Finite Group Databasebeta

← Group #11723027

Character table — Group #11723027

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222224444444444446688881212121212121212121212121212121212121212121212121212181836363636363636365454
order1222333666666666333666666666443666441212121212121212121212121212121212121212121212124424661212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-11111-1-11111-1-111111111-1-1-1-1-1-1-11-1-111-1-1-1-1
χ31111111111111111111111111111111111-1111-1-11111-1-1111111-1-1-1-11111-1-11-111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1111111-1-11111-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-111111-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-1-1-111
χ71111111111111111111111111111-1-11111-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-11-1-111-1-111
χ81111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ9222222-122-12-1-12222-1-122-1-1-1-12-1-122-1-1-1-102-1-100-1-1220022-1-1-1-10000-1-1-1-10020-1-1000000
χ10222222-122-12-1-12222-1-122-1-1-1-12-1-122-1-1-1-10-2-1-100112200-2-2-1-1-1-10000111100-2011000000
χ11222222-122-12-1-12222-1-122-1-1-1-12-1-1-2-2-1-1-1-1021100-1-1-2-2002211110000-1-1-1-100-2011000000
χ12222222-122-12-1-12222-1-122-1-1-1-12-1-1-2-2-1-1-1-10-2110011-2-200-2-21111000011110020-1-1000000
χ1322222-122-12222-1-12-12-1-1-122-1-1-12-122-1-1-1-120222200-1-1-1-100-1-1-1-1-1-1-1-10000000200-1-10000
χ1422222-122-12222-1-12-12-1-1-122-1-1-12-122-1-1-1-1-2022-2-200-1-11100-1-1-1-111110000000-200110000
χ1522222-122-12222-1-12-12-1-1-122-1-1-12-1-2-2-1-1-1-120-2-2220011-1-1001111-1-1-1-10000000-200110000
χ1622222-122-12222-1-12-12-1-1-122-1-1-12-1-2-2-1-1-1-1-20-2-2-2-200111100111111110000000200-1-10000
χ172222-122-122-12222-1-1-12-1-1-1-122-1-1200-1-1-1-12200-1-1220022-1-10000-1-1-1-1-1-1-1-122000000-1-100
χ182222-122-122-12222-1-1-12-1-1-1-122-1-1200-1-1-1-12-200-1-1-2-20022110000-1-1-1-11111-2-20000001100
χ192222-122-122-12222-1-1-12-1-1-1-122-1-1200-1-1-1-1-2200112200-2-2-1-100001111-1-1-1-1-2-20000001100
χ202222-122-122-12222-1-1-12-1-1-1-122-1-1200-1-1-1-1-2-20011-2-200-2-21100001111111122000000-1-100
χ2122-2-2222-2-2-222-22-2-2222-2-22-2-2-22-220022-2-2000000000000000000000000002i−2i0000002i−2i00
χ2222-2-2222-2-2-222-22-2-2222-2-22-2-2-22-220022-2-200000000000000000000000000−2i2i000000−2i2i00
χ2322-2-2-1221-2-2-12-22-21-1-1211-11-2-2-11200-1-1110000−i3i30000003−30000−i3−i3i3i333−3−32i−2i000000−ii00
χ2422-2-2-1221-2-2-12-22-21-1-1211-11-2-2-11200-1-1110000−i3i3000000−330000−i3−i3i3i3−3−333−2i2i000000i−i00
χ2522-2-2-1221-2-2-12-22-21-1-1211-11-2-2-11200-1-1110000i3−i30000003−30000i3i3−i3−i333−3−3−2i2i000000i−i00
χ2622-2-2-1221-2-2-12-22-21-1-1211-11-2-2-11200-1-1110000i3−i3000000−330000i3i3−i3−i3−3−3332i−2i000000−ii00
χ272-22-2222-22-2-2-22-2-222222-2-2-22-2-22-2002-22-20000000000000000000000000000000000002i−2i
χ282-22-2222-22-2-2-22-2-222222-2-2-22-2-22-2002-22-2000000000000000000000000000000000000−2i2i
χ292-2-222222-22-2-2-2-22-2222-22-22-22-2-2-22i−2i2-2-22002i−2i00002i−2i00002i2i−2i−2i00000000000000000000
χ302-2-222222-22-2-2-2-22-2222-22-22-22-2-2-2−2i2i2-2-2200−2i2i0000−2i2i0000−2i−2i2i2i00000000000000000000
χ312-2-2222-12-2-1-211-22-22-1-1-221-11-1-2112i−2i-111-100−ii003−32i−2i0000−i−iii00003−33−30000−i3i3000000
χ322-2-2222-12-2-1-211-22-22-1-1-221-11-1-2112i−2i-111-100−ii00−332i−2i0000−i−iii0000−33−330000i3−i3000000
χ332-2-2222-12-2-1-211-22-22-1-1-221-11-1-211−2i2i-111-100i−i003−3−2i2i0000ii−i−i00003−33−30000i3−i3000000
χ342-2-2222-12-2-1-211-22-22-1-1-221-11-1-211−2i2i-111-100i−i00−33−2i2i0000ii−i−i0000−33−330000−i3i3000000
χ352-2-222-12212-2-2-21-1-2-12-11-1-221-11-212i−2i-111-1002i−2i0000−ii3−300−i−iii3−33−30000000000−i3i30000
χ362-2-222-12212-2-2-21-1-2-12-11-1-221-11-212i−2i-111-1002i−2i0000−ii−3300−i−iii−33−330000000000i3−i30000
χ372-2-222-12212-2-2-21-1-2-12-11-1-221-11-21−2i2i-111-100−2i2i0000i−i3−300ii−i−i3−33−30000000000i3−i30000
χ382-2-222-12212-2-2-21-1-2-12-11-1-221-11-21−2i2i-111-100−2i2i0000i−i−3300ii−i−i−33−330000000000−i3i30000
χ3944444-2-24-2-24-2-2-2-24-2-21-2-2-2-211-2-2144111100-2-20000-2-20000111100000000000000000000
χ4044444-2-24-2-24-2-2-2-24-2-21-2-2-2-211-2-21-4-4111100220000220000-1-1-1-100000000000000000000
χ414444-24-2-24-2-2-2-244-2-21-2-2-211-2-2-21-2001111040000-2-20000-2-2000000001111000000000000
χ424444-24-2-24-2-2-2-244-2-21-2-2-211-2-2-21-20011110-400002200002200000000-1-1-1-1000000000000
χ434444-2-24-2-24-244-2-2-21-2-211-2-2-2-21-2-20011114000-2-20000-2-200000011110000000000000000
χ444444-2-24-2-24-244-2-2-21-2-211-2-2-2-21-2-2001111-400022000022000000-1-1-1-10000000000000000
χ4544-4-444-2-4-424-224-4-44-2-2-4-4-222242-200-2-22200000000000000000000000000000000000000
χ4644-4-44-24-42-444-4-22-4-24-2224-422-2-4-200-2-22200000000000000000000000000000000000000
χ4744-4-44-2-2-4224-22-22-4-2-2122-22-1-1-2210011-1-1000000000000003-33-300000000000000000000
χ4844-4-44-2-2-4224-22-22-4-2-2122-22-1-1-2210011-1-100000000000000-33-3300000000000000000000
χ4944-4-4-24-22-42-2-224-42-21-2221-122-2-1-20011-1-100000000000023−2300000000−3−333000000000000
χ5044-4-4-24-22-42-2-224-42-21-2221-122-2-1-20011-1-1000000000000−23230000000033−3−3000000000000
χ5144-4-4-2-2422-4-24-4-2221-2-2-1-1-222212-20011-1-10000−2i32i3000000000000i3i3−i3−i30000000000000000
χ5244-4-4-2-2422-4-24-4-2221-2-2-1-1-222212-20011-1-100002i3−2i3000000000000−i3−i3i3i30000000000000000
χ534-44-444-2-442-42-2-4-444-2-24-422-22-4-2200-22-2200000000000000000000000000000000000000
χ544-44-44-24-4-2-4-4-44224-24-2-22-4-4-2224200-22-2200000000000000000000000000000000000000
χ554-44-44-2-2-4-22-42-2224-2-21-22221-12-2-1001-11-1000000000000003i−3i−3i3i00000000000000000000
χ564-44-44-2-2-4-22-42-2224-2-21-22221-12-2-1001-11-100000000000000−3i3i3i−3i00000000000000000000
χ574-44-4-24424-42-44-4-4-2-2-24-22224-42-2-400-22-2200000000000000000000000000000000000000
χ584-44-4-24-224222-2-4-4-2-21-2-22-1-1-22212001-11-100000000000000000000003-3-33000000000000
χ594-44-4-24-224222-2-4-4-2-21-2-22-1-1-22212001-11-10000000000000000000000-333-3000000000000
χ604-44-4-2-242-2-42-4422-21-2-21-122-22-1-22001-11-10000000000000000003i−3i−3i3i0000000000000000
χ614-44-4-2-242-2-42-4422-21-2-21-122-22-1-22001-11-1000000000000000000−3i3i3i−3i0000000000000000
χ624-4-444-2-242-2-4222-2-4-2-212-22-2-1122-14i−4i1-1-1100−2i2i0000−2i2i0000ii−i−i00000000000000000000
χ634-4-444-2-242-2-4222-2-4-2-212-22-2-1122-1−4i4i1-1-11002i−2i00002i−2i0000−i−iii00000000000000000000
χ644-4-44-244-2-442-4-4-442-2-242-22-2-4422-400-222-200000000000000000000000000000000000000
χ654-4-44-24-2-2-4-2222-442-21-22-2-112-22-12001-1-1100000023−2300000000000000−33−33000000000000
χ664-4-44-24-2-2-4-2222-442-21-22-2-112-22-12001-1-11000000−2323000000000000003−33−3000000000000
χ674-4-44-2-24-2242-4-42-221-2-2-112-22-2-122001-1-11000000000023−23000000−33−330000000000000000
χ684-4-44-2-24-2242-4-42-221-2-2-112-22-2-122001-1-110000000000−23230000003−33−30000000000000000
χ698888-4-4-4-4-4-4-4-4-4-4-4-422222222222200-1-1-1-100000000000000000000000000000000000000
χ7088-8-8-4-4-4444-4-44-444222-2-22-2-2-22-2200-1-11100000000000000000000000000000000000000
χ718-88-8-4-4-44-4444-444-42222-2-2-22-2-22-200-11-1100000000000000000000000000000000000000
χ728-8-88-4-4-4-44-44444-44222-22-22-22-2-2-200-111-100000000000000000000000000000000000000

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