Finite Group Databasebeta

← Group #69298

Character table — Group #69298

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222222244444444444444888888888888121212121212121224242424
order124423444446888812122424242468812121212122424242424241616161648484848484848482444888816161616
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
χ5111111111111-1-1-1-111-1-1-1-11-1-111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i
χ6111111111111-1-1-1-111-1-1-1-11-1-111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111−i−iii
χ7111111111111-1-1-1-111-1-1-1-11-1-111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−iii
χ8111111111111-1-1-1-111-1-1-1-11-1-111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-11111ii−i−i
χ9111111-1-1-1-11111111111111-1-1-1-1-1-1111-1-1-1-11-11-111-1-111-1-111-1-111-1-11-11-1
χ10111111-1-1-1-11111111111111-1-1-1-1-1-1111-1-1-1-11-11-111-1-111-1-1-1-111-1-111-11-11
χ11111111-1-1-1-11111111111111-1-1-1-1-1-1111-1-1-1-1-11-11-1-111-1-11111-1-111-1-1-11-11
χ12111111-1-1-1-11111111111111-1-1-1-1-1-1111-1-1-1-1-11-11-1-111-1-111-1-111-1-1111-11-1
χ13111111-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-11-1-11111i−i−iiii−i−i−i−iii11-1-1-1-111i−i−ii
χ14111111-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-11-1-11111i−i−iiii−i−i−i−iii-1-11111-1-1−iii−i
χ15111111-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-11-1-11111−iii−i−i−iiiii−i−i11-1-1-1-111−iii−i
χ16111111-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-11-1-11111−iii−i−i−iiiii−i−i-1-11111-1-1i−i−ii
χ1722222-122222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1822222-122222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1922222-122222-1-2-2-2-2-1-11111-1-2-2-1-1-1-1-11111112i2i−2i−2i−i−i−i−iiiii000000000000
χ2022222-122222-1-2-2-2-2-1-11111-1-2-2-1-1-1-1-1111111−2i−2i2i2iiiii−i−i−i−i000000000000
χ2122222-1-2-2-2-22-12222-1-1-1-1-1-1-1-2-21111-1-1-111112-22-2-1-111-1-111000000000000
χ2222222-1-2-2-2-22-12222-1-1-1-1-1-1-1-2-21111-1-1-11111-22-2211-1-111-1-1000000000000
χ2322222-1-2-2-2-22-1-2-2-2-2-1-11111-1221111-111-1-1-1-12i−2i−2i2i−i−iiiii−i−i000000000000
χ2422222-1-2-2-2-22-1-2-2-2-2-1-11111-1221111-111-1-1-1-1−2i2i2i−2iii−i−i−i−iii000000000000
χ252222-220000-2222-2-2222222-2000000-2-2-20000000000000000002i−2i002i−2i0000
χ262222-220000-2222-2-2222222-2000000-2-2-2000000000000000000−2i2i00−2i2i0000
χ272222-220000-22-2-22222-2-2-2-2-2000000-2220000000000000000002i−2i00−2i2i0000
χ282222-220000-22-2-22222-2-2-2-2-2000000-222000000000000000000−2i2i002i−2i0000
χ2922-2-2220000-222i−2i2i−2i-2-22i2i−2i−2i2000000-22i−2i00000000000000002-2002i−2i000000
χ3022-2-2220000-222i−2i2i−2i-2-22i2i−2i−2i2000000-22i−2i0000000000000000-2200−2i2i000000
χ3122-2-2220000-22−2i2i−2i2i-2-2−2i−2i2i2i2000000-2−2i2i00000000000000002-200−2i2i000000
χ3222-2-2220000-22−2i2i−2i2i-2-2−2i−2i2i2i2000000-2−2i2i0000000000000000-22002i−2i000000
χ3322-2-2-222i2i−2i−2i222i−2i−2i2i-2-22i2i−2i−2i-22-22i2i−2i−2i2−2i2i22-2-2000000000000000000000000
χ3422-2-2-222i2i−2i−2i22−2i2i2i−2i-2-2−2i−2i2i2i-2-222i2i−2i−2i22i−2i-2-222000000000000000000000000
χ3522-2-2-22−2i−2i2i2i222i−2i−2i2i-2-22i2i−2i−2i-2-22−2i−2i2i2i2−2i2i-2-222000000000000000000000000
χ3622-2-2-22−2i−2i2i2i22−2i2i2i−2i-2-2−2i−2i2i2i-22-2−2i−2i2i2i22i−2i22-2-2000000000000000000000000
χ3722-2-2-2-12i2i−2i−2i2-12i−2i−2i2i11−i−iii12-2−i−iii-1i−i-1-1110000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ3822-2-2-2-12i2i−2i−2i2-12i−2i−2i2i11−i−iii12-2−i−iii-1i−i-1-1110000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ3922-2-2-2-12i2i−2i−2i2-1−2i2i2i−2i11ii−i−i1-22−i−iii-1−ii11-1-10000ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ4022-2-2-2-12i2i−2i−2i2-1−2i2i2i−2i11ii−i−i1-22−i−iii-1−ii11-1-10000−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ4122-2-2-2-1−2i−2i2i2i2-12i−2i−2i2i11−i−iii1-22ii−i−i-1i−i11-1-10000−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ4222-2-2-2-1−2i−2i2i2i2-12i−2i−2i2i11−i−iii1-22ii−i−i-1i−i11-1-10000ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ4322-2-2-2-1−2i−2i2i2i2-1−2i2i2i−2i11ii−i−i12-2ii−i−i-1−ii-1-1110000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ4422-2-2-2-1−2i−2i2i2i2-1−2i2i2i−2i11ii−i−i12-2ii−i−i-1−ii-1-1110000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ454444-4-20000-4-244-4-4-2-2-2-2-2-220000002220000000000000000000000000000
χ464444-4-20000-4-2-4-444-2-2222220000002-2-20000000000000000000000000000
χ4744-4-44-20000-4-24i−4i4i−4i22−2i−2i2i2i-20000002−2i2i0000000000000000000000000000
χ4844-4-44-20000-4-2−4i4i−4i4i222i2i−2i−2i-200000022i−2i0000000000000000000000000000
χ494-44i−4i042+2i−2−2i2−2i−2+2i0-400004i−4i00000002+2i−2−2i2−2i−2+2i0000000000000000000000000000000
χ504-44i−4i04−2−2i2+2i−2+2i2−2i0-400004i−4i0000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000000
χ514-44i−4i0-22+2i−2−2i2−2i−2+2i020000−2i2i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000−1−i1+i−1+i1−i000i6−i66−6000000000000000000000000
χ524-44i−4i0-22+2i−2−2i2−2i−2+2i020000−2i2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000−1−i1+i−1+i1−i000−i6i6−66000000000000000000000000
χ534-44i−4i0-2−2−2i2+2i−2+2i2−2i020000−2i2i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ130001+i−1−i1−i−1+i000−i6i6−66000000000000000000000000
χ544-44i−4i0-2−2−2i2+2i−2+2i2−2i020000−2i2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ130001+i−1−i1−i−1+i000i6−i66−6000000000000000000000000
χ554-4−4i4i042−2i−2+2i2+2i−2−2i0-40000−4i4i00000002−2i−2+2i2+2i−2−2i0000000000000000000000000000000
χ564-4−4i4i04−2+2i2−2i−2−2i2+2i0-40000−4i4i0000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000000
χ574-4−4i4i0-22−2i−2+2i2+2i−2−2i0200002i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000−1+i1−i−1−i1+i000−i6i66−6000000000000000000000000
χ584-4−4i4i0-22−2i−2+2i2+2i−2−2i0200002i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000−1+i1−i−1−i1+i000i6−i6−66000000000000000000000000
χ594-4−4i4i0-2−2+2i2−2i−2−2i2+2i0200002i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ230001−i−1+i1+i−1−i000i6−i6−66000000000000000000000000
χ604-4−4i4i0-2−2+2i2−2i−2−2i2+2i0200002i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230001−i−1+i1+i−1−i000−i6i66−6000000000000000000000000

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