Finite Group Databasebeta

← Group #11920707

Character table — Group #11920707

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222224466666666888888881212121216161616161616162424242424242424242424242424242424242424363672727272
order122234466612122244888836661212121266121236661212121222666688242424242424242424242424884488
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
χ51-11-111-1-1-111-11-11-1ii−i−i1-1-1111-1-11-1-111-1-1111-1-11-111-1-11-1iiii−i−i−i−i11-1-1i−ii−ii−i
χ61-11-111-1-1-111-11-11-1ii−i−i1-1-1111-1-11-1-111-1-1111-1-1-11-1-111-11iiii−i−i−i−i-1-111i−i−ii−ii
χ71-11-111-1-1-111-11-11-1−i−iii1-1-1111-1-11-1-111-1-1111-1-11-111-1-11-1−i−i−i−iiiii11-1-1−ii−ii−ii
χ81-11-111-1-1-111-11-11-1−i−iii1-1-1111-1-11-1-111-1-1111-1-1-11-1-111-11−i−i−i−iiiii-1-111−iii−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
χ142222-122-1-1-1-1-12222000022222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12200000000-1-1-1-1000000
χ152222-122-1-1-1-1-12222000022222222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2000000001111000000
χ162222-1-2-2-1-1-111-2-22200002222-2-2-2-211-1-1-1-1-1-1111100−i3i3−i3i30000000000−i3i3−i3i3000000
χ172222-1-2-2-1-1-111-2-22200002222-2-2-2-211-1-1-1-1-1-1111100i3−i3i3−i30000000000i3−i3i3−i3000000
χ182-22-222-2-2-222-22-22-22i2i−2i−2i-111-1-1-1112-2-22-111-1-1-11100000000−i−i−i−iiiii00002i−2i0000
χ192-22-222-2-2-222-22-22-2−2i−2i2i2i-111-1-1-1112-2-22-111-1-1-11100000000iiii−i−i−i−i0000−2i2i0000
χ202-22-22-22-2-22-22-222-200002-2-22-2-222-22-222-2-22-2-22200000000000000000000000000
χ212-22-22-22-2-22-22-222-20000-111-111-1-1-22-22-111-111-1-100000000−i3−i3i3i3i3i3−i3−i30000000000
χ222-22-22-22-2-22-22-222-20000-111-111-1-1-22-22-111-111-1-100000000i3i3−i3−i3−i3−i3i3i30000000000
χ232-22-2-12-211-1-112-22-200002-2-2222-2-2-111-1-111-1-1-1112-2-1-1112-200000000-1-111000000
χ242-22-2-12-211-1-112-22-200002-2-2222-2-2-111-1-111-1-1-111-2211-1-1-220000000011-1-1000000
χ252-22-2-1-2211-11-1-222-200002-2-22-2-2221-11-1-111-111-1-100−i3i3i3−i30000000000−i3i3i3−i3000000
χ262-22-2-1-2211-11-1-222-200002-2-22-2-2221-11-1-111-111-1-100i3−i3−i3i30000000000i3−i3−i3i3000000
χ27333333333333-1-1-1-1333300000000-1-1-1-100000000111111-1-100000000-1-1-1-1-1-111-1-1
χ28333333333333-1-1-1-1333300000000-1-1-1-100000000-1-1-1-1-1-111000000001111-1-1-1-111
χ29333333333333-1-1-1-1-3-3-3-300000000-1-1-1-100000000111111-1-100000000-1-1-1-111-1-111
χ30333333333333-1-1-1-1-3-3-3-300000000-1-1-1-100000000-1-1-1-1-1-1110000000011111111-1-1
χ313-33-333-3-3-333-3-11-113i3i−3i−3i00000000-111-1000000001-111-1-1-1100000000-1-111−iii−i−ii
χ323-33-333-3-3-333-3-11-113i3i−3i−3i00000000-111-100000000-11-1-1111-10000000011-1-1−ii−iii−i
χ333-33-333-3-3-333-3-11-11−3i−3i3i3i00000000-111-1000000001-111-1-1-1100000000-1-111i−i−iii−i
χ343-33-333-3-3-333-3-11-11−3i−3i3i3i00000000-111-100000000-11-1-1111-10000000011-1-1i−ii−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
χ3744-4-44004-4-4000000−2i22i2−2i22i211-1-13−33−3000011-1-13−33−300000000ζ5+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
χ434-44-4-24-422-2-224-44-40000-222-2-2-222-222-21-1-1111-1-100000000000000000000000000
χ444-44-4-2-4422-22-2-444-40000-222-222-2-22-22-21-1-11-1-11100000000000000000000000000
χ454-4-44400-44-400000022−22−22221-11-13−3−3300001-11-13−3−3300000000ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ70000000000
χ464-4-44400-44-400000022−22−22221-11-1−333−300001-11-1−333−300000000ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ230000000000
χ474-4-44400-44-400000022−22−2222-22-2200000000-22-220000000000002−2−22−222−20000000000
χ484-4-44400-44-4000000−222222−221-11-13−3−3300001-11-13−3−3300000000−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ70000000000
χ494-4-44400-44-4000000−222222−221-11-1−333−300001-11-1−333−300000000−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ230000000000
χ504-4-44400-44-4000000−222222−22-22-2200000000-22-22000000000000−222−22−2−220000000000
χ5166666-6-6666-6-622-2-200000000000022-2-20000000000000000000000000000000000
χ526666-366-3-3-3-3-3-2-2-2-200000000000011110000000022-1-1-1-1-2-2000000001111000000
χ536666-366-3-3-3-3-3-2-2-2-2000000000000111100000000-2-211112200000000-1-1-1-1000000
χ546666-3-6-6-3-3-33322-2-2000000000000-1-1110000000000−i3i3−i3i30000000000i3−i3i3−i3000000
χ556666-3-6-6-3-3-33322-2-2000000000000-1-1110000000000i3−i3i3−i30000000000−i3i3−i3i3000000
χ566-66-66-66-6-66-662-2-220000000000002-22-20000000000000000000000000000000000
χ576-66-6-36-633-3-33-22-220000000000001-1-11000000002-2-1-111-220000000011-1-1000000
χ586-66-6-36-633-3-33-22-220000000000001-1-1100000000-2211-1-12-200000000-1-111000000
χ596-66-6-3-6633-33-32-2-22000000000000-11-110000000000−i3i3i3−i30000000000i3−i3−i3i3000000
χ606-66-6-3-6633-33-32-2-22000000000000-11-110000000000i3−i3−i3i30000000000−i3i3i3−i3000000
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
χ648-8-88-4004-4400000000002-22-223−23−23230000-11-11−333−300000000000000000000000000
χ658-8-88-4004-4400000000002-22-2−232323−230000-11-113−3−3300000000000000000000000000
χ668-8-88-4004-440000000000-44-44000000002-22-2000000000000000000000000000000

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