Finite Group Databasebeta

← Group #85665

Character table — Group #85665

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1111111133333333666666666666666616161616161616161616161616161616
order124488882244888822224444888888883366121212122424242424242424
χ1111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ41111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ51111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ61111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ711-1-1ii−i−i11-1-1ii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ811-1-1ii−i−i11-1-1ii−i−i-1-1-1-11111iiii−i−i−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14
χ911-1-1ii−i−i11-1-1ii−i−i-1-1-1-11111iiii−i−i−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22
χ1011-1-1−i−iii11-1-1−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ1111-1-1−i−iii11-1-1−i−iii-1-1-1-11111−i−i−i−iiiii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14
χ1211-1-1−i−iii11-1-1−i−iii-1-1-1-11111−i−i−i−iiiii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22
χ132-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000-1-111i−ii−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ142-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000001+i321−i32−1−i32−1+i32ζ22−ζ22ζ14−ζ14−ζ7ζ7ζ13−ζ13−ζ23ζ23ζ5−ζ5
χ152-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000001−i321+i32−1+i32−1−i32ζ14−ζ14ζ22−ζ22−ζ23ζ23ζ5−ζ5−ζ7ζ7ζ13−ζ13
χ162-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000-1-111i−ii−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ172-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000001+i321−i32−1−i32−1+i32ζ22−ζ22ζ14−ζ14ζ7−ζ7−ζ13ζ13ζ23−ζ23−ζ5ζ5
χ182-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000001−i321+i32−1+i32−1−i32ζ14−ζ14ζ22−ζ22ζ23−ζ23−ζ5ζ5ζ7−ζ7−ζ13ζ13
χ192-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000-1-111−ii−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ202-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000001+i321−i32−1−i32−1+i32−ζ22ζ22−ζ14ζ14ζ13−ζ13−ζ7ζ7ζ5−ζ5−ζ23ζ23
χ212-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000001−i321+i32−1+i32−1−i32−ζ14ζ14−ζ22ζ22ζ5−ζ5−ζ23ζ23ζ13−ζ13−ζ7ζ7
χ222-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000-1-111−ii−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ232-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000001+i321−i32−1−i32−1+i32−ζ22ζ22−ζ14ζ14−ζ13ζ13ζ7−ζ7−ζ5ζ5ζ23−ζ23
χ242-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000001−i321+i32−1+i32−1−i32−ζ14ζ14−ζ22ζ22−ζ5ζ5ζ23−ζ23−ζ13ζ13ζ7−ζ7
χ253333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2633333333-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-10000000000000000
χ2733333333-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1-13-1-10000000000000000
χ2833333333-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1-13-10000000000000000
χ2933333333-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1-130000000000000000
χ303333-3-3-3-33333-3-3-3-3-1-1-1-1-1-1-1-1111111110000000000000000
χ313333-3-3-3-3-1-1-1-111113-1-1-13-1-1-1-3111-31110000000000000000
χ323333-3-3-3-3-1-1-1-11111-13-1-1-13-1-11-3111-3110000000000000000
χ333333-3-3-3-3-1-1-1-11111-1-13-1-1-13-111-3111-310000000000000000
χ343333-3-3-3-3-1-1-1-11111-1-1-13-1-1-13111-3111-30000000000000000
χ3533-3-33i3i−3i−3i33-3-33i3i−3i−3i1111-1-1-1-1−i−i−i−iiiii0000000000000000
χ3633-3-33i3i−3i−3i-1-111−i−iii111-3-1-1-13−i−i−i3iiii−3i0000000000000000
χ3733-3-33i3i−3i−3i-1-111−i−iii11-31-1-13-1−i−i3i−iii−3ii0000000000000000
χ3833-3-33i3i−3i−3i-1-111−i−iii1-311-13-1-1−i3i−i−ii−3iii0000000000000000
χ3933-3-33i3i−3i−3i-1-111−i−iii-31113-1-1-13i−i−i−i−3iiii0000000000000000
χ4033-3-3−3i−3i3i3i33-3-3−3i−3i3i3i1111-1-1-1-1iiii−i−i−i−i0000000000000000
χ4133-3-3−3i−3i3i3i-1-111ii−i−i111-3-1-1-13iii−3i−i−i−i3i0000000000000000
χ4233-3-3−3i−3i3i3i-1-111ii−i−i11-31-1-13-1ii−3ii−i−i3i−i0000000000000000
χ4333-3-3−3i−3i3i3i-1-111ii−i−i1-311-13-1-1i−3iii−i3i−i−i0000000000000000
χ4433-3-3−3i−3i3i3i-1-111ii−i−i-31113-1-1-1−3iiii3i−i−i−i0000000000000000
χ456-66i−6i6ζ7+6ζ23−6ζ7−6ζ23−6ζ5−6ζ136ζ5+6ζ13-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ466-66i−6i−6ζ7−6ζ236ζ7+6ζ236ζ5+6ζ13−6ζ5−6ζ13-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ476-6−6i6i−6ζ5−6ζ136ζ5+6ζ136ζ7+6ζ23−6ζ7−6ζ23-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ486-6−6i6i6ζ5+6ζ13−6ζ5−6ζ13−6ζ7−6ζ236ζ7+6ζ23-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000

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