Finite Group Databasebeta

← Group #11786444

Character table — Group #11786444

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888881212121212121212181818181818181824242424242424242424242424242424242424243636363636363636
order122222223344666666666666661212121212121212444444442222444444441212121212121212121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111-1-1-11-1111-11111-1-1-1-1-111-1-1-11111-1-1-1-1ii−i−iii−i−i11-1-1-1-111i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ10111-1-1-11-1111-11111-1-1-1-1-111-1-1-11111-1-1-1-1ii−i−iii−i−i11-1-1-1-111−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ11111-1-1-11-1111-11111-1-1-1-1-111-1-1-11111-1-1-1-1−i−iii−i−iii11-1-1-1-111i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ12111-1-1-11-1111-11111-1-1-1-1-111-1-1-11111-1-1-1-1−i−iii−i−iii11-1-1-1-111−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ13111-1-1-11-111-111111-1-1-1-1-111-1-1-1-1-1-1-11111ii−i−i−i−iii-1-111-1-111i−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ14111-1-1-11-111-111111-1-1-1-1-111-1-1-1-1-1-1-11111ii−i−i−i−iii-1-111-1-111−iii−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ15111-1-1-11-111-111111-1-1-1-1-111-1-1-1-1-1-1-11111−i−iiiii−i−i-1-111-1-111i−i−iiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ16111-1-1-11-111-111111-1-1-1-1-111-1-1-1-1-1-1-11111−i−iiiii−i−i-1-111-1-111−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ17222222222222222222222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222-2-222222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000000000000000
χ19222-2-2-22-2222-22222-2-2-2-2-222-2-2-22222-2-2-2-200000000-2-22222-2-20000000000000000000000000000
χ20222-2-2-22-222-222222-2-2-2-2-222-2-2-2-2-2-2-222220000000022-2-222-2-20000000000000000000000000000
χ2122-222-2-2-2220022-2-22222-2-2-2-2-2-200000000000000002-22-20000000000000000000000002−22−22−22−2
χ2222-222-2-2-2220022-2-22222-2-2-2-2-2-200000000000000002-22-2000000000000000000000000−22−22−22−22
χ2322-222-2-2-2220022-2-22222-2-2-2-2-2-20000000000000000-22-220000000000000000000000002−22−2−22−22
χ2422-222-2-2-2220022-2-22222-2-2-2-2-2-20000000000000000-22-22000000000000000000000000−22−222−22−2
χ2522-2-2-22-22220022-2-2-2-2-2-22-2-222200000000000000002-2-220000000000000000000000002−2−222−2−22
χ2622-2-2-22-22220022-2-2-2-2-2-22-2-222200000000000000002-2-22000000000000000000000000−222−2−222−2
χ2722-2-2-22-22220022-2-2-2-2-2-22-2-22220000000000000000-222-20000000000000000000000002−2−22−222−2
χ2822-2-2-22-22220022-2-2-2-2-2-22-2-22220000000000000000-222-2000000000000000000000000−222−22−2−22
χ292-2-22-222-22200-2-2-2-222-2-22222-2-20000000000002i−2i2i−2i00002-22-200000000000000002i−2i2i−2i00000000
χ302-2-22-222-22200-2-2-2-222-2-22222-2-2000000000000−2i2i−2i2i00002-22-20000000000000000−2i2i−2i2i00000000
χ312-2-22-222-22200-2-2-2-222-2-22222-2-2000000002i−2i2i−2i00000000-22-220000000000002i−2i2i−2i000000000000
χ322-2-22-222-22200-2-2-2-222-2-22222-2-200000000−2i2i−2i2i00000000-22-22000000000000−2i2i−2i2i000000000000
χ332-2-2-22-2222200-2-2-2-2-2-222-222-2220000000000002-2-220000-222-200000000000000002-2-2200000000
χ342-2-2-22-2222200-2-2-2-2-2-222-222-222000000000000-222-20000-222-20000000000000000-222-200000000
χ352-2-2-22-2222200-2-2-2-2-2-222-222-222000000002-2-22000000002-2-220000000000002-2-22000000000000
χ362-2-2-22-2222200-2-2-2-2-2-222-222-22200000000-222-2000000002-2-22000000000000-222-2000000000000
χ37444444441-2441-21-21-21-211-2-2-2111-2-211-2-22222222200000000000000000000-1-1-1-1-1-1-1-100000000
χ38444444441-2441-21-21-21-211-2-2-2111-2-211-2-2-2-2-2-2-2-2-2-2000000000000000000001111111100000000
χ39444444441-2-4-41-21-21-21-211-2-2-21-1-122-1-1222222-2-2-2-200000000000000000000-1-1-1-1111100000000
χ40444444441-2-4-41-21-21-21-211-2-2-21-1-122-1-122-2-2-2-22222000000000000000000001111-1-1-1-100000000
χ4144444444-2144-21-21-21-21-2-2111-2-2-211-2-21100000000000000002222-1-1-1-1-1-1-1-10000000000000000
χ4244444444-2144-21-21-21-21-2-2111-2-2-211-2-2110000000000000000-2-2-2-2111111110000000000000000
χ4344444444-21-4-4-21-21-21-21-2-2111-222-1-122-1-1000000000000000022-2-2-1-1-1-111110000000000000000
χ4444444444-21-4-4-21-21-21-21-2-2111-222-1-122-1-10000000000000000-2-2221111-1-1-1-10000000000000000
χ45444-4-4-44-41-24-41-21-2-12-12-11-222-111-2-2-1-1222i2i−2i−2i2i2i−2i−2i00000000000000000000−i−iii−i−iii00000000
χ46444-4-4-44-41-24-41-21-2-12-12-11-222-111-2-2-1-122−2i−2i2i2i−2i−2i2i2i00000000000000000000ii−i−iii−i−i00000000
χ47444-4-4-44-41-2-441-21-2-12-12-11-222-1-1-12211-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000−i−iiiii−i−i00000000
χ48444-4-4-44-41-2-441-21-2-12-12-11-222-1-1-12211-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000ii−i−i−i−iii00000000
χ49444-4-4-44-4-214-4-21-212-12-12-21-1-12-2-21122-1-100000000000000002i−2i2i−2i−i−iii−i−iii0000000000000000
χ50444-4-4-44-4-214-4-21-212-12-12-21-1-12-2-21122-1-10000000000000000−2i2i−2i2iii−i−iii−i−i0000000000000000
χ51444-4-4-44-4-21-44-21-212-12-12-21-1-1222-1-1-2-21100000000000000002i−2i−2i2i−i−iiiii−i−i0000000000000000
χ52444-4-4-44-4-21-44-21-212-12-12-21-1-1222-1-1-2-2110000000000000000−2i2i2i−2iii−i−i−i−iii0000000000000000
χ534-444-4-4-444400-4-44444-4-4-4-4-4-4440000000000000000000000000000000000000000000000000000
χ544-444-4-4-44-21002-1-21-212-122-1-11-2003i−3i003i−3i000000000000000000003−33−3−i3i3−i3i30000000000000000
χ554-444-4-4-44-21002-1-21-212-122-1-11-2003i−3i003i−3i00000000000000000000−33−33i3−i3i3−i30000000000000000
χ564-444-4-4-44-21002-1-21-212-122-1-11-200−3i3i00−3i3i000000000000000000003−33−3i3−i3i3−i30000000000000000
χ574-444-4-4-44-21002-1-21-212-122-1-11-200−3i3i00−3i3i00000000000000000000−33−33−i3i3−i3i30000000000000000
χ584-44-444-4-44400-4-444-4-4444-4-44-4-40000000000000000000000000000000000000000000000000000
χ594-44-444-4-4-21002-1-212-1-21-22-11-12003i−3i00−3i3i00000000000000000000−i3i3i3−i3−333−30000000000000000
χ604-44-444-4-4-21002-1-212-1-21-22-11-12003i−3i00−3i3i00000000000000000000i3−i3−i3i33−3−330000000000000000
χ614-44-444-4-4-21002-1-212-1-21-22-11-1200−3i3i003i−3i00000000000000000000−i3i3i3−i33−3−330000000000000000
χ624-44-444-4-4-21002-1-212-1-21-22-11-1200−3i3i003i−3i00000000000000000000i3−i3−i3i3−333−30000000000000000
χ634-4-44-444-41-200-12-121-2-1211-2-22-13-3003-3002i−2i2i−2i2i−2i2i−2i00000000000000000000−ii−ii−ii−ii00000000
χ644-4-44-444-41-200-12-121-2-1211-2-22-13-3003-300−2i2i−2i2i−2i2i−2i2i00000000000000000000i−ii−ii−ii−i00000000
χ654-4-44-444-41-200-12-121-2-1211-2-22-1-3300-33002i−2i2i−2i−2i2i−2i2i00000000000000000000−ii−iii−ii−i00000000
χ664-4-44-444-41-200-12-121-2-1211-2-22-1-3300-3300−2i2i−2i2i2i−2i2i−2i00000000000000000000i−ii−i−ii−ii00000000
χ674-4-4-44-4441-200-12-12-121-2-11-22-213-300-33002-2-222-2-2200000000000000000000-111-1-111-100000000
χ684-4-4-44-4441-200-12-12-121-2-11-22-213-300-3300-222-2-222-2000000000000000000001-1-111-1-1100000000
χ694-4-4-44-4441-200-12-12-121-2-11-22-21-33003-3002-2-22-222-200000000000000000000-111-11-1-1100000000
χ704-4-4-44-4441-200-12-12-121-2-11-22-21-33003-300-222-22-2-22000000000000000000001-1-11-111-100000000
χ7188-888-8-8-82-4002-4-242-42-4-2-2444-20000000000000000000000000000000000000000000000000000
χ7288-888-8-8-8-4200-424-2-42-4244-2-2-240000000000000000000000000000000000000000000000000000
χ7388-8-8-88-882-4002-4-24-24-242-24-4-420000000000000000000000000000000000000000000000000000
χ7488-8-8-88-88-4200-424-24-24-2-44-222-40000000000000000000000000000000000000000000000000000
χ758-888-8-8-882-400-242-42-4-24-2-244-420000000000000000000000000000000000000000000000000000
χ768-88-888-8-82-400-242-4-242-42-24-44-20000000000000000000000000000000000000000000000000000
χ778-8-88-888-8-42004-24-2-424-2-4-422-240000000000000000000000000000000000000000000000000000
χ788-8-8-88-888-42004-24-24-2-424-42-22-40000000000000000000000000000000000000000000000000000

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