Finite Group Databasebeta

← Group #11791855

Character table — Group #11791855

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222244444444444444444444888888121212121212121212121212121212121212121212121212181818182424242436364848484872727272
order12222244443366666666661212121212121212661212121244444444121212121212121212121212121212122222444444121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-11-11-111-1-1
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-1-11-11-1-111
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-11-1-1-11-11-1-1-111
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-11-11-1-1-11-1111-1-1
χ91111-1-111-1-111111-1-111-1-111111-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-11-111-1-1i−ii−i
χ101111-1-111-1-111111-1-111-1-111111-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-1111-1-1-111−ii−ii
χ111111-1-111-1-111111-1-111-1-111111-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-11-111-1-1−ii−ii
χ121111-1-111-1-111111-1-111-1-111111-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-1111-1-1-111i−ii−i
χ131111-1-1-1-11111111-1-111-1-11-1-1-1-11111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-11-1-11-111-1-11i−i−ii
χ141111-1-1-1-11111111-1-111-1-11-1-1-1-11111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-111-1-11-111-1−iii−i
χ151111-1-1-1-11111111-1-111-1-11-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-11-1-11-111-1-11−iii−i
χ161111-1-1-1-11111111-1-111-1-11-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-111-1-11-111-1i−i−ii
χ17222222222222222222222222222222222222000000000000000000000000-2-2-2-20000-2-200000000
χ18222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000-2-2-2-200002200000000
χ192222-2-222-2-222222-2-222-2-222222-2-2-2-2-2-222-2-2000000000000000000000000-2-2220000-2200000000
χ202222-2-2-2-22222222-2-222-2-22-2-2-2-22222-2-2-2-222000000000000000000000000-2-22200002-200000000
χ2122-2-22-200002222-22-2-2-22-2-2000000002-2000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i2-2-2200000000000000
χ2222-2-22-200002222-22-2-2-22-2-2000000002-200000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i2-2-2200000000000000
χ2322-2-22-200002222-22-2-2-22-2-2000000002-200002-22-2000022-2-222-2-200000000-222-200000000000000
χ2422-2-22-200002222-22-2-2-22-2-2000000002-20000-22-220000-2-222-2-22200000000-222-200000000000000
χ2522-2-2-2200002222-2-22-2-2-22-200000000-22000000002-2-220000000022-2-2-2-2222-22-200000000000000
χ2622-2-2-2200002222-2-22-2-2-22-200000000-2200000000-222-200000000-2-22222-2-22-22-200000000000000
χ2722-2-2-2200002222-2-22-2-2-22-200000000-2200002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000-22-2200000000000000
χ2822-2-2-2200002222-2-22-2-2-22-200000000-220000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000-22-2200000000000000
χ2944444444441-21-21111-211-211111111-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3044444444441-21-21111-211-211111111-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111000000000000000000
χ314444444444-21-21-2-2-2-21-2-21-2-2-2-2-2-2-2-21111110000000000000000000000000000222200-1-1-1-10000
χ324444444444-21-21-2-2-2-21-2-21-2-2-2-2-2-2-2-21111110000000000000000000000000000-2-2-2-20011110000
χ33444444-4-4-4-41-21-21111-211-2-1-1-1-1-1-1-1-1-2-222222222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000
χ34444444-4-4-4-41-21-21111-211-2-1-1-1-1-1-1-1-1-2-22222-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000
χ35444444-4-4-4-4-21-21-2-2-2-21-2-212222222211-1-1-1-100000000000000000000000000002-22-200-11-110000
χ36444444-4-4-4-4-21-21-2-2-2-21-2-212222222211-1-1-1-10000000000000000000000000000-22-22001-11-10000
χ374444-4-444-4-41-21-21-1-11-2-1-1-21111-1-1-1-122-2-2222i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000
χ384444-4-444-4-41-21-21-1-11-2-1-1-21111-1-1-1-122-2-222−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000
χ394444-4-444-4-4-21-21-222-21221-2-2-2-22222-1-111-1-1000000000000000000000000000022-2-200-1-1110000
χ404444-4-444-4-4-21-21-222-21221-2-2-2-22222-1-111-1-10000000000000000000000000000-2-2220011-1-10000
χ414444-4-4-4-4441-21-21-1-11-2-1-1-2-1-1-1-111112222-2-22i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000
χ424444-4-4-4-4441-21-21-1-11-2-1-1-2-1-1-1-111112222-2-2−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000
χ434444-4-4-4-444-21-21-222-212212222-2-2-2-2-1-1-1-11100000000000000000000000000002-2-2200-111-10000
χ444444-4-4-4-444-21-21-222-212212222-2-2-2-2-1-1-1-1110000000000000000000000000000-222-2001-1-110000
χ4544-4-44-400001-21-2-11-1-121-123i3i−3i−3i3i3i−3i−3i-2200002-22-22i−2i2i−2i-1-111-1-111−i−iii−i−iii000000000000000000
χ4644-4-44-400001-21-2-11-1-121-123i3i−3i−3i3i3i−3i−3i-220000-22-22−2i2i−2i2i11-1-111-1-1ii−i−iii−i−i000000000000000000
χ4744-4-44-400001-21-2-11-1-121-12−3i−3i3i3i−3i−3i3i3i-2200002-22-2−2i2i−2i2i-1-111-1-111ii−i−iii−i−i000000000000000000
χ4844-4-44-400001-21-2-11-1-121-12−3i−3i3i3i−3i−3i3i3i-220000-22-222i−2i2i−2i11-1-111-1-1−i−iii−i−iii000000000000000000
χ4944-4-4-4400001-21-2-1-11-12-1123i3i−3i−3i−3i−3i3i3i2-200002i−2i−2i2i-222-2−i−iiiii−i−i11-1-1-1-111000000000000000000
χ5044-4-4-4400001-21-2-1-11-12-1123i3i−3i−3i−3i−3i3i3i2-20000−2i2i2i−2i2-2-22ii−i−i−i−iii-1-11111-1-1000000000000000000
χ5144-4-4-4400001-21-2-1-11-12-112−3i−3i3i3i3i3i−3i−3i2-200002i−2i−2i2i2-2-22−i−iiiii−i−i-1-11111-1-1000000000000000000
χ5244-4-4-4400001-21-2-1-11-12-112−3i−3i3i3i3i3i−3i−3i2-20000−2i2i2i−2i-222-2ii−i−i−i−iii11-1-1-1-111000000000000000000
χ534-44-400004i−4i1-2-1213-3-1-2-3323i−3i3i−3ii−ii−i00002i−2i00000000−i3i3−i3i3−i3i3−i3i33−33−33−33−3000000000000000000
χ544-44-400004i−4i1-2-1213-3-1-2-3323i−3i3i−3ii−ii−i00002i−2i00000000i3−i3i3−i3i3−i3i3−i3−33−33−33−33000000000000000000
χ554-44-400004i−4i1-2-121-33-1-23-32−3i3i−3i3ii−ii−i00002i−2i000000003−33−3−33−33−i3i3−i3i3i3−i3i3−i3000000000000000000
χ564-44-400004i−4i1-2-121-33-1-23-32−3i3i−3i3ii−ii−i00002i−2i00000000−33−333−33−3i3−i3i3−i3−i3i3−i3i3000000000000000000
χ574-44-400004i−4i44-4-4400-4400-400004i−4i4i−4i0000−4i4i000000000000000000000000000000000000000000
χ584-44-40000−4i4i1-2-1213-3-1-2-332−3i3i−3i3i−ii−ii0000−2i2i00000000−i3i3−i3i3−i3i3−i3i3−33−33−33−33000000000000000000
χ594-44-40000−4i4i1-2-1213-3-1-2-332−3i3i−3i3i−ii−ii0000−2i2i00000000i3−i3i3−i3i3−i3i3−i33−33−33−33−3000000000000000000
χ604-44-40000−4i4i1-2-121-33-1-23-323i−3i3i−3i−ii−ii0000−2i2i000000003−33−3−33−33i3−i3i3−i3−i3i3−i3i3000000000000000000
χ614-44-40000−4i4i1-2-121-33-1-23-323i−3i3i−3i−ii−ii0000−2i2i00000000−33−333−33−3−i3i3−i3i3i3−i3i3−i3000000000000000000
χ624-44-40000−4i4i44-4-4400-4400-40000−4i4i−4i4i00004i−4i000000000000000000000000000000000000000000
χ634-4-44004-4001-2-12-13312-3-3-21-1-113-3-33002-20000000000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000000000
χ644-4-44004-4001-2-12-13312-3-3-21-1-113-3-33002-20000000000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000000000
χ654-4-44004-4001-2-12-1-3-31233-21-1-11-333-3002-200000000003−3−33−333−33−3−33−333−3000000000000000000
χ664-4-44004-4001-2-12-1-3-31233-21-1-11-333-3002-20000000000−333−33−3−33−333−33−3−33000000000000000000
χ674-4-44004-40044-4-4-4004-40044-4-44000000-4400000000000000000000000000000000000000000000
χ684-4-4400-44001-2-12-13312-3-3-2-111-1-333-300-220000000000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3000000000000000000
χ694-4-4400-44001-2-12-13312-3-3-2-111-1-333-300-220000000000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3000000000000000000
χ704-4-4400-44001-2-12-1-3-31233-2-111-13-3-3300-2200000000003−3−33−333−3−333−33−3−33000000000000000000
χ714-4-4400-44001-2-12-1-3-31233-2-111-13-3-3300-220000000000−333−33−3−333−3−33−333−3000000000000000000
χ724-4-4400-440044-4-4-4004-4004-444-40000004-400000000000000000000000000000000000000000000
χ7388-8-88-80000-42-424-444-2-44-2000000002-20000000000000000000000000000000000000000000000
χ7488-8-8-880000-42-4244-44-24-4-200000000-220000000000000000000000000000000000000000000000
χ758-88-800008i−8i-424-2-4004200-20000−4i4i−4i4i0000−2i2i000000000000000000000000000000000000000000
χ768-88-80000−8i8i-424-2-4004200-200004i−4i4i−4i00002i−2i000000000000000000000000000000000000000000
χ778-8-88008-800-424-2400-4-2002-444-4000000-2200000000000000000000000000000000000000000000
χ788-8-8800-8800-424-2400-4-20024-4-440000002-200000000000000000000000000000000000000000000

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