Finite Group Databasebeta

← Group #11920702

Character table — Group #11920702

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222224466666666888888881212121216161616161616162424242424242424242424242424242424242424363672727272
order1222344666121222448888366612121212661212366612121212448812121212242424242424242424242424884488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1
χ31111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-11-11-11-11-11-11-111-1-11-1-11-1-1111-11-11-1-1111-1-1i−ii−iii−i−i1111-1-1-1-1ii−i−i1-1i−ii−i
χ611-1-11-11-11-11-11-11-111-1-11-1-11-1-1111-11-11-1-1111-1-1−ii−ii−i−iii1111-1-1-1-1−i−iii1-1−ii−ii
χ711-1-11-11-11-11-11-11-1-1-1111-1-11-1-1111-11-11-1-1111-1-1i−ii−iii−i−i-1-1-1-11111ii−i−i-11−ii−ii
χ811-1-11-11-11-11-11-11-1-1-1111-1-11-1-1111-11-11-1-1111-1-1−ii−ii−i−iii-1-1-1-11111−i−iii-11i−ii−i
χ922222222222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-10000220000
χ102222222222222222-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000111111110000-2-20000
χ1122222-2-2222-2-2-2-22200002222-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000
χ1222222-2-2222-2-2-2-2220000-1-1-1-11111-2-222-1-1-1-111110000000033−3−333−3−30000000000
χ1322222-2-2222-2-2-2-2220000-1-1-1-11111-2-222-1-1-1-1111100000000−3−333−3−3330000000000
χ142222-122-1-1-1-1-12222000022222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100000000-1-1-1-1000000
χ152222-122-1-1-1-1-12222000022222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111000000001111000000
χ162222-1-2-2-1-1-111-2-22200002222-2-2-2-211-1-1-1-1-1-111110000−i3i3−i3i300000000−i3i3−i3i3000000
χ172222-1-2-2-1-1-111-2-22200002222-2-2-2-211-1-1-1-1-1-111110000i3−i3i3−i300000000i3−i3i3−i3000000
χ1822-2-222-2-22-2-22-222-200002-2-2222-2-2-222-22-2-22-2-22200000000000000000000000000
χ1922-2-222-2-22-2-22-222-20000-111-1-1-111-222-2-111-111-1-10000000033−3−3−3−3330000000000
χ2022-2-222-2-22-2-22-222-20000-111-1-1-111-222-2-111-111-1-100000000−3−33333−3−30000000000
χ2122-2-22-22-22-22-22-22-222-2-2-111-111-1-12-22-2-111-1-1-11100000000-1-1-1-1111100002-20000
χ2222-2-22-22-22-22-22-22-2-2-222-111-111-1-12-22-2-111-1-1-111000000001111-1-1-1-10000-220000
χ2322-2-2-12-21-111-1-222-200002-2-2222-2-21-1-11-111-111-1-100003−3−33000000003−3−33000000
χ2422-2-2-12-21-111-1-222-200002-2-2222-2-21-1-11-111-111-1-10000−333−300000000−333−3000000
χ2522-2-2-1-221-11-112-22-200002-2-22-2-222-11-11-111-1-1-1112i−2i2i−2i−i−iii00000000−i−iii000000
χ2622-2-2-1-221-11-112-22-200002-2-22-2-222-11-11-111-1-1-111−2i2i−2i2iii−i−i00000000ii−i−i000000
χ27333333333333-1-1-1-1333300000000-1-1-1-10000000011-1-1111100000000-1-1-1-1-1-111-1-1
χ28333333333333-1-1-1-1333300000000-1-1-1-100000000-1-111-1-1-1-1000000001111-1-1-1-111
χ29333333333333-1-1-1-1-3-3-3-300000000-1-1-1-10000000011-1-1111100000000-1-1-1-111-1-111
χ30333333333333-1-1-1-1-3-3-3-300000000-1-1-1-100000000-1-111-1-1-1-10000000011111111-1-1
χ3133-3-33-33-33-33-3-11-1133-3-300000000-11-1100000000i−i−iiii−i−i00000000−i−iii-11i−i−ii
χ3233-3-33-33-33-33-3-11-1133-3-300000000-11-1100000000−iii−i−i−iii00000000ii−i−i-11−iii−i
χ3333-3-33-33-33-33-3-11-11-3-33300000000-11-1100000000i−i−iiii−i−i00000000−i−iii1-1−iii−i
χ3433-3-33-33-33-33-3-11-11-3-33300000000-11-1100000000−iii−i−i−iii00000000ii−i−i1-1i−i−ii
χ354444-244-2-2-2-2-244440000-2-2-2-2-2-2-2-2-2-2-2-21111111100000000000000000000000000
χ364444-2-4-4-2-2-222-4-4440000-2-2-2-2222222-2-21111-1-1-1-100000000000000000000000000
χ3744-4-4-24-42-222-2-444-40000-222-2-2-2222-2-221-1-11-1-11100000000000000000000000000
χ3844-4-4-2-442-22-224-44-40000-222-222-2-2-22-221-1-1111-1-100000000000000000000000000
χ394-44-4400-4-44000000−2i22i2−2i22i211-1-13−33−3000011-1-13−33−300000000ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ230000000000
χ404-44-4400-4-44000000−2i22i2−2i22i211-1-1−33−33000011-1-1−33−3300000000ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ70000000000
χ414-44-4400-4-44000000−2i22i2−2i22i2-2-22200000000-2-222000000000000−i2i2i2−i2−i2i2i2−i20000000000
χ424-44-4400-4-440000002i2−2i22i2−2i211-1-13−33−3000011-1-13−33−300000000−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ230000000000
χ434-44-4400-4-440000002i2−2i22i2−2i211-1-1−33−33000011-1-1−33−3300000000−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ70000000000
χ444-44-4400-4-440000002i2−2i22i2−2i2-2-22200000000-2-222000000000000i2−i2−i2i2i2−i2−i2i20000000000
χ454-4-444004-4-4000000−2i22i22i2−2i21-11-13−3−3300001-11-1−333−300000000ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ70000000000
χ464-4-444004-4-4000000−2i22i22i2−2i21-11-1−333−300001-11-13−3−3300000000ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ230000000000
χ474-4-444004-4-4000000−2i22i22i2−2i2-22-2200000000-22-22000000000000−i2i2i2−i2i2−i2−i2i20000000000
χ484-4-444004-4-40000002i2−2i2−2i22i21-11-13−3−3300001-11-1−333−300000000−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ70000000000
χ494-4-444004-4-40000002i2−2i2−2i22i21-11-1−333−300001-11-13−3−3300000000−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ230000000000
χ504-4-444004-4-40000002i2−2i2−2i22i2-22-2200000000-22-22000000000000i2−i2−i2i2−i2i2i2−i20000000000
χ5166666-6-6666-6-622-2-200000000000022-2-20000000000000000000000000000000000
χ526666-366-3-3-3-3-3-2-2-2-200000000000011110000000022-2-2-1-1-1-1000000001111000000
χ536666-366-3-3-3-3-3-2-2-2-2000000000000111100000000-2-222111100000000-1-1-1-1000000
χ546666-3-6-6-3-3-33322-2-2000000000000-1-111000000000000−i3i3−i3i300000000i3−i3i3−i3000000
χ556666-3-6-6-3-3-33322-2-2000000000000-1-111000000000000i3−i3i3−i300000000−i3i3−i3i3000000
χ5666-6-666-6-66-6-662-2-220000000000002-2-220000000000000000000000000000000000
χ5766-6-6-36-63-333-32-2-22000000000000-111-10000000000003−3−3300000000−333−3000000
χ5866-6-6-36-63-333-32-2-22000000000000-111-1000000000000−333−3000000003−3−33000000
χ5966-6-6-3-663-33-33-22-220000000000001-11-1000000002i−2i−2i2i−i−iii00000000ii−i−i000000
χ6066-6-6-3-663-33-33-22-220000000000001-11-100000000−2i2i2i−2iii−i−i00000000−i−iii000000
χ618-88-8-40044-4000000000022-2-223−2323−230000-1-111−33−3300000000000000000000000000
χ628-88-8-40044-4000000000022-2-2−2323−23230000-1-1113−33−300000000000000000000000000
χ638-88-8-40044-40000000000-4-4440000000022-2-2000000000000000000000000000000
χ648-8-88-400-44400000000002-22-223−23−23230000-11-113−3−3300000000000000000000000000
χ658-8-88-400-44400000000002-22-2−232323−230000-11-11−333−300000000000000000000000000
χ668-8-88-400-4440000000000-44-44000000002-22-2000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.