Finite Group Databasebeta

← Group #68366

Character table — Group #68366

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size11112222222244444444466666688888888888881212121212161624242424
order122234444666488881212121222444444881224242424242424244888812122488
χ1111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-111-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-11111-1-1
χ61111111111111-1-1-1-11111111111-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111
χ71111111111111-1-1-1-11111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-11111-11111-1-111-1-1
χ911111-1-1-1-11111ii−i−i-1-1-1-111-1-1-1-11-1i−i1ii−i−iii−i−i1ii−i−i1-11-1i−i
χ1011111-1-1-1-11111ii−i−i-1-1-1-111-1-1-1-1-11−ii1ii−i−i−i−iii1ii−i−i-11-11−ii
χ1111111-1-1-1-11111ii−i−i-1-1-1-1-1-111111-1i−i1ii−i−iii−i−i-1−i−iii1-1-11−ii
χ1211111-1-1-1-11111ii−i−i-1-1-1-1-1-11111-11−ii1ii−i−i−i−iii-1−i−iii-111-1i−i
χ1311111-1-1-1-11111−i−iii-1-1-1-111-1-1-1-11-1−ii1−i−iii−i−iii1−i−iii1-11-1−ii
χ1411111-1-1-1-11111−i−iii-1-1-1-111-1-1-1-1-11i−i1−i−iiiii−i−i1−i−iii-11-11i−i
χ1511111-1-1-1-11111−i−iii-1-1-1-1-1-111111-1−ii1−i−iii−i−iii-1ii−i−i1-1-11i−i
χ1611111-1-1-1-11111−i−iii-1-1-1-1-1-11111-11i−i1−i−iiiii−i−i-1ii−i−i-111-1−ii
χ172222222-2-2222-2000022-2-22222-2-20000-200000000-20000000000
χ182222222-2-2222-2000022-2-2-2-2-2-2220000-20000000020000000000
χ1922222-2-222222-20000-2-22222-2-2220000-200000000-20000000000
χ2022222-2-222222-20000-2-222-2-222-2-20000-20000000020000000000
χ212222-12222-1-1-122222-1-1-1-10000002222-1-1-1-1-1-1-1-1-100000-1-10000
χ222222-12222-1-1-122222-1-1-1-1000000-2-2-2-2-1-1-1-1-1111100000110000
χ232222-12222-1-1-12-2-2-2-2-1-1-1-100000022-2-2-11111111100000-1-10000
χ242222-12222-1-1-12-2-2-2-2-1-1-1-1000000-2-222-11111-1-1-1-100000110000
χ252222-1-2-2-2-2-1-1-122i2i−2i−2i11110000002-22i−2i-1−i−iii−i−iii00000-110000
χ262222-1-2-2-2-2-1-1-122i2i−2i−2i1111000000-22−2i2i-1−i−iiiii−i−i000001-10000
χ272222-1-2-2-2-2-1-1-12−2i−2i2i2i11110000002-2−2i2i-1ii−i−iii−i−i00000-110000
χ282222-1-2-2-2-2-1-1-12−2i−2i2i2i1111000000-222i−2i-1ii−i−i−i−iii000001-10000
χ2922-2-22002i−2i-22-201+i−1−i1−i−1+i002i−2i2-2002i−2i000001+i−1−i1−i−1+i000001+i−1−i1−i−1+i000000
χ3022-2-22002i−2i-22-201+i−1−i1−i−1+i002i−2i-2200−2i2i000001+i−1−i1−i−1+i00000−1−i1+i−1+i1−i000000
χ3122-2-22002i−2i-22-20−1−i1+i−1+i1−i002i−2i2-2002i−2i00000−1−i1+i−1+i1−i00000−1−i1+i−1+i1−i000000
χ3222-2-22002i−2i-22-20−1−i1+i−1+i1−i002i−2i-2200−2i2i00000−1−i1+i−1+i1−i000001+i−1−i1−i−1+i000000
χ3322-2-2200−2i2i-22-201−i−1+i1+i−1−i00−2i2i2-200−2i2i000001−i−1+i1+i−1−i000001−i−1+i1+i−1−i000000
χ3422-2-2200−2i2i-22-201−i−1+i1+i−1−i00−2i2i-22002i−2i000001−i−1+i1+i−1−i00000−1+i1−i−1−i1+i000000
χ3522-2-2200−2i2i-22-20−1+i1−i−1−i1+i00−2i2i2-200−2i2i00000−1+i1−i−1−i1+i00000−1+i1−i−1−i1+i000000
χ3622-2-2200−2i2i-22-20−1+i1−i−1−i1+i00−2i2i-22002i−2i00000−1+i1−i−1−i1+i000001−i−1+i1+i−1−i000000
χ374444-244-4-4-2-2-2-40000-2-222000000000020000000000000000000
χ384444-2-4-444-2-2-2-4000022-2-2000000000020000000000000000000
χ3944-4-4-2004i−4i2-2202+2i−2−2i2−2i−2+2i00−2i2i00000000000−1−i1+i−1+i1−i000000000000000
χ4044-4-4-2004i−4i2-220−2−2i2+2i−2+2i2−2i00−2i2i000000000001+i−1−i1−i−1+i000000000000000
χ4144-4-4-200−4i4i2-2202−2i−2+2i2+2i−2−2i002i−2i00000000000−1+i1−i−1−i1+i000000000000000
χ4244-4-4-200−4i4i2-220−2+2i2−2i−2−2i2+2i002i−2i000000000001−i−1+i1+i−1−i000000000000000
χ434-44-444i−4i00-4-44000004i−4i00000000000000000000000000000000
χ444-44-44−4i4i00-4-4400000−4i4i00000000000000000000000000000000
χ454-44-4-24i−4i0022-200000−2i2i00000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000
χ464-44-4-24i−4i0022-200000−2i2i00000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000
χ474-44-4-2−4i4i0022-2000002i−2i00000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000
χ484-44-4-2−4i4i0022-2000002i−2i00000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000
χ494-4-44400004-4-4000000000004i−4i00000000000000000000000000
χ504-4-44400004-4-400000000000−4i4i00000000000000000000000000
χ518-8-88-40000-444000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.