Finite Group Databasebeta

← Group #70922

Character table — Group #70922

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222222244444444444444888888888888121212121212121224242424
order1244234688888888121224242424446121212121224242424242424668812122424242416161616161616162488
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-11-1-111111111-1-111-1-1-1-11111-1-1-1-111-1-1
χ611111111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-11-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-111
χ711111111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-11-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-111
χ811111111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-11-1-11111-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ911-1-1-1111ii−i−i11-1-1-1-1ii−i−ii−i-1ii−i−i1i−i11-1-11-111i−i-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ1011-1-1-1111ii−i−i11-1-1-1-1ii−i−ii−i-1ii−i−i1i−i11-1-11-111i−i-1-1ii−i−i-1-111−i−iii-11−ii
χ1111-1-1-1111ii−i−i11-1-1-1-1ii−i−ii−i-1ii−i−i1i−i11-1-1-11-1-1−ii11−i−iii11-1-1ii−i−i-11−ii
χ1211-1-1-1111ii−i−i11-1-1-1-1ii−i−ii−i-1ii−i−i1i−i11-1-1-11-1-1−ii11−i−iii-1-111−i−iii1-1i−i
χ1311-1-1-1111−i−iii11-1-1-1-1−i−iii−ii-1−i−iii1−ii11-1-11-111−ii-1-1−i−iii11-1-1−i−iii1-1−ii
χ1411-1-1-1111−i−iii11-1-1-1-1−i−iii−ii-1−i−iii1−ii11-1-11-111−ii-1-1−i−iii-1-111ii−i−i-11i−i
χ1511-1-1-1111−i−iii11-1-1-1-1−i−iii−ii-1−i−iii1−ii11-1-1-11-1-1i−i11ii−i−i11-1-1−i−iii-11i−i
χ1611-1-1-1111−i−iii11-1-1-1-1−i−iii−ii-1−i−iii1−ii11-1-1-11-1-1i−i11ii−i−i-1-111ii−i−i1-1−ii
χ17222222222222-2-2-2-2222222-2-22-2-2-2-2222-2-2-2-2000000000000000000000000
χ1822222222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2000000000000000000000000
χ1922222-12-122222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ2022222-12-122222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ2122222-12-12222-2-2-2-2-1-1-1-1-1-1-2-2-11111-1-1-1111100−i3i300−i3i3−i3i3−i3i3000000000000
χ2222222-12-12222-2-2-2-2-1-1-1-1-1-1-2-2-11111-1-1-1111100i3−i300i3−i3i3−i3i3−i3000000000000
χ2322222-12-1-2-2-2-22222-1-11111-2-2-11111-111-1-1-1-122-1-1-2-2-1-11111000000000000
χ2422222-12-1-2-2-2-22222-1-11111-2-2-11111-111-1-1-1-1-2-2112211-1-1-1-1000000000000
χ2522222-12-1-2-2-2-2-2-2-2-2-1-1111122-1-1-1-1-1-111111100−i3i300−i3i3i3−i3i3−i3000000000000
χ2622222-12-1-2-2-2-2-2-2-2-2-1-1111122-1-1-1-1-1-111111100i3−i300i3−i3−i3i3−i3i3000000000000
χ272222-22-222-22-2000022222200-20000-2-2-200000000000000002−22−22−22−20000
χ282222-22-222-22-2000022222200-20000-2-2-20000000000000000−22−22−22−220000
χ292222-22-22-22-22000022-2-2-2-200-20000-22200000000000000002−22−2−22−220000
χ302222-22-22-22-22000022-2-2-2-200-20000-2220000000000000000−22−222−22−20000
χ3122-2-222-222i−2i−2i2i0000-2-22i2i−2i−2i0020000-2−2i2i00000000000000002−2−22i2−i2−i2i20000
χ3222-2-222-222i−2i−2i2i0000-2-22i2i−2i−2i0020000-2−2i2i0000000000000000−222−2−i2i2i2−i20000
χ3322-2-222-22−2i2i2i−2i0000-2-2−2i−2i2i2i0020000-22i−2i00000000000000002−2−22−i2i2i2−i20000
χ3422-2-222-22−2i2i2i−2i0000-2-2−2i−2i2i2i0020000-22i−2i0000000000000000−222−2i2−i2−i2i20000
χ3522-2-2-22222i2i−2i−2i-2-222-2-22i2i−2i−2i−2i2i-2−2i−2i2i2i22i−2i-2-222000000000000000000000000
χ3622-2-2-2222−2i−2i2i2i-2-222-2-2−2i−2i2i2i2i−2i-22i2i−2i−2i2−2i2i-2-222000000000000000000000000
χ3722-2-2-2-12-12i2i−2i−2i22-2-211−i−iii2i−2i1−i−iii-1−ii-1-1112-2-1-12i−2i11−i−iii000000000000
χ3822-2-2-2-12-12i2i−2i−2i22-2-211−i−iii2i−2i1−i−iii-1−ii-1-111-2211−2i2i-1-1ii−i−i000000000000
χ3922-2-2-2-12-12i2i−2i−2i-2-22211−i−iii−2i2i1ii−i−i-1−ii11-1-100−i3i300i3−i33−3−33000000000000
χ4022-2-2-2-12-12i2i−2i−2i-2-22211−i−iii−2i2i1ii−i−i-1−ii11-1-100i3−i300−i3i3−333−3000000000000
χ4122-2-2-2-12-1−2i−2i2i2i22-2-211ii−i−i−2i2i1ii−i−i-1i−i-1-1112-2-1-1−2i2i11ii−i−i000000000000
χ4222-2-2-2-12-1−2i−2i2i2i22-2-211ii−i−i−2i2i1ii−i−i-1i−i-1-111-22112i−2i-1-1−i−iii000000000000
χ4322-2-2-2-12-1−2i−2i2i2i-2-22211ii−i−i2i−2i1−i−iii-1i−i11-1-100−i3i300i3−i3−333−3000000000000
χ4422-2-2-2-12-1−2i−2i2i2i-2-22211ii−i−i2i−2i1−i−iii-1i−i11-1-100i3−i300−i3i33−3−33000000000000
χ454444-4-2-4-24-44-40000-2-2-2-2-2-200200002220000000000000000000000000000
χ464444-4-2-4-2-44-440000-2-2222200200002-2-20000000000000000000000000000
χ4744-4-44-2-4-24i−4i−4i4i000022−2i−2i2i2i00-2000022i−2i0000000000000000000000000000
χ4844-4-44-2-4-2−4i4i4i−4i0000222i2i−2i−2i00-200002−2i2i0000000000000000000000000000
χ494-44i−4i040-4000022−22−2i22i24i−4i0000000000000022−22−2i22i2000000000000000000000000
χ504-44i−4i040-40000−22222i2−2i24i−4i00000000000000−22222i2−2i2000000000000000000000000
χ514-44i−4i0-202000022−22−2i22i2−2i2i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000−22i2−i2000000000000000000000000
χ524-44i−4i0-202000022−22−2i22i2−2i2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000−22i2−i2000000000000000000000000
χ534-44i−4i0-2020000−22222i2−2i2−2i2i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220002−2−i2i2000000000000000000000000
χ544-44i−4i0-2020000−22222i2−2i2−2i2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220002−2−i2i2000000000000000000000000
χ554-4−4i4i040-4000022−222i2−2i2−4i4i0000000000000022−222i2−2i2000000000000000000000000
χ564-4−4i4i040-40000−2222−2i22i2−4i4i00000000000000−2222−2i22i2000000000000000000000000
χ574-4−4i4i0-202000022−222i2−2i22i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000−22−i2i2000000000000000000000000
χ584-4−4i4i0-202000022−222i2−2i22i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000−22−i2i2000000000000000000000000
χ594-4−4i4i0-2020000−2222−2i22i22i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220002−2i2−i2000000000000000000000000
χ604-4−4i4i0-2020000−2222−2i22i22i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220002−2i2−i2000000000000000000000000

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