Finite Group Databasebeta

← Group #11920685

Character table — Group #11920685

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222224466666666888888881212121216161616161616162424242424242424242424242424242424242424363672727272
order12442346121261222444444366612121212661212366612121212448812121212121212121212121224242424442488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-1-1111-1-1-111-1-1ii−i−i111-1-111-1-11-11-11-1-1111-1-1i−ii−iiiii−i−i−i−iii−i−iii−i−ii−i1-11-1
χ611-1-1-1111-1-1-111-1-1ii−i−i111-1-111-1-11-11-11-1-1111-1-1−ii−iiiiii−i−i−i−i−i−iii−i−iiii−i-11-11
χ711-1-1-1111-1-1-111-1-1−i−iii111-1-111-1-11-11-11-1-1111-1-1i−ii−i−i−i−i−iiiiiii−i−iii−i−i−ii-11-11
χ811-1-1-1111-1-1-111-1-1−i−iii111-1-111-1-11-11-11-1-1111-1-1−ii−ii−i−i−i−iiiii−i−iii−i−iii−ii1-11-1
χ922222222222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000220000
χ10222222222222222-2-2-2-22-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100001111111100000000-2-20000
χ1122222-12-1-1-1-1-12220000222222222-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-1-1-1-1-1000000
χ1222222-12-1-1-1-1-12220000222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000011111111000000
χ132222-22-2222-2-2-22-20000222-2-2-2-222-222-22-2-22-2-22200000000000000000000000000
χ142222-22-2222-2-2-22-200002-1-11111-1-1-222-2-111-111-1-1000033−3−333−3−300000000000000
χ152222-22-2222-2-2-22-200002-1-11111-1-1-222-2-111-111-1-10000−3−333−3−33300000000000000
χ162222-2-1-2-1-1-111-22-20000222-2-2-2-2221-1-11-111-111-1-1000000000000−i3i3−i3i3−i3i3−i3i3000000
χ172222-2-1-2-1-1-111-22-20000222-2-2-2-2221-1-11-111-111-1-1000000000000i3−i3i3−i3i3−i3i3−i3000000
χ1822-2-222-22-2-22-2-2-22000022222-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000
χ1922-2-222-22-2-22-2-2-2200002-1-1-1-11111-2-222-1-1-1-111110000−i3−i3i3i3i3i3−i3−i300000000000000
χ2022-2-222-22-2-22-2-2-2200002-1-1-1-11111-2-222-1-1-1-111110000i3i3−i3−i3−i3−i3i3i300000000000000
χ2122-2-22-1-2-111-11-2-22000022222-2-2-2-211-1-1-1-1-1-111110000000000003−3−333−3−33000000
χ2222-2-22-1-2-111-11-2-22000022222-2-2-2-211-1-1-1-1-1-11111000000000000−333−3−333−3000000
χ2322-2-2-2222-2-2-222-2-22i2i−2i−2i2-1-111-1-1112-22-2-111-1-1-1110000−i−i−i−iiiii000000002i−2i0000
χ2422-2-2-2222-2-2-222-2-2−2i−2i2i2i2-1-111-1-1112-22-2-111-1-1-1110000iiii−i−i−i−i00000000−2i2i0000
χ2522-2-2-2-12-1111-12-2-20000222-2-222-2-2-11-11-111-1-1-1112i−2i2i−2i00000000−i−iii−i−iii000000
χ2622-2-2-2-12-1111-12-2-20000222-2-222-2-2-11-11-111-1-1-111−2i2i−2i2i00000000ii−i−iii−i−i000000
χ27333333333333-1-1-13333-100000000-1-1-1-10000000011-1-1000000001111-1-1-1-1-1-1-1-111
χ28333333333333-1-1-13333-100000000-1-1-1-100000000-1-11100000000-1-1-1-11111-1-111-1-1
χ29333333333333-1-1-1-3-3-3-3-100000000-1-1-1-10000000011-1-1000000001111-1-1-1-11111-1-1
χ30333333333333-1-1-1-3-3-3-3-100000000-1-1-1-100000000-1-11100000000-1-1-1-1111111-1-111
χ3133-3-3-3333-3-3-33-1113i3i−3i−3i-100000000-11-1100000000i−i−ii00000000ii−i−i−i−iii−ii-111-1
χ3233-3-3-3333-3-3-33-1113i3i−3i−3i-100000000-11-1100000000−iii−i00000000−i−iiiii−i−i−ii1-1-11
χ3333-3-3-3333-3-3-33-111−3i−3i3i3i-100000000-11-1100000000i−i−ii00000000ii−i−i−i−iiii−i1-1-11
χ3433-3-3-3333-3-3-33-111−3i−3i3i3i-100000000-11-1100000000−iii−i00000000−i−iiiii−i−ii−i-111-1
χ3544444-24-2-2-2-2-244400004-2-2-2-2-2-2-2-2-2-2-2-21111111100000000000000000000000000
χ364444-4-2-4-2-2-222-44-400004-2-22222-2-22-2-221-1-11-1-11100000000000000000000000000
χ3744-4-44-2-4-222-22-4-4400004-2-2-2-2222222-2-21111-1-1-1-100000000000000000000000000
χ3844-4-4-4-24-2222-24-4-400004-2-222-2-222-22-221-1-1111-1-100000000000000000000000000
χ394-44i−4i040-44i−4i000002+2i−2−2i2−2i−2+2i01-1−i3i33−3i−i00001−i3i3-13−3i−i0000ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11−ζ2−ζ7ζ2+ζ700000000000000
χ404-44i−4i040-44i−4i000002+2i−2−2i2−2i−2+2i01-1i3−i3−33i−i00001i3−i3-1−33i−i0000ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7−ζ10−ζ11ζ10+ζ1100000000000000
χ414-44i−4i040-44i−4i000002+2i−2−2i2−2i−2+2i0-220000−2i2i0000-200200−2i2i0000−1−i1+i−1−i1+i−1+i1−i1−i−1+i00000000000000
χ424-44i−4i040-44i−4i00000−2−2i2+2i−2+2i2−2i01-1−i3i33−3i−i00001−i3i3-13−3i−i0000−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11ζ2+ζ7−ζ2−ζ700000000000000
χ434-44i−4i040-44i−4i00000−2−2i2+2i−2+2i2−2i01-1i3−i3−33i−i00001i3−i3-1−33i−i0000−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7ζ10+ζ11−ζ10−ζ1100000000000000
χ444-44i−4i040-44i−4i00000−2−2i2+2i−2+2i2−2i0-220000−2i2i0000-200200−2i2i00001+i−1−i1+i−1−i1−i−1+i−1+i1−i00000000000000
χ454-4−4i4i040-4−4i4i000002−2i−2+2i2+2i−2−2i01-1−i3i3−33−ii00001−i3i3-1−33−ii0000ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11−ζ2+ζ7ζ2−ζ700000000000000
χ464-4−4i4i040-4−4i4i000002−2i−2+2i2+2i−2−2i01-1i3−i33−3−ii00001i3−i3-13−3−ii0000ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7−ζ10+ζ11ζ10−ζ1100000000000000
χ474-4−4i4i040-4−4i4i000002−2i−2+2i2+2i−2−2i0-2200002i−2i0000-2002002i−2i0000−1+i1−i−1+i1−i−1−i1+i1+i−1−i00000000000000
χ484-4−4i4i040-4−4i4i00000−2+2i2−2i−2−2i2+2i01-1−i3i3−33−ii00001−i3i3-1−33−ii0000−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11ζ2−ζ7−ζ2+ζ700000000000000
χ494-4−4i4i040-4−4i4i00000−2+2i2−2i−2−2i2+2i01-1i3−i33−3−ii00001i3−i3-13−3−ii0000−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7ζ10−ζ11−ζ10+ζ1100000000000000
χ504-4−4i4i040-4−4i4i00000−2+2i2−2i−2−2i2+2i0-2200002i−2i0000-2002002i−2i00001−i−1+i1−i−1+i1+i−1−i−1−i1+i00000000000000
χ5166666-36-3-3-3-3-3-2-2-20000-20000000011110000000022-2-200000000-1-1-1-11111000000
χ5266666-36-3-3-3-3-3-2-2-20000-200000000111100000000-2-222000000001111-1-1-1-1000000
χ536666-66-6666-6-62-220000-2000000002-2-220000000000000000000000000000000000
χ546666-6-3-6-3-3-3332-220000-200000000-111-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ556666-6-3-6-3-3-3332-220000-200000000-111-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ5666-6-666-66-6-66-622-20000-20000000022-2-20000000000000000000000000000000000
χ5766-6-66-3-6-333-3322-20000-200000000-1-111000000000000000000003−3−33−333−3000000
χ5866-6-66-3-6-333-3322-20000-200000000-1-11100000000000000000000−333−33−3−33000000
χ5966-6-6-6-36-3333-3-2220000-2000000001-11-1000000002i−2i−2i2i00000000−i−iiiii−i−i000000
χ6066-6-6-6-36-3333-3-2220000-2000000001-11-100000000−2i2i2i−2i00000000ii−i−i−i−iii000000
χ618-88i−8i0-404−4i4i00000000002-2−2i32i323−232i−2i0000-1i3−i31−33−ii00000000000000000000000000
χ628-88i−8i0-404−4i4i00000000002-22i3−2i3−23232i−2i0000-1−i3i313−3−ii00000000000000000000000000
χ638-88i−8i0-404−4i4i0000000000-440000−4i4i0000200-2002i−2i00000000000000000000000000
χ648-8−8i8i0-4044i−4i00000000002-2−2i32i3−2323−2i2i0000-1i3−i313−3i−i00000000000000000000000000
χ658-8−8i8i0-4044i−4i00000000002-22i3−2i323−23−2i2i0000-1−i3i31−33i−i00000000000000000000000000
χ668-8−8i8i0-4044i−4i0000000000-4400004i−4i0000200-200−2i2i00000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.