Finite Group Databasebeta

← Group #11920708

Character table — Group #11920708

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222224466666666888888881212121216161616161616162424242424242424242424242424242424242424363672727272
order1222344666121222448888366612121212661212366612121212448812121212242424242424242424242424882288
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
χ51-11-111-1-11-11-11-1-11ii−i−i1-1-1111-1-11-11-11-1-1111-1-1i−ii−iii−i−iiiii−i−i−i−iii−i−ii−i1-11-1
χ61-11-111-1-11-11-11-1-11ii−i−i1-1-1111-1-11-11-11-1-1111-1-1−ii−ii−i−iiiiiii−i−i−i−i−i−iiii−i-11-11
χ71-11-111-1-11-11-11-1-11−i−iii1-1-1111-1-11-11-11-1-1111-1-1i−ii−iii−i−i−i−i−i−iiiiiii−i−i−ii-11-11
χ81-11-111-1-11-11-11-1-11−i−iii1-1-1111-1-11-11-11-1-1111-1-1−ii−ii−i−iii−i−i−i−iiiii−i−iii−ii1-11-1
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
χ182-22-222-2-22-22-22-2-222i2i−2i−2i-111-1-1-1112-22-2-111-1-1-11100000000−i−i−i−iiiii00002i−2i0000
χ192-22-222-2-22-22-22-2-22−2i−2i2i2i-111-1-1-1112-22-2-111-1-1-11100000000iiii−i−i−i−i0000−2i2i0000
χ202-22-22-22-22-2-22-22-2200002-2-22-2-222-222-22-2-22-2-22200000000000000000000000000
χ212-22-22-22-22-2-22-22-220000-111-111-1-1-222-2-111-111-1-100000000−i3−i3i3i3i3i3−i3−i30000000000
χ222-22-22-22-22-2-22-22-220000-111-111-1-1-222-2-111-111-1-100000000i3i3−i3−i3−i3−i3i3i30000000000
χ232-22-2-12-21-11-112-2-2200002-2-2222-2-2-11-11-111-1-1-1112i−2i2i−2i−i−iii00000000−i−iii000000
χ242-22-2-12-21-11-112-2-2200002-2-2222-2-2-11-11-111-1-1-111−2i2i−2i2iii−i−i00000000ii−i−i000000
χ252-22-2-1-221-111-1-22-2200002-2-22-2-2221-1-11-111-111-1-100003−3−33000000003−3−33000000
χ262-22-2-1-221-111-1-22-2200002-2-22-2-2221-1-11-111-111-1-10000−333−300000000−333−3000000
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
χ313-33-333-3-33-33-3-111-13i3i−3i−3i00000000-11-1100000000i−i−iiii−i−i00000000−i−iii−ii1-1-11
χ323-33-333-3-33-33-3-111-13i3i−3i−3i00000000-11-1100000000−iii−i−i−iii00000000ii−i−i−ii-111-1
χ333-33-333-3-33-33-3-111-1−3i−3i3i3i00000000-11-1100000000i−i−iiii−i−i00000000−i−iiii−i-111-1
χ343-33-333-3-33-33-3-111-1−3i−3i3i3i00000000-11-1100000000−iii−i−i−iii00000000ii−i−ii−i1-1-11
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
χ3744-4-44004-4-4000000−2i22i2−2i22i211-1-13−33−3000011-1-13−33−300000000ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ230000000000
χ3844-4-44004-4-4000000−2i22i2−2i22i211-1-1−33−33000011-1-1−33−3300000000ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ70000000000
χ3944-4-44004-4-4000000−2i22i2−2i22i2-2-22200000000-2-222000000000000−i2i2i2−i2−i2i2i2−i20000000000
χ4044-4-44004-4-40000002i2−2i22i2−2i211-1-13−33−3000011-1-13−33−300000000−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ230000000000
χ4144-4-44004-4-40000002i2−2i22i2−2i211-1-1−33−33000011-1-1−33−3300000000−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ70000000000
χ4244-4-44004-4-40000002i2−2i22i2−2i2-2-22200000000-2-222000000000000i2−i2−i2i2i2−i2−i2i20000000000
χ434-44-4-24-42-22-224-4-440000-222-2-2-222-22-221-1-1111-1-100000000000000000000000000
χ444-44-4-2-442-222-2-44-440000-222-222-2-22-2-221-1-11-1-11100000000000000000000000000
χ454-4-44400-4-4400000022−22−22221-11-13−3−3300001-11-13−3−3300000000ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ70000000000
χ464-4-44400-4-4400000022−22−22221-11-1−333−300001-11-1−333−300000000ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ230000000000
χ474-4-44400-4-4400000022−22−2222-22-2200000000-22-220000000000002−2−22−222−20000000000
χ484-4-44400-4-44000000−222222−221-11-13−3−3300001-11-13−3−3300000000−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ70000000000
χ494-4-44400-4-44000000−222222−221-11-1−333−300001-11-1−333−300000000−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ230000000000
χ504-4-44400-4-44000000−222222−22-22-2200000000-22-22000000000000−222−22−2−220000000000
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
χ566-66-66-66-66-6-662-22-20000000000002-2-220000000000000000000000000000000000
χ576-66-6-36-63-33-33-222-20000000000001-11-1000000002i−2i−2i2i−i−iii00000000ii−i−i000000
χ586-66-6-36-63-33-33-222-20000000000001-11-100000000−2i2i2i−2iii−i−i00000000−i−iii000000
χ596-66-6-3-663-333-32-22-2000000000000-111-10000000000003−3−3300000000−333−3000000
χ606-66-6-3-663-333-32-22-2000000000000-111-1000000000000−333−3000000003−3−33000000
χ6188-8-8-400-444000000000022-2-223−2323−230000-1-111−33−3300000000000000000000000000
χ6288-8-8-400-444000000000022-2-2−2323−23230000-1-1113−33−300000000000000000000000000
χ6388-8-8-400-4440000000000-4-4440000000022-2-2000000000000000000000000000000
χ648-8-88-40044-400000000002-22-223−23−23230000-11-11−333−300000000000000000000000000
χ658-8-88-40044-400000000002-22-2−232323−230000-11-113−3−3300000000000000000000000000
χ668-8-88-40044-40000000000-44-44000000002-22-2000000000000000000000000000000

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