Finite Group Databasebeta

← Group #11722991

Character table — Group #11722991

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222224444444444446688881212121212121212121212121212121212121212121212121212181836363636363636365454
order12223336666666663336666666664436662466666666121212121212121212121212121212122244661212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-11111111111-1-111-1-11111-1-1-1-1-1-11-1-1-111-1-1-1-1
χ31111111111111111111111111111111111-11-1-1-1-1-1-1-1-11111111111111111-1-1-11-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-1-1-111
χ51111111111111111111111111111-1-111111111111111-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1
χ61111111111111111111111111111-1-111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ71111111111111111111111111111-1-11111-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-1-1-111-1-111
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
χ9222222-122-1-12-12222-1-122-1-1-1-1-12-100-1-1-1-12222-1-1-1-1-1-100-1-100220000-1-1-1-12200-1-1000000
χ10222222-122-1-12-12222-1-122-1-1-1-1-12-100-1-1-1-12-222-1-1-1-1-1-1001100-2-200001111-2-20011000000
χ11222222-122-1-12-12222-1-122-1-1-1-1-12-100-1-1-1-1-22-2-211111100-1-100220000-1-1-1-1-2-20011000000
χ12222222-122-1-12-12222-1-122-1-1-1-1-12-100-1-1-1-1-2-2-2-2111111001100-2-2000011112200-1-1000000
χ1322222-122-122-1222-1-12-1-1-122-1-1-1-1222-1-1-1-120-1-122-1-1-1-1-1-1002200-1-1-1-10000002000-1-10000
χ1422222-122-122-1222-1-12-1-1-122-1-1-1-1222-1-1-1-1-2011-2-21111-1-1002200-1-1-1-1000000-2000110000
χ1522222-122-122-1222-1-12-1-1-122-1-1-1-12-2-2-1-1-1-120-1-122-1-1-1-11100-2-2001111000000-2000110000
χ1622222-122-122-1222-1-12-1-1-122-1-1-1-12-2-2-1-1-1-1-2011-2-211111100-2-20011110000002000-1-10000
χ172222-122-122222-1-12-1-12-1-1-1-1222-1-122-1-1-1-102000000002222-1-1-1-1-1-1-1-1-1-1-1-100020000-1-100
χ182222-122-122222-1-12-1-12-1-1-1-1222-1-122-1-1-1-10-20000000022-2-2-1-111-1-1-1-11111000-200001100
χ192222-122-122222-1-12-1-12-1-1-1-1222-1-1-2-2-1-1-1-10200000000-2-22211-1-11111-1-1-1-1000-200001100
χ202222-122-122222-1-12-1-12-1-1-1-1222-1-1-2-2-1-1-1-10-200000000-2-2-2-211111111111100020000-1-100
χ2122-2-22222-22-2-2-2-2-222222-22-22-2-2-2-20022-2-20000000000000000000000000000000000002i−2i
χ2222-2-22222-22-2-2-2-2-222222-22-22-2-2-2-20022-2-2000000000000000000000000000000000000−2i2i
χ232-22-2222-22-22-2-2-22-2222-22-22-22-2-2-22i−2i2-22-200000000002i−2i002i−2i002i2i−2i−2i0000000000000000
χ242-22-2222-22-22-2-2-22-2222-22-22-22-2-2-2−2i2i2-22-20000000000−2i2i00−2i2i00−2i−2i2i2i0000000000000000
χ252-22-22-12-2-1-221-2-221-12-11-1-221-111-22i−2i-11-1100−i3i300−i3−i3i3i3−ii002i−2i00−i−iii00000000003−30000
χ262-22-22-12-2-1-221-2-221-12-11-1-221-111-22i−2i-11-1100i3−i300i3i3−i3−i3−ii002i−2i00−i−iii0000000000−330000
χ272-22-22-12-2-1-221-2-221-12-11-1-221-111-2−2i2i-11-1100−i3i300−i3−i3i3i3i−i00−2i2i00ii−i−i0000000000−330000
χ282-22-22-12-2-1-221-2-221-12-11-1-221-111-2−2i2i-11-1100i3−i300i3i3−i3−i3i−i00−2i2i00ii−i−i00000000003−30000
χ292-22-2-12212-22-2-21-1-2-1-121-11-1-22-2112i−2i-11-1100000000002i−2i00−ii3−3−i−iii33−3−300000000−i3i300
χ302-22-2-12212-22-2-21-1-2-1-121-11-1-22-2112i−2i-11-1100000000002i−2i00−ii−33−i−iii−3−33300000000i3−i300
χ312-22-2-12212-22-2-21-1-2-1-121-11-1-22-211−2i2i-11-110000000000−2i2i00i−i3−3ii−i−i33−3−300000000i3−i300
χ322-22-2-12212-22-2-21-1-2-1-121-11-1-22-211−2i2i-11-110000000000−2i2i00i−i−33ii−i−i−3−33300000000−i3i300
χ332-2-22222-2-2-2-2222-2-2222-2-2-2-2-2-2222002-2-22000000000000000000000000002-2002-2000000
χ342-2-22222-2-2-2-2222-2-2222-2-2-2-2-2-2222002-2-2200000000000000000000000000-2200-22000000
χ352-2-2222-1-2-2112-12-2-22-1-1-2-21111-12-100-111-10000−i3i3−i3i3−i3i300−i3i300000000−i3i3−i3i32-200-11000000
χ362-2-2222-1-2-2112-12-2-22-1-1-2-21111-12-100-111-10000−i3i3−i3i3−i3i300i3−i300000000i3−i3i3−i3-22001-1000000
χ372-2-2222-1-2-2112-12-2-22-1-1-2-21111-12-100-111-10000i3−i3i3−i3i3−i300−i3i300000000−i3i3−i3i3-22001-1000000
χ382-2-2222-1-2-2112-12-2-22-1-1-2-21111-12-100-111-10000i3−i3i3−i3i3−i300i3−i300000000i3−i3i3−i32-200-11000000
χ3944444-2-24-2-2-2-2-244-2-2-21-2-2-2-2111-2-200111140-2-2-2-211110000000000000000000000000000
χ4044444-2-24-2-2-2-2-244-2-2-21-2-2-2-2111-2-2001111-402222-1-1-1-10000000000000000000000000000
χ414444-24-2-24-2-24-2-2-24-21-2-2-211-2-2-2-21001111040000000000-2-200-2-200001111000000000000
χ424444-24-2-24-2-24-2-2-24-21-2-2-211-2-2-2-210011110-400000000002200220000-1-1-1-1000000000000
χ434444-2-24-2-244-24-2-2-21-2-211-2-2-2-2-21-24411110000000000-2-200-2-20011110000000000000000
χ444444-2-24-2-244-24-2-2-21-2-211-2-2-2-2-21-2-4-41111000000000022002200-1-1-1-10000000000000000
χ4544-4-444-24-4-22-42-4-444-2-24-4-22-222-4200-2-22200000000000000000000000000000000000000
χ4644-4-44-24424-42-4-4-4-2-24-2-224-4-2222-400-2-22200000000000000000000000000000000000000
χ4744-4-44-2-242-2222-4-4-2-2-21-22-221-1-1220011-1-10000003-3-330000000000000000000000000000
χ4844-4-44-2-242-2222-4-4-2-2-21-22-221-1-1220011-1-1000000-333-30000000000000000000000000000
χ4944-4-4-244-2-44-4-4-4224-2-24-22-224-4-42200-2-22200000000000000000000000000000000000000
χ5044-4-4-24-2-2-4-22-42224-21-2-221-1-2222-10011-1-100000000000000000000003i−3i−3i3i000000000000
χ5144-4-4-24-2-2-4-22-42224-21-2-221-1-2222-10011-1-10000000000000000000000−3i3i3i−3i000000000000
χ5244-4-4-2-24-224-42-422-21-2-21-1-22-222-120011-1-10000000000000000003i−3i3i−3i0000000000000000
χ5344-4-4-2-24-224-42-422-21-2-21-1-22-222-120011-1-1000000000000000000−3i3i−3i3i0000000000000000
χ544-44-444-2-442-2-42-44-44-2-2-442-22-22-4200-22-2200000000000000000000000000000000000000
χ554-44-44-2-2-4-22-222-442-2-212-22-2-11-122001-11-100−2i32i300i3i3−i3−i30000000000000000000000000000
χ564-44-44-2-2-4-22-222-442-2-212-22-2-11-122001-11-1002i3−2i300−i3−i3i3i30000000000000000000000000000
χ574-44-4-24-2242-2-422-2-4-21-22-2-112-222-1001-11-1000000000000000023−230000−3−333000000000000
χ584-44-4-24-2242-2-422-2-4-21-22-2-112-222-1001-11-10000000000000000−2323000033−3−3000000000000
χ594-44-4-2-242-2-442-42-221-2-2-112-22-22-124i−4i1-11-10000000000−2i2i00−2i2i00ii−i−i0000000000000000
χ604-44-4-2-242-2-442-42-221-2-2-112-22-22-12−4i4i1-11-100000000002i−2i002i−2i00−i−iii0000000000000000
χ614-4-444-24-42-4-4-244-42-24-222-4-422-2-2400-222-200000000000000000000000000000000000000
χ624-4-444-2-2-4222-2-24-42-2-212222-1-11-2-2001-1-110000−2i32i3i3−i3i3−i30000000000000000000000000000
χ634-4-444-2-2-4222-2-24-42-2-212222-1-11-2-2001-1-1100002i3−2i3−i3i3−i3i30000000000000000000000000000
χ644-4-44-2442-4-4-444-22-4-2-242222-4-44-2-200-222-200000000000000000000000000000000000000
χ654-4-44-24-22-4224-2-22-4-21-222-1-122-2-21001-1-11000000000000−2i32i300000000i3−i3i3−i3000000000000
χ664-4-44-24-22-4224-2-22-4-21-222-1-122-2-21001-1-110000000000002i3−2i300000000−i3i3−i3i3000000000000
χ674-4-44-2-2422-4-4-24-2221-2-2-1-12222-21-2001-1-110000000000000000003-3-330000000000000000
χ684-4-44-2-2422-4-4-24-2221-2-2-1-12222-21-2001-1-11000000000000000000-333-30000000000000000
χ698888-4-4-4-4-4-4-4-4-4-4-4-422222222222200-1-1-1-100000000000000000000000000000000000000
χ7088-8-8-4-4-4-44-444444-42222-22-22-2-2-2-200-1-11100000000000000000000000000000000000000
χ718-88-8-4-4-44-44-4444-44222-22-22-22-2-2-200-11-1100000000000000000000000000000000000000
χ728-8-88-4-4-44444-4-4-444222-2-2-2-2-2-222200-111-100000000000000000000000000000000000000

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