Finite Group Databasebeta

← Group #11723007

Character table — Group #11723007

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222224444444444446688881212121212121212121212121212121212121212121212121212181836363636363636365454
order12223336666666663336666666664436664412121212121212121212121212121212121212121212121244226666121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1111111-1-111-1-111111111-1-1-1-1-1-11-111-1-1-1-1-1-1
χ31111111111111111111111111111111111-111111-1-111-1-1111111-1-1-1-11111-1-1-11-1-111-1-1-1-1
χ41111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1111111-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-111111-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-111
χ71111111111111111111111111111-1-11111-11-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-11-111-1-1-1-111
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
χ9222222-1222-122-1-122-1-122-1-1-1-12-1-122-1-1-1-10222-1-100-1-10022-1-1-1-10000-1-1-1-1000200-1-10000
χ10222222-1222-122-1-122-1-122-1-1-1-12-1-122-1-1-1-10-222-1-1001100-2-2-1-1-1-100001111000-200110000
χ11222222-1222-122-1-122-1-122-1-1-1-12-1-1-2-2-1-1-1-102-2-21100-1-1002211110000-1-1-1-1000-200110000
χ12222222-1222-122-1-122-1-122-1-1-1-12-1-1-2-2-1-1-1-10-2-2-211001100-2-2111100001111000200-1-10000
χ1322222-1222-12-1-1222-12-1-1-122-1-1-12-122-1-1-1-120-1-122-1-1002200-1-1-1-1-1-1-1-100000020-1-1000000
χ1422222-1222-12-1-1222-12-1-1-122-1-1-12-122-1-1-1-1-20-1-1221100-2-200-1-1-1-11111000000-2011000000
χ1522222-1222-12-1-1222-12-1-1-122-1-1-12-1-2-2-1-1-1-12011-2-2-1-10022001111-1-1-1-1000000-2011000000
χ1622222-1222-12-1-1222-12-1-1-122-1-1-12-1-2-2-1-1-1-1-2011-2-21100-2-2001111111100000020-1-1000000
χ172222-122-1-1222222-1-1-12-1-1-1-122-1-1200-1-1-1-12200002222-1-1-1-10000-1-1-1-1-1-1-1-122000000-1-100
χ182222-122-1-1222222-1-1-12-1-1-1-122-1-1200-1-1-1-12-2000022-2-2-1-1110000-1-1-1-11111-2-20000001100
χ192222-122-1-1222222-1-1-12-1-1-1-122-1-1200-1-1-1-1-220000-2-22211-1-100001111-1-1-1-1-2-20000001100
χ202222-122-1-1222222-1-1-12-1-1-1-122-1-1200-1-1-1-1-2-20000-2-2-2-2111100001111111122000000-1-100
χ2122-2-22222-2-2-22-22-2-22222-22-2-2-2-2-220022-2-20000000000000000000000000000000000002i−2i
χ2222-2-22222-2-2-22-22-2-22222-22-2-2-2-2-220022-2-2000000000000000000000000000000000000−2i2i
χ232-22-2222-2-2-2-2-22-222222-2-2-2-22-222-2002-22-2000000000000000000000000002-20000002-200
χ242-22-2222-2-2-2-2-22-222222-2-2-2-22-222-2002-22-200000000000000000000000000-22000000-2200
χ252-22-2-12211-2-2-22-22-1-1-1211112-2-1-1-200-11-110000000000−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i32-2000000-1100
χ262-22-2-12211-2-2-22-22-1-1-1211112-2-1-1-200-11-110000000000−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i3-220000001-100
χ272-22-2-12211-2-2-22-22-1-1-1211112-2-1-1-200-11-110000000000i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i3-220000001-100
χ282-22-2-12211-2-2-22-22-1-1-1211112-2-1-1-200-11-110000000000i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i32-2000000-1100
χ292-2-22222-2222-2-2-2-2-2222-22-22-22-2-2-22i−2i2-2-22002i−2i2i−2i000000002i2i−2i−2i00000000000000000000
χ302-2-22222-2222-2-2-2-2-2222-22-22-22-2-2-2−2i2i2-2-2200−2i2i−2i2i00000000−2i−2i2i2i00000000000000000000
χ312-2-2222-1-222-1-2-211-22-1-1-221-11-1-2112i−2i-111-1002i−2i−ii003−30000−i−iii00003−33−3000000−i3i30000
χ322-2-2222-1-222-1-2-211-22-1-1-221-11-1-2112i−2i-111-1002i−2i−ii00−330000−i−iii0000−33−33000000i3−i30000
χ332-2-2222-1-222-1-2-211-22-1-1-221-11-1-211−2i2i-111-100−2i2ii−i003−30000ii−i−i00003−33−3000000i3−i30000
χ342-2-2222-1-222-1-2-211-22-1-1-221-11-1-211−2i2i-111-100−2i2ii−i00−330000ii−i−i0000−33−33000000−i3i30000
χ352-2-222-12-22-1211-2-2-2-12-11-1-221-11-212i−2i-111-100−ii2i−2i3−3000000−i−iii3−33−300000000−i3i3000000
χ362-2-222-12-22-1211-2-2-2-12-11-1-221-11-212i−2i-111-100−ii2i−2i−33000000−i−iii−33−3300000000i3−i3000000
χ372-2-222-12-22-1211-2-2-2-12-11-1-221-11-21−2i2i-111-100i−i−2i2i3−3000000ii−i−i3−33−300000000i3−i3000000
χ382-2-222-12-22-1211-2-2-2-12-11-1-221-11-21−2i2i-111-100i−i−2i2i−33000000ii−i−i−33−3300000000−i3i3000000
χ3944444-2-244-2-2-2-2-2-24-2-21-2-2-2-211-2-2144111100-2-2-2-200000000111100000000000000000000
χ4044444-2-244-2-2-2-2-2-24-2-21-2-2-2-211-2-21-4-4111100222200000000-1-1-1-100000000000000000000
χ414444-24-2-2-24-244-2-2-2-21-2-2-211-2-2-21-200111104000000-2-200-2-2000000001111000000000000
χ424444-24-2-2-24-244-2-2-2-21-2-2-211-2-2-21-20011110-400000022002200000000-1-1-1-1000000000000
χ434444-2-24-2-2-24-2-244-21-2-211-2-2-2-21-2-2001111400000-2-200-2-200000011110000000000000000
χ444444-2-24-2-2-24-2-244-21-2-211-2-2-2-21-2-2001111-400000220022000000-1-1-1-10000000000000000
χ4544-4-444-24-4-424-4-22-44-2-24-4-2222-42-200-2-22200000000000000000000000000000000000000
χ4644-4-44-244-42-4-224-4-4-24-2-224-4222-4-200-2-22200000000000000000000000000000000000000
χ4744-4-44-2-24-422-22-22-4-2-21-22-22-1-12210011-1-1000000000000003-33-300000000000000000000
χ4844-4-44-2-24-422-22-22-4-2-21-22-22-1-12210011-1-100000000000000-33-3300000000000000000000
χ4944-4-4-244-22-4-44-44-42-2-24-22-22-4-422400-2-22200000000000000000000000000000000000000
χ5044-4-4-24-2-22-424-4-222-21-2-221-1222-1-20011-1-100000000000000000000003i−3i−3i3i000000000000
χ5144-4-4-24-2-22-424-4-222-21-2-221-1222-1-20011-1-10000000000000000000000−3i3i3i−3i000000000000
χ5244-4-4-2-24-222-4-224-421-2-21-1-2222-12-20011-1-10000000000000000003i−3i−3i3i0000000000000000
χ5344-4-4-2-24-222-4-224-421-2-21-1-2222-12-20011-1-1000000000000000000−3i3i3i−3i0000000000000000
χ544-44-444-2-4-4-42-442-244-2-2-4-422-224-2200-22-2200000000000000000000000000000000000000
χ554-44-44-24-4-42-42-2-444-24-222-4-4-22-24200-22-2200000000000000000000000000000000000000
χ564-44-44-2-2-4-4222-22-24-2-2122221-1-2-2-1001-11-1000000000000003i−3i−3i3i00000000000000000000
χ574-44-44-2-2-4-4222-22-24-2-2122221-1-2-2-1001-11-100000000000000−3i3i3i−3i00000000000000000000
χ584-44-4-24-222-42-442-2-2-21-222-1-1-22-212001-11-1000000000000−2i32i300000000i3i3−i3−i3000000000000
χ594-44-4-24-222-42-442-2-2-21-222-1-1-22-212001-11-10000000000002i3−2i300000000−i3−i3i3i3000000000000
χ604-44-4-2-24222-42-2-44-21-2-2-1-122-221-22001-11-10000000000−2i32i3000000i3i3−i3−i30000000000000000
χ614-44-4-2-24222-42-2-44-21-2-2-1-122-221-22001-11-100000000002i3−2i3000000−i3−i3i3i30000000000000000
χ624-4-444-2-2-44-2-22222-4-2-212-22-2-1122-14i−4i1-1-1100−2i2i−2i2i00000000ii−i−i00000000000000000000
χ634-4-444-2-2-44-2-22222-4-2-212-22-2-1122-1−4i4i1-1-11002i−2i2i−2i00000000−i−iii00000000000000000000
χ644-4-44-2442-244-4-4-4-42-2-242-22-2-4422-400-222-200000000000000000000000000000000000000
χ654-4-44-24-22-24-2-4-4222-21-22-2-112-22-12001-1-110000000023−23000000000000−33−33000000000000
χ664-4-44-24-22-24-2-4-4222-21-22-2-112-22-12001-1-1100000000−23230000000000003−33−3000000000000
χ674-4-44-2-242-2-2422-4-421-2-2-112-22-2-122001-1-1100000023−230000000000−33−330000000000000000
χ684-4-44-2-242-2-2422-4-421-2-2-112-22-2-122001-1-11000000−232300000000003−33−30000000000000000
χ698888-4-4-4-4-4-4-4-4-4-4-4-422222222222200-1-1-1-100000000000000000000000000000000000000
χ7088-8-8-4-4-4-4444-44-4442222-22-2-2-2-2-2200-1-11100000000000000000000000000000000000000
χ718-88-8-4-4-444444-44-4-4222-2-2-2-22-222-200-11-1100000000000000000000000000000000000000
χ728-8-88-4-4-44-4-4-444444222-22-22-22-2-2-200-111-100000000000000000000000000000000000000

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