Finite Group Databasebeta

← Group #11772201

Character table — Group #11772201

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size111122448888888888888888181818181818181836363636363636367272727272727272
order1244244436661212121212121212121212128888888816161616161616161616161616161616
χ1111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ6111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ7111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ911-1-1-11i−i11-1-111-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ1011-1-1-11i−i11-1-111-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ1111-1-1-11i−i11-1-111-1-1iiii−i−i−i−i11-1-1ii−i−i-1-111−i−iiiζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ1211-1-1-11i−i11-1-111-1-1iiii−i−i−i−i11-1-1ii−i−i-1-111−i−iii−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ1311-1-1-11−ii11-1-111-1-1−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iiiζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ1411-1-1-11−ii11-1-111-1-1−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ1511-1-1-11−ii11-1-111-1-1−i−i−i−iiiii11-1-1−i−iii-1-111ii−i−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ1611-1-1-11−ii11-1-111-1-1−i−i−i−iiiii11-1-1−i−iii-1-111ii−i−i−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ17222222222222222222222222-2-2-2-2-2-2-2-20000000000000000
χ18222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000
χ192222-2-20022-2-2-2-2220000000000002-22-2i2−i2i2−i2i2−i2i2−i200000000
χ202222-2-20022-2-2-2-2220000000000002-22-2−i2i2−i2i2−i2i2−i2i200000000
χ212222-2-20022-2-2-2-222000000000000-22-22i2−i2i2−i2−i2i2−i2i200000000
χ222222-2-20022-2-2-2-222000000000000-22-22−i2i2−i2i2i2−i2i2−i200000000
χ2322-2-22-2002222-2-2-2-20000000000002i−2i−2i2ii2−i2−i2i2−222−200000000
χ2422-2-22-2002222-2-2-2-20000000000002i−2i−2i2i−i2i2i2−i22−2−2200000000
χ2522-2-22-2002222-2-2-2-2000000000000−2i2i2i−2ii2−i2−i2i22−2−2200000000
χ2622-2-22-2002222-2-2-2-2000000000000−2i2i2i−2i−i2i2i2−i2−222−200000000
χ2722-2-2-222i−2i22-2-222-2-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i0000000000000000
χ2822-2-2-22−2i2i22-2-222-2-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i0000000000000000
χ294-44i−4i00004-400004i−4i000000002i2−2i222−2200000000000000000000
χ304-44i−4i00004-400004i−4i00000000−2i22i2−222200000000000000000000
χ314-4−4i4i00004-40000−4i4i000000002i2−2i2−222200000000000000000000
χ324-4−4i4i00004-40000−4i4i00000000−2i22i222−2200000000000000000000
χ3388888888-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ34888888-8-8-1-1-1-1-1-1-1-111111111000000000000000000000000
χ358888-8-800-1-11111-1-13i3i−3i−3i3i3i−3i−3i000000000000000000000000
χ368888-8-800-1-11111-1-1−3i−3i3i3i−3i−3i3i3i000000000000000000000000
χ3788-8-88-800-1-1-1-1111133-3-3-3-333000000000000000000000000
χ3888-8-88-800-1-1-1-11111-3-33333-3-3000000000000000000000000
χ3988-8-8-888i−8i-1-111-1-111−i−i−i−iiiii000000000000000000000000
χ4088-8-8-88−8i8i-1-111-1-111iiii−i−i−i−i000000000000000000000000
χ418-88i−8i0000-113-33i−3i−ii3-33i−3i3i−3i3-3000000000000000000000000
χ428-88i−8i0000-113-33i−3i−ii-33−3i3i−3i3i-33000000000000000000000000
χ438-88i−8i0000-11-33−3i3i−ii3i−3i3-3-33−3i3i000000000000000000000000
χ448-88i−8i0000-11-33−3i3i−ii−3i3i-333-33i−3i000000000000000000000000
χ458-8−8i8i0000-113-3−3i3ii−i3-3−3i3i−3i3i3-3000000000000000000000000
χ468-8−8i8i0000-113-3−3i3ii−i-333i−3i3i−3i-33000000000000000000000000
χ478-8−8i8i0000-11-333i−3ii−i3i−3i-333-3−3i3i000000000000000000000000
χ488-8−8i8i0000-11-333i−3ii−i−3i3i3-3-333i−3i000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.