Finite Group Databasebeta

← Group #11792422

Character table — Group #11792422

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111224444444444448888888888812121212181818182424242424242424242424242424484848487272727272
order1244243366661212121212124612121212121212121222442244224466668812121212612242444488
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-11-11111-1-11111-1-1-1-11-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111-11-11-1-1-1-111-1-1-1-111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111-11-1-1-1-11-1-1-1-111111111-11-1111-1-1-1-111-1-111-1-1-111-1-1
χ6111111111111111111-11-1-1-1-11-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-111-1-1-111
χ7111111111111111111-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-111
χ8111111111111111111-11-1-1-1-11-1-1-1-1-1-1-1-111111-11-1-1-11111-1-111-1-111-111-1-1
χ9222222222222222222222222222220000-2-2-2-2000000000000000000-20000
χ10222222222222222222-22-2-2-2-22-2-2-2-20000-2-2-2-200000000000000000020000
χ112222-2-222-2-22222-2-2220-20000-2000000002-2-220000000000000000000002-2
χ122222-2-222-2-22222-2-2220-20000-2000000002-2-22000000000000000000000-22
χ132222-2-222-2-22222-2-2220-20000-200000000-222-200000000000000000002-200
χ142222-2-222-2-22222-2-2220-20000-200000000-222-20000000000000000000-2200
χ1522-2-22-2222222-2-2-2-2-2-2020000-200000000-2-22220-2000220000-2-2000000000
χ1622-2-22-2222222-2-2-2-2-2-2020000-200000000-2-222-202000-2-2000022000000000
χ1722-2-22-2222222-2-2-2-2-2-2020000-2000022-2-222-2-20000220000-2-200000000000
χ1822-2-22-2222222-2-2-2-2-2-2020000-20000-2-22222-2-20000-2-200002200000000000
χ1922-2-2-2222-2-222-2-222-2-20-200002000000002-22-2000000002i−2i0000002i−2i00000
χ2022-2-2-2222-2-222-2-222-2-20-200002000000002-22-200000000−2i2i000000−2i2i00000
χ2122-2-2-2222-2-222-2-222-2-20-20000200000000-22-22020-200000000002-20000000
χ2222-2-2-2222-2-222-2-222-2-20-20000200000000-22-220-2020000000000-220000000
χ234444441-2-2-21-2-2-2-2-21141-2-2-2-2111110000000002020000220000-1-1-1-100000
χ244444441-2-2-21-2-2-2-2-21141-2-2-2-211111000000000-20-20000-2-20000111100000
χ254444441-2-2-21-2-2-2-2-211-4122221-1-1-1-10000000002020000-2-20000-1-11100000
χ264444441-2-2-21-2-2-2-2-211-4122221-1-1-1-1000000000-20-2000022000011-1-100000
χ27444444-2111-211111-2-24-21111-2-2-2-2-2222200002020-1-1-1-100-1-1-1-1000000000
χ28444444-2111-211111-2-24-21111-2-2-2-2-2-2-2-2-20000-20-201111001111000000000
χ29444444-2111-211111-2-2-4-2-1-1-1-1-2222222220000-20-20-1-11100-1-111000000000
χ30444444-2111-211111-2-2-4-2-1-1-1-1-22222-2-2-2-20000202011-1-10011-1-1000000000
χ3144-4-44-4-2111-21-1-1-1-1220-233-3-32000022-2-2000020-20-1-1-1-1001111000000000
χ3244-4-44-4-2111-21-1-1-1-1220-233-3-320000-2-2220000-2020111100-1-1-1-1000000000
χ3344-4-44-4-2111-21-1-1-1-1220-2-3-3332000022-2-20000-2020-1-1110011-1-1000000000
χ3444-4-44-4-2111-21-1-1-1-1220-2-3-33320000-2-222000020-2011-1-100-1-111000000000
χ3544-4-4-441-2221-222-2-2-1-10-1000013i3i−3i−3i00000000020-200002i−2i0000-11−ii00000
χ3644-4-4-441-2221-222-2-2-1-10-1000013i3i−3i−3i000000000-2020000−2i2i00001-1i−i00000
χ3744-4-4-441-2221-222-2-2-1-10-100001−3i−3i3i3i00000000020-20000−2i2i0000-11i−i00000
χ3844-4-4-441-2221-222-2-2-1-10-100001−3i−3i3i3i000000000-20200002i−2i00001-1−ii00000
χ394-44i−4i004400-4-44i−4i004i−4i000000000002-22i−2i000000002-200002i−2i00000000000
χ404-44i−4i004400-4-44i−4i004i−4i00000000000-22−2i2i00000000-220000−2i2i00000000000
χ414-44i−4i00-213-32-1i−i3i−3i−2i2i003−3−i3i30−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ112-22i−2i00000000-11−i3i300−ii3−3000000000
χ424-44i−4i00-213-32-1i−i3i−3i−2i2i003−3−i3i30−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11-22−2i2i000000001-1i3−i300i−i−33000000000
χ434-44i−4i00-213-32-1i−i3i−3i−2i2i00−33i3−i30ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ112-22i−2i00000000-11i3−i300−ii−33000000000
χ444-44i−4i00-213-32-1i−i3i−3i−2i2i00−33i3−i30ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11-22−2i2i000000001-1−i3i300i−i3−3000000000
χ454-4−4i4i004400-4-4−4i4i00−4i4i000000000002-2−2i2i000000002-20000−2i2i00000000000
χ464-4−4i4i004400-4-4−4i4i00−4i4i00000000000-222i−2i00000000-2200002i−2i00000000000
χ474-4−4i4i00-213-32-1−ii−3i3i2i−2i003−3i3−i30ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ112-2−2i2i00000000-11i3−i300i−i3−3000000000
χ484-4−4i4i00-213-32-1−ii−3i3i2i−2i003−3i3−i30ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11-222i−2i000000001-1−i3i300−ii−33000000000
χ494-4−4i4i00-213-32-1−ii−3i3i2i−2i00−33−i3i30−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ112-2−2i2i00000000-11−i3i300i−i−33000000000
χ504-4−4i4i00-213-32-1−ii−3i3i2i−2i00−33−i3i30−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11-222i−2i000000001-1i3−i300−ii3−3000000000
χ518888-8-82-4442-4-4-444220-20000-200000000000000000000000000000000000
χ528888-8-8-42-2-2-4222-2-2-4-4040000400000000000000000000000000000000000
χ5388-8-88-82-4-4-42-44444-2-2020000-200000000000000000000000000000000000
χ5488-8-8-88-42-2-2-42-2-22244040000-400000000000000000000000000000000000
χ558-88i−8i002-400-24−4i4i002i−2i0023−23−2i32i30ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000000000000
χ568-88i−8i002-400-24−4i4i002i−2i00−23232i3−2i30−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000000000000
χ578-88i−8i00-42-664-22i−2i−6i6i−4i4i000000000000000000000000000000000000000000
χ588-8−8i8i002-400-244i−4i00−2i2i0023−232i3−2i30−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000000000000
χ598-8−8i8i002-400-244i−4i00−2i2i00−2323−2i32i30ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000000000000
χ608-8−8i8i00-42-664-2−2i2i6i−6i4i−4i000000000000000000000000000000000000000000

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