Finite Group Databasebeta

← Group #11722964

Character table — Group #11722964

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222224444444444446688881212121212121212121212121212121212121212121212121212181836363636363636365454
order12223336666666663336666666664436662266666666666666661212121212121212444412121212121222
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-111-1-111-1-11111-1-1-1-111111111-1-11-111-1-1-1-1-1-1
χ31111111111111111111111111111111111-11-1-111-1-111-1-1-1-1111111111111-1-1-11-1-111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111
χ51111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-111111-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111
χ71111111111111111111111111111-1-11111-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111
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
χ9222222-122-1-12222-12-1-122-1-1-1-1-1-1200-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000000022000000-1-100
χ10222222-122-1-12222-12-1-122-1-1-1-1-1-1200-1-1-1-12-222-2-2-1-111-1-1-1-1111100000000-2-20000001100
χ11222222-122-1-12222-12-1-122-1-1-1-1-1-1200-1-1-1-1-22-2-22211-1-11111-1-1-1-100000000-2-20000001100
χ12222222-122-1-12222-12-1-122-1-1-1-1-1-1200-1-1-1-1-2-2-2-2-2-21111111111110000000022000000-1-100
χ1322222-122-1222-12-12-12-1-1-1222-1-1-1-122-1-1-1-10200-1-100220000-1-1-1-122-1-1-1-1-1-1000200-1-10000
χ1422222-122-1222-12-12-12-1-1-1222-1-1-1-122-1-1-1-10-2001100-2-20000111122-1-1-1-1-1-1000-200110000
χ1522222-122-1222-12-12-12-1-1-1222-1-1-1-1-2-2-1-1-1-10200-1-100220000-1-1-1-1-2-2111111000-200110000
χ1622222-122-1222-12-12-12-1-1-1222-1-1-1-1-2-2-1-1-1-10-2001100-2-200001111-2-2111111000200-1-10000
χ172222-122-1222-12-122-1-12-1-1-1-1-1222-122-1-1-1-120-1-1002200-1-1-1-10000-1-122-1-1-1-10020-1-1000000
χ182222-122-1222-12-122-1-12-1-1-1-1-1222-122-1-1-1-1-201100-2-20011110000-1-122-1-1-1-100-2011000000
χ192222-122-1222-12-122-1-12-1-1-1-1-1222-1-2-2-1-1-1-120-1-1002200-1-1-1-1000011-2-2111100-2011000000
χ202222-122-1222-12-122-1-12-1-1-1-1-1222-1-2-2-1-1-1-1-201100-2-2001111000011-2-211110020-1-1000000
χ2122-2-2222222-2-2-2-2-2-22222-22-2-22-2-2-22i−2i22-2-20000000000000000002i−2i2i−2i2i2i−2i−2i000000000000
χ2222-2-2222222-2-2-2-2-2-22222-22-2-22-2-2-2−2i2i22-2-2000000000000000000−2i2i−2i2i−2i−2i2i2i000000000000
χ2322-2-22-122-12-2-21-21-2-12-1-112-2-2-11112i−2i-1-1110000−i3i300000000−i3−i3i3i32i−2i−ii−i−iii0000003−30000
χ2422-2-22-122-12-2-21-21-2-12-1-112-2-2-11112i−2i-1-1110000i3−i300000000i3i3−i3−i32i−2i−ii−i−iii000000−330000
χ2522-2-22-122-12-2-21-21-2-12-1-112-2-2-1111−2i2i-1-1110000−i3i300000000−i3−i3i3i3−2i2ii−iii−i−i000000−330000
χ2622-2-22-122-12-2-21-21-2-12-1-112-2-2-1111−2i2i-1-1110000i3−i300000000i3i3−i3−i3−2i2ii−iii−i−i0000003−30000
χ2722-2-2-122-122-21-21-2-2-1-12-11-1112-2-212i−2i-1-11100−i3i3000000−i3−i3i3i30000−ii2i−2i−i−iii00003−3000000
χ2822-2-2-122-122-21-21-2-2-1-12-11-1112-2-212i−2i-1-11100i3−i3000000i3i3−i3−i30000−ii2i−2i−i−iii0000−33000000
χ2922-2-2-122-122-21-21-2-2-1-12-11-1112-2-21−2i2i-1-11100−i3i3000000−i3−i3i3i30000i−i−2i2iii−i−i0000−33000000
χ3022-2-2-122-122-21-21-2-2-1-12-11-1112-2-21−2i2i-1-11100i3−i3000000i3i3−i3−i30000i−i−2i2iii−i−i00003−3000000
χ312-22-2222-2-2-2-222-2-22222-2-2-22-2-22-22002-22-2000000000000000000000000002-20000002-200
χ322-22-2222-2-2-2-222-2-22222-2-2-22-2-22-22002-22-200000000000000000000000000-22000000-2200
χ332-22-222-1-2-21122-2-2-12-1-1-2-21-111-11200-11-11000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000002-2000000-1100
χ342-22-222-1-2-21122-2-2-12-1-1-2-21-111-11200-11-11000000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i300000000-220000001-100
χ352-22-222-1-2-21122-2-2-12-1-1-2-21-111-11200-11-11000000i3−i3−i3i3i3−i3i3−i3−i3i3−i3i300000000-220000001-100
χ362-22-222-1-2-21122-2-2-12-1-1-2-21-111-11200-11-11000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000002-2000000-1100
χ372-2-22222-2-2-22-2-222-2222-22-2-22-2-22-2002-2-220000000000000000000000000000000000002-2
χ382-2-22222-2-2-22-2-222-2222-22-2-22-2-22-2002-2-22000000000000000000000000000000000000-22
χ3944444-2-24-2-2-24-24-2-2-2-21-2-2-2-2-2111-20011110400-2-200-2-20000111100000000000000000000
χ4044444-2-24-2-2-24-24-2-2-2-21-2-2-2-2-2111-20011110-4002200220000-1-1-1-100000000000000000000
χ414444-24-2-24-2-2-24-24-2-21-2-2-2111-2-2-2-200111140-2-200-2-2001111000000000000000000000000
χ424444-24-2-24-2-2-24-24-2-21-2-2-2111-2-2-2-2001111-4022002200-1-1-1-1000000000000000000000000
χ434444-2-24-2-244-2-2-2-241-2-211-2-2-2-2-2-21441111000000000000000000-2-2-2-21111000000000000
χ444444-2-24-2-244-2-2-2-241-2-211-2-2-2-2-2-21-4-411110000000000000000002222-1-1-1-1000000000000
χ4544-4-444-244-22-4-4-4-424-2-24-4-222-222-400-2-22200000000000000000000000000000000000000
χ4644-4-44-2-24-2-22-42-422-2-21-22-2221-1-120011-1-10000−2i32i300000000i3i3−i3−i300000000000000000000
χ4744-4-44-2-24-2-22-42-422-2-21-22-2221-1-120011-1-100002i3−2i300000000−i3−i3i3i300000000000000000000
χ4844-4-4-24-2-24-222-42-42-21-2-221-1-1-22220011-1-100−2i32i3000000i3i3−i3−i3000000000000000000000000
χ4944-4-4-24-2-24-222-42-42-21-2-221-1-1-22220011-1-1002i3−2i3000000−i3−i3i3i3000000000000000000000000
χ5044-4-4-2-24-2-24-42222-41-2-21-1-222-222-14i−4i11-1-1000000000000000000−2i2i−2i2iii−i−i000000000000
χ5144-4-4-2-24-2-24-42222-41-2-21-1-222-222-1−4i4i11-1-10000000000000000002i−2i2i−2i−i−iii000000000000
χ524-44-44-24-42-4-44-2-424-24-222-44-42-22-200-22-2200000000000000000000000000000000000000
χ534-44-44-2-2-42224-2-42-2-2-21222-22-11-1-2001-11-100000000−2i32i30000i3−i3i3−i300000000000000000000
χ544-44-44-2-2-42224-2-42-2-2-21222-22-11-1-2001-11-1000000002i3−2i30000−i3i3−i3i300000000000000000000
χ554-44-4-2442-4-4-4-242-44-2-24222-22-44-4-200-22-2200000000000000000000000000000000000000
χ564-44-4-24-22-422-242-4-2-21-222-11-12-22-2001-11-1000000−2i32i300i3−i3i3−i3000000000000000000000000
χ574-44-4-24-22-422-242-4-2-21-222-11-12-22-2001-11-10000002i3−2i300−i3i3−i3i3000000000000000000000000
χ584-44-4-2-2422-4-4-2-22241-2-2-1-12-222-221001-11-100000000000000000000003-33-3000000000000
χ594-44-4-2-2422-4-4-2-22241-2-2-1-12-222-221001-11-10000000000000000000000-33-33000000000000
χ604-4-4444-2-4-42-2-4-44424-2-2-4422-222-2-400-222-200000000000000000000000000000000000000
χ614-4-444-24-42-44-424-2-4-24-22-2-4-4422-2200-222-200000000000000000000000000000000000000
χ624-4-444-2-2-422-2-424-22-2-212-222-2-1-112001-1-11000000000000003-3-3300000000000000000000
χ634-4-444-2-2-422-2-424-22-2-212-222-2-1-112001-1-1100000000000000-333-300000000000000000000
χ644-4-44-2442-4-442-4-24-4-2-242-222-2-4-44200-222-200000000000000000000000000000000000000
χ654-4-44-24-22-42-22-4-242-21-22-2-1-1122-22001-1-1100000000003-3-33000000000000000000000000
χ664-4-44-24-22-42-22-4-242-21-22-2-1-1122-22001-1-110000000000-333-3000000000000000000000000
χ674-4-44-2-2422-4422-2-2-41-2-2-1122-222-2-1001-1-1100000000000000000000003i−3i−3i3i000000000000
χ684-4-44-2-2422-4422-2-2-41-2-2-1122-222-2-1001-1-110000000000000000000000−3i3i3i−3i000000000000
χ698888-4-4-4-4-4-4-4-4-4-4-4-422222222222200-1-1-1-100000000000000000000000000000000000000
χ7088-8-8-4-4-4-4-4-44444442222-22-2-22-2-2-200-1-11100000000000000000000000000000000000000
χ718-88-8-4-4-44444-4-444-4222-2-2-22-2-22-2200-11-1100000000000000000000000000000000000000
χ728-8-88-4-4-4444-444-4-44222-22-2-22-2-22-200-111-100000000000000000000000000000000000000

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