Finite Group Databasebeta

← Group #73010

Character table — Group #73010

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size111111112222666688888888888888881212121212121212121224242424
order1222444488884444366612121212242424242424242488888888884488
χ11111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111-1-1-1-1ii−i−i11-1-11111-1-1-1-1iiii−i−i−i−ii−i11-1-1ii−i−i1-1i−i
χ61111-1-1-1-1ii−i−i11-1-11111-1-1-1-1iiii−i−i−i−ii−i-1-111−i−iii-11−ii
χ71111-1-1-1-1−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−ii11-1-1−i−iii1-1−ii
χ81111-1-1-1-1−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−ii-1-111ii−i−i-11i−i
χ92222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122000000000000
χ1022222222-2-2-2-22222-1-1-1-1-1-1-1-111111111-2-2000000000000
χ112222-2-2-2-22i2i−2i−2i22-2-2-1-1-1-11111−i−i−i−iiiii2i−2i000000000000
χ122222-2-2-2-2−2i−2i2i2i22-2-2-1-1-1-11111iiii−i−i−i−i−2i2i000000000000
χ1322-2-222-2-22-22-20000-111-111-1-111-1-111-1-1002−22−22−22−20000
χ1422-2-222-2-22-22-20000-111-111-1-111-1-111-1-100−22−22−22−220000
χ1522-2-222-2-2-22-220000-111-111-1-1-1-111-1-111002−22−2−22−220000
χ1622-2-222-2-2-22-220000-111-111-1-1-1-111-1-11100−22−222−22−20000
χ1722-2-2-2-2222i−2i−2i2i0000-111-1-1-111ii−i−i−i−iii002−2−22i2−i2−i2i20000
χ1822-2-2-2-2222i−2i−2i2i0000-111-1-1-111ii−i−i−i−iii00−222−2−i2i2i2−i20000
χ1922-2-2-2-222−2i2i2i−2i0000-111-1-1-111−i−iiiii−i−i002−2−22−i2i2i2−i20000
χ2022-2-2-2-222−2i2i2i−2i0000-111-1-1-111−i−iiiii−i−i00−222−2i2−i2−i2i20000
χ212-22-22i−2i2i−2i00002-22i−2i22-2-22i−2i2i−2i0000000000000000000000
χ222-22-22i−2i2i−2i00002-22i−2i-1-111−ii−ii−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000000000
χ232-22-22i−2i2i−2i00002-22i−2i-1-111−ii−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000000000
χ242-22-2−2i2i−2i2i00002-2−2i2i22-2-2−2i2i−2i2i0000000000000000000000
χ252-22-2−2i2i−2i2i00002-2−2i2i-1-111i−ii−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000000000
χ262-22-2−2i2i−2i2i00002-2−2i2i-1-111i−ii−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000000000
χ27333333333333-1-1-1-10000000000000000-1-111111111-1-1-1-1
χ28333333333333-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1-11111
χ2933333333-3-3-3-3-1-1-1-10000000000000000111111-1-1-1-1-1-111
χ3033333333-3-3-3-3-1-1-1-1000000000000000011-1-1-1-1111111-1-1
χ313333-3-3-3-33i3i−3i−3i-1-1110000000000000000−ii11-1-1ii−i−i-11−ii
χ323333-3-3-3-33i3i−3i−3i-1-1110000000000000000−ii-1-111−i−iii1-1i−i
χ333333-3-3-3-3−3i−3i3i3i-1-1110000000000000000i−i11-1-1−i−iii-11i−i
χ343333-3-3-3-3−3i−3i3i3i-1-1110000000000000000i−i-1-111ii−i−i1-1−ii
χ3544-4-444-4-44-44-400001-1-11-1-111-1-111-1-11100000000000000
χ3644-4-444-4-4-44-4400001-1-11-1-11111-1-111-1-100000000000000
χ3744-4-4-4-4444i−4i−4i4i00001-1-1111-1-1−i−iiiii−i−i00000000000000
χ3844-4-4-4-444−4i4i4i−4i00001-1-1111-1-1ii−i−i−i−iii00000000000000
χ394-4-444i−4i−4i4i000000001-11-1−iii−i−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000000000
χ404-4-444i−4i−4i4i000000001-11-1−iii−iζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000000000
χ414-4-444i−4i−4i4i00000000-22-222i−2i−2i2i0000000000000000000000
χ424-4-44−4i4i4i−4i000000001-11-1i−i−iiζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000000000
χ434-4-44−4i4i4i−4i000000001-11-1i−i−ii−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000000000
χ444-4-44−4i4i4i−4i00000000-22-22−2i2i2i−2i0000000000000000000000
χ456-66-66i−6i6i−6i0000-22−2i2i000000000000000000000000000000
χ466-66-6−6i6i−6i6i0000-222i−2i000000000000000000000000000000

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