Finite Group Databasebeta

← Group #11722996

Character table — Group #11722996

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222224444444444446688881212121212121212121212121212121212121212121212121212181836363636363636365454
order1222333666666666333666666666443666246666666612121212121212121212121212121212444412121212121222
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-11111111111-1-1-1-1111111-1-1-1-1-1-11-111-1-1-1-1-1-1
χ31111111111111111111111111111111111-11-1-1-1-1-1-1-1-11111111111111111-1-1-11-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111
χ51111111111111111111111111111-1-111111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
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
χ71111111111111111111111111111-1-11111-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-111-1-1-1-111
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
χ9222222-122-122-12-122-1-122-1-1-1-1-12-100-1-1-1-12222-1-1-1-1-1-10022-1-1000000-1-1-1-1220000-1-10000
χ10222222-122-122-12-122-1-122-1-1-1-1-12-100-1-1-1-12-222-1-1-1-1-1-100-2-2110000001111-2-20000110000
χ11222222-122-122-12-122-1-122-1-1-1-1-12-100-1-1-1-1-22-2-21111110022-1-1000000-1-1-1-1-2-20000110000
χ12222222-122-122-12-122-1-122-1-1-1-1-12-100-1-1-1-1-2-2-2-211111100-2-2110000001111220000-1-10000
χ1322222-122-122-12-122-12-1-1-122-1-1-1-1222-1-1-1-120-1-122-1-1-1-1-1-1000022-1-1-1-100000020-1-1000000
χ1422222-122-122-12-122-12-1-1-122-1-1-1-1222-1-1-1-1-2011-2-21111-1-1000022-1-1-1-1000000-2011000000
χ1522222-122-122-12-122-12-1-1-122-1-1-1-12-2-2-1-1-1-120-1-122-1-1-1-1110000-2-21111000000-2011000000
χ1622222-122-122-12-122-12-1-1-122-1-1-1-12-2-2-1-1-1-1-2011-2-21111110000-2-2111100000020-1-1000000
χ172222-122-122-12222-1-1-12-1-1-1-1222-1-122-1-1-1-1020000000022-1-122-1-1-1-1-1-1-1-1-1-100020000-1-100
χ182222-122-122-12222-1-1-12-1-1-1-1222-1-122-1-1-1-10-2000000002211-2-2-1-1-1-1-1-11111000-200001100
χ192222-122-122-12222-1-1-12-1-1-1-1222-1-1-2-2-1-1-1-10200000000-2-2-1-122111111-1-1-1-1000-200001100
χ202222-122-122-12222-1-1-12-1-1-1-1222-1-1-2-2-1-1-1-10-200000000-2-211-2-2111111111100020000-1-100
χ2122-2-2222-22-22-22-2-2-22222-2-2-22-2-2-222i−2i22-2-200000000002i−2i00002i−2i2i2i−2i−2i0000000000000000
χ2222-2-2222-22-22-22-2-2-22222-2-2-22-2-2-22−2i2i22-2-20000000000−2i2i0000−2i2i−2i−2i2i2i0000000000000000
χ2322-2-22-12-2-1-22121-2-2-12-1-11-2-2-111122i−2i-1-11100−i3i300−i3−i3i3i3−ii00002i−2i−i−iii000000003−3000000
χ2422-2-22-12-2-1-22121-2-2-12-1-11-2-2-111122i−2i-1-11100i3−i300i3i3−i3−i3−ii00002i−2i−i−iii00000000−33000000
χ2522-2-22-12-2-1-22121-2-2-12-1-11-2-2-11112−2i2i-1-11100−i3i300−i3−i3i3i3i−i0000−2i2iii−i−i00000000−33000000
χ2622-2-22-12-2-1-22121-2-2-12-1-11-2-2-11112−2i2i-1-11100i3−i300i3i3−i3−i3i−i0000−2i2iii−i−i000000003−3000000
χ2722-2-2-12212-2-1-22-2-21-1-12-11112-2-21-12i−2i-1-11100000000002i−2i−i3i300−ii−i−iii−i3−i3i3i3000000003−300
χ2822-2-2-12212-2-1-22-2-21-1-12-11112-2-21-12i−2i-1-11100000000002i−2ii3−i300−ii−i−iiii3i3−i3−i300000000−3300
χ2922-2-2-12212-2-1-22-2-21-1-12-11112-2-21-1−2i2i-1-1110000000000−2i2i−i3i300i−iii−i−i−i3−i3i3i300000000−3300
χ3022-2-2-12212-2-1-22-2-21-1-12-11112-2-21-1−2i2i-1-1110000000000−2i2ii3−i300i−iii−i−ii3i3−i3−i3000000003−300
χ312-22-22222-22-2-2-22-2-2222-222-2-22-2-2-2002-22-2000000000000000000000000002i−2i00002i−2i0000
χ322-22-22222-22-2-2-22-2-2222-222-2-22-2-2-2002-22-200000000000000000000000000−2i2i0000−2i2i0000
χ332-22-222-12-2-1-2-2121-22-1-1-22-111-11-2100-11-110000−i3i3−i3i3−i3i300003−30000003−33−32i−2i0000−ii0000
χ342-22-222-12-2-1-2-2121-22-1-1-22-111-11-2100-11-110000−i3i3−i3i3−i3i30000−33000000−33−33−2i2i0000i−i0000
χ352-22-222-12-2-1-2-2121-22-1-1-22-111-11-2100-11-110000i3−i3i3−i3i3−i300003−30000003−33−3−2i2i0000i−i0000
χ362-22-222-12-2-1-2-2121-22-1-1-22-111-11-2100-11-110000i3−i3i3−i3i3−i30000−33000000−33−332i−2i0000−ii0000
χ372-2-22222-2-2-2-22-2-222222-2-2-22-2-222-2002-2-220000000000000000000000000000000000002-2
χ382-2-22222-2-2-2-22-2-222222-2-2-22-2-222-2002-2-22000000000000000000000000000000000000-22
χ3944444-2-24-2-24-2-2-2-24-2-21-2-2-2-2111-2-200111140-2-2-2-211110000000000000000000000000000
χ4044444-2-24-2-24-2-2-2-24-2-21-2-2-2-2111-2-2001111-402222-1-1-1-10000000000000000000000000000
χ414444-24-2-24-2-24-24-2-2-21-2-2-211-2-2-2-21001111040000000000-2-2-2-20000001111000000000000
χ424444-24-2-24-2-24-24-2-2-21-2-2-211-2-2-2-210011110-400000000002222000000-1-1-1-1000000000000
χ434444-2-24-2-24-2-24-24-21-2-211-2-2-2-2-21-24411110000000000-2-20000-2-211110000000000000000
χ444444-2-24-2-24-2-24-24-21-2-211-2-2-2-2-21-2-4-41111000000000022000022-1-1-1-10000000000000000
χ4544-4-444-2-4424-4-2-42-44-2-24-422-222-4-200-2-22200000000000000000000000000000000000000
χ4644-4-44-2-2-4-2242-222-4-2-21-22221-1-12-20011-1-100−2i32i300i3i3−i3−i30000000000000000000000000000
χ4744-4-44-2-2-4-2242-222-4-2-21-22221-1-12-20011-1-1002i3−2i300−i3−i3i3i30000000000000000000000000000
χ4844-4-4-24-2242-2-4-2-422-21-2-22-1-1-222210011-1-1000000000000−2i32i300000000i3i3−i3−i3000000000000
χ4944-4-4-24-2242-2-4-2-422-21-2-22-1-1-222210011-1-10000000000002i3−2i300000000−i3−i3i3i3000000000000
χ5044-4-4-2-242-2-4-2242-421-2-21-122-222-1-24i−4i11-1-10000000000−2i2i0000−2i2iii−i−i0000000000000000
χ5144-4-4-2-242-2-4-2242-421-2-21-122-222-1-2−4i4i11-1-100000000002i−2i00002i−2i−i−iii0000000000000000
χ524-44-44-24424-42-4-2-4-4-24-22-24-42-222-400-22-2200000000000000000000000000000000000000
χ534-44-44-2-242-2-422-22-4-2-212-2-22-11-122001-11-10000−2i32i3i3−i3i3−i30000000000000000000000000000
χ544-44-44-2-242-2-422-22-4-2-212-2-22-11-122001-11-100002i3−2i3−i3i3−i3i30000000000000000000000000000
χ554-44-4-244-2-442-4-44-42-2-242-2-22-44-42200-22-2200000000000000000000000000000000000000
χ564-44-4-24-2-2-4-22-42422-21-22-21-12-222-1001-11-10000000000000023−23000000−33−33000000000000
χ574-44-4-24-2-2-4-22-42422-21-22-21-12-222-1001-11-100000000000000−23230000003−33−3000000000000
χ584-44-4-2-24-22422-4-2-421-2-2-11-222-22-12001-11-10000000000000000003i−3i3i−3i0000000000000000
χ594-44-4-2-24-22422-4-2-421-2-2-11-222-22-12001-11-1000000000000000000−3i3i−3i3i0000000000000000
χ604-4-4444-2-4-42-442-4-244-2-2-4-42-222-24200-222-200000000000000000000000000000000000000
χ614-4-444-24-42-4-4-2-4244-24-222-4422-2-2-400-222-200000000000000000000000000000000000000
χ624-4-444-2-2-422-4-222-24-2-21222-2-1-11-22001-1-110000003-3-330000000000000000000000000000
χ634-4-444-2-2-422-4-222-24-2-21222-2-1-11-22001-1-11000000-333-30000000000000000000000000000
χ644-4-44-2442-4-424-4-44-2-2-24222-2-4-44-2200-222-200000000000000000000000000000000000000
χ654-4-44-24-22-42242-4-2-2-21-222-1122-2-2-1001-1-1100000000000000000000003i−3i−3i3i000000000000
χ664-4-44-24-22-42242-4-2-2-21-222-1122-2-2-1001-1-110000000000000000000000−3i3i3i−3i000000000000
χ674-4-44-2-2422-42-2-424-21-2-2-1-12-222-212001-1-110000000000000000003-3-330000000000000000
χ684-4-44-2-2422-42-2-424-21-2-2-1-12-222-212001-1-11000000000000000000-333-30000000000000000
χ698888-4-4-4-4-4-4-4-4-4-4-4-422222222222200-1-1-1-100000000000000000000000000000000000000
χ7088-8-8-4-4-44-44-44-44442222-2-2-22-2-2-2200-1-11100000000000000000000000000000000000000
χ718-88-8-4-4-4-44-4444-444222-222-2-22-2-2-200-11-1100000000000000000000000000000000000000
χ728-8-88-4-4-44444-444-4-4222-2-2-22-2-222-200-111-100000000000000000000000000000000000000

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