Finite Group Databasebeta

← Group #13180658

Character table — Group #13180658

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111144444444668888999916161616161616161616161616161616242424245454545454545454545472727272108108108108
order124433661212121224361212224433336666121212121212121266121224888888886612124444
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111-1-1-1-111111111111111111111-1-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ4111111111111111111-1-1-1-111111111111111111111-1-1−i−i−i−iiiii-1-1-1-1−i−iii
χ511-1-11111-1-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-111-1-11-11-1
χ611-1-11111-1-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-11-1-111-1-11111-1-1-11-11
χ711-1-11111-1-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111-1ii−i−i−i−iii-1-111i−i−ii
χ811-1-11111-1-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111-1−i−iiiii−i−i-1-111−iii−i
χ922222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222200000000-1-1-1-10000
χ1022222222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-20000000011110000
χ1122-2-22222-2-2-2-2-22-1-11122-2-2-1-1-1-1-1-1-1-111111111-2-222-2200000000-1-1110000
χ1222-2-22222-2-2-2-2-22-1-111-2-222-1-1-1-1-1-1-1-111111111-2-2222-20000000011-1-10000
χ132-22i−2i22-2-22i2i−2i−2i00-11i−i2-22i−2i-1-1-1-11111iiii−i−i−i−i0000002−2−i2i22−2−i2i21-1i−i0000
χ142-22i−2i22-2-22i2i−2i−2i00-11i−i2-22i−2i-1-1-1-11111iiii−i−i−i−i000000−22i2−i2−22i2−i21-1i−i0000
χ152-22i−2i22-2-22i2i−2i−2i00-11i−i-22−2i2i-1-1-1-11111iiii−i−i−i−i000000−i2i2−22i2−i22−2-11−ii0000
χ162-22i−2i22-2-22i2i−2i−2i00-11i−i-22−2i2i-1-1-1-11111iiii−i−i−i−i000000i2−i22−2−i2i2−22-11−ii0000
χ172-2−2i2i22-2-2−2i−2i2i2i00-11−ii2-2−2i2i-1-1-1-11111−i−i−i−iiiii0000002−2i2−i22−2i2−i21-1−ii0000
χ182-2−2i2i22-2-2−2i−2i2i2i00-11−ii2-2−2i2i-1-1-1-11111−i−i−i−iiiii000000−22−i2i2−22−i2i21-1−ii0000
χ192-2−2i2i22-2-2−2i−2i2i2i00-11−ii-222i−2i-1-1-1-11111−i−i−i−iiiii000000−i2i22−2i2−i2−22-11i−i0000
χ202-2−2i2i22-2-2−2i−2i2i2i00-11−ii-222i−2i-1-1-1-11111−i−i−i−iiiii000000i2−i2−22−i2i22−2-11i−i0000
χ21333333333333-1-1000033330000000000000000-1-1-1-1-1-1111111110000-1-1-1-1
χ22333333333333-1-1000033330000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111
χ23333333333333-1-10000-3-3-3-30000000000000000-1-1-1-111iiii−i−i−i−i0000−i−iii
χ24333333333333-1-10000-3-3-3-30000000000000000-1-1-1-111−i−i−i−iiiii0000ii−i−i
χ2533-3-33333-3-3-3-31-1000033-3-3000000000000000011-1-11-111-1-111-1-10000-11-11
χ2633-3-33333-3-3-3-31-1000033-3-3000000000000000011-1-11-1-1-111-1-11100001-11-1
χ2733-3-33333-3-3-3-31-10000-3-333000000000000000011-1-1-11ii−i−i−i−iii0000−iii−i
χ2833-3-33333-3-3-3-31-10000-3-333000000000000000011-1-1-11−i−iiiii−i−i0000i−i−ii
χ2944441-21-21-21-2444444000011-2-211-2-211-2-211-2-21-21-2000000000000000000
χ3044441-21-21-21-244-2-2-2-20000−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i32111-21-2000000000000000000
χ3144441-21-21-21-244-2-2-2-20000−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i32111-21-2000000000000000000
χ324444-21-21-21-214444440000-2-211-2-211-2-211-2-211-21-21000000000000000000
χ334444-21-21-21-2144-2-2-2-2000011−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i32-21-21000000000000000000
χ344444-21-21-21-2144-2-2-2-2000011−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i32-21-21000000000000000000
χ3544-4-41-21-2-12-12-4444-4-4000011-2-211-2-2-1-122-1-122-121-2000000000000000000
χ3644-4-41-21-2-12-12-44-2-2220000−1−3i32−1+3i3211−1−3i32−1+3i32111+3i321−3i32-1-11+3i321−3i32-1-1-121-2000000000000000000
χ3744-4-41-21-2-12-12-44-2-2220000−1+3i32−1−3i3211−1+3i32−1−3i32111−3i321+3i32-1-11−3i321+3i32-1-1-121-2000000000000000000
χ3844-4-4-21-212-12-1-4444-4-40000-2-211-2-21122-1-122-1-12-1-21000000000000000000
χ3944-4-4-21-212-12-1-44-2-222000011−1−3i32−1+3i3211−1−3i32−1+3i32-1-11+3i321−3i32-1-11+3i321−3i322-1-21000000000000000000
χ4044-4-4-21-212-12-1-44-2-222000011−1+3i32−1−3i3211−1+3i32−1−3i32-1-11−3i321+3i32-1-11−3i321+3i322-1-21000000000000000000
χ414-44i−4i44-4-44i4i−4i−4i001-1−ii4-44i−4i1111-1-1-1-1−i−i−i−iiiii00000000000000-11−ii0000
χ424-44i−4i44-4-44i4i−4i−4i001-1−ii-44−4i4i1111-1-1-1-1−i−i−i−iiiii000000000000001-1i−i0000
χ434-4−4i4i44-4-4−4i−4i4i4i001-1i−i4-4−4i4i1111-1-1-1-1iiii−i−i−i−i00000000000000-11i−i0000
χ444-4−4i4i44-4-4−4i−4i4i4i001-1i−i-444i−4i1111-1-1-1-1iiii−i−i−i−i000000000000001-1−ii0000
χ458-88i−8i2-4-242i−4i−2i4i002-2−2i2i00001−3i321+3i32-1-1−1+3i32−1−3i32112ζ14−ζ22−ζ14+2ζ22ii−2ζ14+ζ22ζ14−2ζ22−i−i0000000000000000000000
χ468-88i−8i2-4-242i−4i−2i4i002-2−2i2i00001+3i321−3i32-1-1−1−3i32−1+3i3211−ζ14+2ζ222ζ14−ζ22iiζ14−2ζ22−2ζ14+ζ22−i−i0000000000000000000000
χ478-88i−8i2-4-242i−4i−2i4i00-444i−4i0000-1-12211-2-2ii−2i−2i−i−i2i2i0000000000000000000000
χ488-88i−8i-424-2−4i2i4i−2i002-2−2i2i0000-1-11−3i321+3i3211−1+3i32−1−3i32ii2ζ14−ζ22−ζ14+2ζ22−i−i−2ζ14+ζ22ζ14−2ζ220000000000000000000000
χ498-88i−8i-424-2−4i2i4i−2i002-2−2i2i0000-1-11+3i321−3i3211−1−3i32−1+3i32ii−ζ14+2ζ222ζ14−ζ22−i−iζ14−2ζ22−2ζ14+ζ220000000000000000000000
χ508-88i−8i-424-2−4i2i4i−2i00-444i−4i000022-1-1-2-211−2i−2iii2i2i−i−i0000000000000000000000
χ518-8−8i8i2-4-24−2i4i2i−4i002-22i−2i00001−3i321+3i32-1-1−1+3i32−1−3i3211−2ζ14+ζ22ζ14−2ζ22−i−i2ζ14−ζ22−ζ14+2ζ22ii0000000000000000000000
χ528-8−8i8i2-4-24−2i4i2i−4i002-22i−2i00001+3i321−3i32-1-1−1−3i32−1+3i3211ζ14−2ζ22−2ζ14+ζ22−i−i−ζ14+2ζ222ζ14−ζ22ii0000000000000000000000
χ538-8−8i8i2-4-24−2i4i2i−4i00-44−4i4i0000-1-12211-2-2−i−i2i2iii−2i−2i0000000000000000000000
χ548-8−8i8i-424-24i−2i−4i2i002-22i−2i0000-1-11−3i321+3i3211−1+3i32−1−3i32−i−i−2ζ14+ζ22ζ14−2ζ22ii2ζ14−ζ22−ζ14+2ζ220000000000000000000000
χ558-8−8i8i-424-24i−2i−4i2i002-22i−2i0000-1-11+3i321−3i3211−1−3i32−1+3i32−i−iζ14−2ζ22−2ζ14+ζ22ii−ζ14+2ζ222ζ14−ζ220000000000000000000000
χ568-8−8i8i-424-24i−2i−4i2i00-44−4i4i000022-1-1-2-2112i2i−i−i−2i−2iii0000000000000000000000
χ57121212123-63-63-63-6-4-4000000000000000000000000-12-12000000000000000000
χ5812121212-63-63-63-63-4-40000000000000000000000002-12-1000000000000000000
χ591212-12-123-63-6-36-364-40000000000000000000000001-2-12000000000000000000
χ601212-12-12-63-636-36-34-4000000000000000000000000-212-1000000000000000000

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