Finite Group Databasebeta

← Group #11920704

Character table — Group #11920704

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222224466666666888888881212121216161616161616162424242424242424242424242424242424242424363672727272
order12442346121261222448888366612121212661212366612121212448812121212242424242424242424242424884488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ31111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ511-1-1-1111-1-1-111-11-111-1-11-1-11-1-1111-11-11-1-1111-1-1i−ii−iii−i−iii−i−i1111-1-1-1-11-1i−ii−i
χ611-1-1-1111-1-1-111-11-111-1-11-1-11-1-1111-11-11-1-1111-1-1−ii−ii−i−iii−i−iii1111-1-1-1-11-1−ii−ii
χ711-1-1-1111-1-1-111-11-1-1-1111-1-11-1-1111-11-11-1-1111-1-1i−ii−iii−i−iii−i−i-1-1-1-11111-11−ii−ii
χ811-1-1-1111-1-1-111-11-1-1-1111-1-11-1-1111-11-11-1-1111-1-1−ii−ii−i−iii−i−iii-1-1-1-11111-11i−ii−i
χ922222222222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1220000
χ102222222222222222-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000011111111-2-20000
χ1122222-12-1-1-1-1-12222000022222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ1222222-12-1-1-1-1-12222000022222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ132222-22-2222-2-2-222-200002-2-2222-2-2-222-22-2-22-2-22200000000000000000000000000
χ142222-22-2222-2-2-222-20000-111-1-1-111-222-2-111-111-1-100000000000033−3−333−3−3000000
χ152222-22-2222-2-2-222-20000-111-1-1-111-222-2-111-111-1-1000000000000−3−333−3−333000000
χ162222-2-1-2-1-1-111-222-200002-2-2222-2-21-1-11-111-111-1-10000−i3i3−i3i3−i3i3−i3i300000000000000
χ172222-2-1-2-1-1-111-222-200002-2-2222-2-21-1-11-111-111-1-10000i3−i3i3−i3i3−i3i3−i300000000000000
χ1822-2-222-22-2-22-2-2-22200002222-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000
χ1922-2-222-22-2-22-2-2-2220000-1-1-1-11111-2-222-1-1-1-1111100000000000033−3−3−3−333000000
χ2022-2-222-22-2-22-2-2-2220000-1-1-1-11111-2-222-1-1-1-11111000000000000−3−33333−3−3000000
χ2122-2-22-1-2-111-11-2-22200002222-2-2-2-211-1-1-1-1-1-1111100003−3−333−3−3300000000000000
χ2222-2-22-1-2-111-11-2-22200002222-2-2-2-211-1-1-1-1-1-111110000−333−3−333−300000000000000
χ2322-2-2-2222-2-2-222-22-222-2-2-111-111-1-12-22-2-111-1-1-111000000000000-1-1-1-111112-20000
χ2422-2-2-2222-2-2-222-22-2-2-222-111-111-1-12-22-2-111-1-1-1110000000000001111-1-1-1-1-220000
χ2522-2-2-2-12-1111-12-22-200002-2-22-2-222-11-11-111-1-1-1112i−2i2i−2i−i−iii−i−iii00000000000000
χ2622-2-2-2-12-1111-12-22-200002-2-22-2-222-11-11-111-1-1-111−2i2i−2i2iii−i−iii−i−i00000000000000
χ27333333333333-1-1-1-1333300000000-1-1-1-10000000011-1-11111-1-1-1-100000000-1-111-1-1
χ28333333333333-1-1-1-1333300000000-1-1-1-100000000-1-111-1-1-1-1111100000000-1-1-1-111
χ29333333333333-1-1-1-1-3-3-3-300000000-1-1-1-10000000011-1-11111-1-1-1-10000000011-1-111
χ30333333333333-1-1-1-1-3-3-3-300000000-1-1-1-100000000-1-111-1-1-1-11111000000001111-1-1
χ3133-3-3-3333-3-3-33-11-1133-3-300000000-11-1100000000i−i−iiii−i−i−i−iii00000000-11i−i−ii
χ3233-3-3-3333-3-3-33-11-1133-3-300000000-11-1100000000−iii−i−i−iiiii−i−i00000000-11−iii−i
χ3333-3-3-3333-3-3-33-11-11-3-33300000000-11-1100000000i−i−iiii−i−i−i−iii000000001-1−iii−i
χ3433-3-3-3333-3-3-33-11-11-3-33300000000-11-1100000000−iii−i−i−iiiii−i−i000000001-1i−i−ii
χ3544444-24-2-2-2-2-244440000-2-2-2-2-2-2-2-2-2-2-2-21111111100000000000000000000000000
χ364444-4-2-4-2-2-222-444-40000-222-2-2-2222-2-221-1-11-1-11100000000000000000000000000
χ3744-4-44-2-4-222-22-4-4440000-2-2-2-2222222-2-21111-1-1-1-100000000000000000000000000
χ3844-4-4-4-24-2222-24-44-40000-222-222-2-2-22-221-1-1111-1-100000000000000000000000000
χ394-44i−4i040-44i−4i00000022−22−2i22i21−i3i3-1i−i3−300001−i3i3-13−3i−i000000000000ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7000000
χ404-44i−4i040-44i−4i00000022−22−2i22i21i3−i3-1i−i−3300001i3−i3-1−33i−i000000000000ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23000000
χ414-44i−4i040-44i−4i00000022−22−2i22i2-2002−2i2i000000-200200−2i2i0000000000002−2−22i2−i2−i2i2000000
χ424-44i−4i040-44i−4i000000−22222i2−2i21−i3i3-1i−i3−300001−i3i3-13−3i−i000000000000−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7000000
χ434-44i−4i040-44i−4i000000−22222i2−2i21i3−i3-1i−i−3300001i3−i3-1−33i−i000000000000−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23000000
χ444-44i−4i040-44i−4i000000−22222i2−2i2-2002−2i2i000000-200200−2i2i000000000000−222−2−i2i2i2−i2000000
χ454-4−4i4i040-4−4i4i00000022−222i2−2i21−i3i3-1−ii−3300001−i3i3-1−33−ii000000000000ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23000000
χ464-4−4i4i040-4−4i4i00000022−222i2−2i21i3−i3-1−ii3−300001i3−i3-13−3−ii000000000000ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7000000
χ474-4−4i4i040-4−4i4i00000022−222i2−2i2-20022i−2i000000-2002002i−2i0000000000002−2−22−i2i2i2−i2000000
χ484-4−4i4i040-4−4i4i000000−2222−2i22i21−i3i3-1−ii−3300001−i3i3-1−33−ii000000000000−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23000000
χ494-4−4i4i040-4−4i4i000000−2222−2i22i21i3−i3-1−ii3−300001i3−i3-13−3−ii000000000000−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7000000
χ504-4−4i4i040-4−4i4i000000−2222−2i22i2-20022i−2i000000-2002002i−2i000000000000−222−2i2−i2−i2i2000000
χ5166666-36-3-3-3-3-3-2-2-2-200000000000011110000000022-2-2-1-1-1-1111100000000000000
χ5266666-36-3-3-3-3-3-2-2-2-2000000000000111100000000-2-2221111-1-1-1-100000000000000
χ536666-66-6666-6-62-2-220000000000002-2-220000000000000000000000000000000000
χ546666-6-3-6-3-3-3332-2-22000000000000-111-1000000000000−i3i3−i3i3i3−i3i3−i300000000000000
χ556666-6-3-6-3-3-3332-2-22000000000000-111-1000000000000i3−i3i3−i3−i3i3−i3i300000000000000
χ5666-6-666-66-6-66-622-2-200000000000022-2-20000000000000000000000000000000000
χ5766-6-66-3-6-333-3322-2-2000000000000-1-1110000000000003−3−33−333−300000000000000
χ5866-6-66-3-6-333-3322-2-2000000000000-1-111000000000000−333−33−3−3300000000000000
χ5966-6-6-6-36-3333-3-22-220000000000001-11-1000000002i−2i−2i2i−i−iiiii−i−i00000000000000
χ6066-6-6-6-36-3333-3-22-220000000000001-11-100000000−2i2i2i−2iii−i−i−i−iii00000000000000
χ618-88i−8i0-404−4i4i00000000002−2i32i3-22i−2i23−230000-1i3−i31−33−ii00000000000000000000000000
χ628-88i−8i0-404−4i4i000000000022i3−2i3-22i−2i−23230000-1−i3i313−3−ii00000000000000000000000000
χ638-88i−8i0-404−4i4i0000000000-4004−4i4i000000200-2002i−2i00000000000000000000000000
χ648-8−8i8i0-4044i−4i00000000002−2i32i3-2−2i2i−23230000-1i3−i313−3i−i00000000000000000000000000
χ658-8−8i8i0-4044i−4i000000000022i3−2i3-2−2i2i23−230000-1−i3i31−33i−i00000000000000000000000000
χ668-8−8i8i0-4044i−4i0000000000-40044i−4i000000200-200−2i2i00000000000000000000000000

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