-1111-1-1-111-1-1-1-11111-111-1-111-1-1-1-11111-11-111-11-11-1-1111-1-11-1-111-111-1-1-11-1-11-11
χ1311-11111-111-111111-1-1-1-111111-1-111-1-111-1-111111-11-1-11-11-111-1-11-1-11-1-1111-1-11111-1-11-1-1
χ1411-11111-111-111111-1-1-1-11111-1-1111-1-111-1-1-1-111-1-1-1-111-11111-1-11-11-11-1-1-1-11-11-1-11-11-111
χ1511-11111-111-11-1-111-1-1-1-1111111-1-1-111-1-1-1-111111-11-1-1111-1-1-111-11-1-11-1111-1-11-1-1-11-1-111
χ1611-11111-111-11-1-111-1-1-1-11111-111-1-111-1-1-1-1-1-111-1-1-1-111111-1-111-1111-1-1-1-1-11-1111-1111-1-1
χ172222222222220022222222-2-20000000002-200-2-2020202020000000000-20000-2-200000000
χ182222222222-2-20022222222-2-20000000002-200-2-20-20-20-20-20000000000-200002200000000
χ19222-1-122-1220022-1-122-1-1-1-122222-1-1-1-122-1200-1-1-1020-10202-1-1-1-100022-100-1-10000000-1-10
χ20222-1-122-1220022-1-122-1-1-1-122-22-2-1-1-1-122-1200-1-110-201020-2-1-1-1-1000-2-2-100110000000110
χ21222-1-122-12200-2-2-1-122-1-1-1-1222-221111-2-2-1200-1-1-1020-10-2021111000-2-2-100-1-10000000110
χ22222-1-122-12200-2-2-1-122-1-1-1-122-2-2-21111-2-2-1200-1-110-2010-20-2111100022-100110000000-1-10
χ2322-22222-2222-20022-2-2-2-222-2-2000000000-2200-2-202020-20-2000000000020000-2200000000
χ2422-22222-222-220022-2-2-2-222-2-2000000000-2200-2-20-20-202020000000000200002-200000000
χ2522-2-1-1221220022-1-1-2-211-1-1222-2-2-1-111221-200-1-1-102010-20-2-1-1110002-2100-110000000-110
χ2622-2-1-1221220022-1-1-2-211-1-122-2-22-1-111221-200-1-110-20-10-202-1-111000-221001-100000001-10
χ2722-2-1-12212200-2-2-1-1-2-211-1-12222-211-1-1-2-21-200-1-1-10201020-211-1-1000-22100-1100000001-10
χ2822-2-1-12212200-2-2-1-1-2-211-1-122-22211-1-1-2-21-200-1-110-20-1020211-1-10002-21001-10000000-110
χ292-202-2220-2-2002i−2i220000-2-2-220002i−2i002i−2i002i−2i2-20000000002i−2i000000002i−2i00002-2000000
χ302-202-2220-2-2002i−2i220000-2-2-220002i−2i002i−2i00−2i2i2-20000000002i−2i00000000−2i2i0000-22000000
χ312-202-2220-2-200−2i2i220000-2-2-22000−2i2i00−2i2i002i−2i2-2000000000−2i2i000000002i−2i0000-22000000
χ322-202-2220-2-200−2i2i220000-2-2-22000−2i2i00−2i2i00−2i2i2-2000000000−2i2i00000000−2i2i00002-2000000
χ33444441-24-214400-211-2-2-21-20020200000010220021-1-22-201-10000002000-1-1-1-1000000-1000
χ34444441-24-214400-211-2-2-21-200-20-200000010-2-200-211-2-2-2011000000-200011110000001000
χ35444441-24-21-4-400-211-2-2-21-20020200000010-2-2002-1-12220-1-1000000-200011-1-10000001000
χ36444441-24-21-4-400-211-2-2-21-200-20-2000000102200-2-112-220-110000002000-1-111000000-1000
χ3744444-2141-244221-2-2111-21000202222-1-1-2000000-20101-1-20-1-1-1-122000000000000-1-10000
χ3844444-2141-244-2-21-2-2111-21000-20-2-2-2-211-2000000-201011-201111-2-2000000000000110000
χ3944444-2141-2-4-4221-2-2111-21000202222-1-1-200000020-10-1-120-1-1-1-1-2-2000000000000110000
χ4044444-2141-2-4-4-2-21-2-2111-21000-20-2-2-2-211-200000020-10-1120111122000000000000-1-10000
χ41444-2-244-2440000-2-244-2-2-2-2-4-4000000000-2-40022000000000000000000200000000000000
χ4244-4441-2-4-214-400-21-12221-20020-2000000-10-2-20021-1-2-220-11000000200011-11000000-1000
χ4344-4441-2-4-214-400-21-12221-200-202000000-102200-211-2220-1-1000000-2000-1-11-10000001000
χ4444-4441-2-4-21-4400-21-12221-20020-2000000-1022002-1-12-2-2011000000-2000-1-1-110000001000
χ4544-4441-2-4-21-4400-21-12221-200-202000000-10-2-200-2-1122-201-10000002000111-1000000-1000
χ4644-444-21-41-24-4221-22-1-1-1-21000-2022-2-2-1-12000000-2010-1120-1-111-220000000000001-10000
χ4744-444-21-41-24-4-2-21-22-1-1-1-2100020-2-222112000000-2010-1-12011-1-12-2000000000000-110000
χ4844-444-21-41-2-44221-22-1-1-1-21000-2022-2-2-1-1200000020-1011-20-1-1112-2000000000000-110000
χ4944-444-21-41-2-44-2-21-22-1-1-1-2100020-2-22211200000020-101-1-2011-1-1-220000000000001-10000
χ5044-4-2-2442440000-2-2-4-422-2-2-4-4000000000240022000000000000000000-200000000000000
χ514-404-4440-4-40000440000-4-44-40000000000000-44000000000000000000000000000000000
χ524-40-22440-4-40000-2-20000224-40000023−230000002-20000000000023−2300000000000000000000
χ534-40-22440-4-40000-2-20000224-400000−23230000002-200000000000−232300000000000000000000
χ544-40-22440-4-4004i−4i-2-2000022-44000−2i2i004i−4i0000-22000000000−2i2i0000000000000000000000
χ554-40-22440-4-400−4i4i-2-2000022-440002i−2i00−4i4i0000-220000000002i−2i0000000000000000000000
χ56888-4-42-4-4-4200002-12-422-1200404000000-100000-20-20-2000-2000000000000110000000000
χ57888-4-42-4-4-4200002-12-422-1200-40-4000000-100000202020002000000000000-1-10000000000
χ58888-4-4-42-42-40044-12-42-1-12-100040-2-2-2-2-2-2200000000000-200111100000000000000000000
χ59888-4-4-42-42-400-4-4-12-42-1-12-1000-40222222200000000000200-1-1-1-100000000000000000000
χ6088-8-4-42-44-4200002-1-24-2-2-120040-4000000100000-20-20200020000000000001-10000000000
χ6188-8-4-42-44-4200002-1-24-2-2-1200-4040000001000002020-2000-2000000000000-110000000000
χ6288-8-4-4-4242-40044-124-2112-1000-40-2-222-2-2-20000000000020011-1-100000000000000000000
χ6388-8-4-4-4242-400-4-4-124-2112-10004022-2-222-200000000000-200-1-11100000000000000000000
χ648-808-82-404-20000-420000-2400000000000004i−4i000000000000000000000−2i2i000000000000
χ658-808-82-404-20000-420000-240000000000000−4i4i0000000000000000000002i−2i000000000000
χ668-808-8-420-24004i−4i2-400004-2000004i−4i00−2i2i000000000000000−2i2i0000000000000000000000
χ678-808-8-420-2400−4i4i2-400004-200000−4i4i002i−2i0000000000000002i−2i0000000000000000000000
χ688-80-44-420-24004i−4i-1200−3i33i3-2100000−2i2i23−23−2i2i000000000000000i−i−3300000000000000000000
χ698-80-44-420-24004i−4i-12003i3−3i3-2100000−2i2i−2323−2i2i000000000000000i−i3−300000000000000000000
χ708-80-44-420-2400−4i4i-1200−3i33i3-21000002i−2i−23232i−2i000000000000000−ii3−300000000000000000000
χ718-80-44-420-2400−4i4i-12003i3−3i3-21000002i−2i23−232i−2i000000000000000−ii−3300000000000000000000
χ7216-160-884-808-400004-200002-400000000000000000000000000000000000000000000000000

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