Finite Group Databasebeta

← Group #11714231

Character table — Group #11714231

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size1111111166666666121212121212121212122424242424242424242432323232323232324848
order12224444224444444488888888444444888836661212121288
χ11111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ31111-1-1-1-1-1-11111-1-11-1iiii−i−i−i−i1-1ii−i−iii−i−i1111-1-1-1-1i−i
χ41111-1-1-1-1-1-11111-1-11-1−i−i−i−iiiii1-1−i−iii−i−iii1111-1-1-1-1−ii
χ5222222222222222222000000002200000000-1-1-1-1-1-1-1-100
χ62222-2-2-2-2-2-22222-2-22-2000000002-200000000-1-1-1-1111100
χ722-2-222-2-22-22-200000022−2−222−2−20000002−22−2-111-111-1-100
χ822-2-222-2-22-22-2000000−2−222−2−222000000−22−22-111-111-1-100
χ922-2-2-2-222-222-2000000i2i2−i2−i2−i2−i2i2i2000000i2−i2−i2i2-111-1-1-11100
χ1022-2-2-2-222-222-2000000−i2−i2i2i2i2i2−i2−i2000000−i2i2i2−i2-111-1-1-11100
χ112-22-22i−2i2i−2i00002-22i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i001+i−1−i1−i−1+i0000-11-11i−ii−i00
χ122-22-22i−2i2i−2i00002-22i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−1−i1+i−1+i1−i0000-11-11i−ii−i00
χ132-22-2−2i2i−2i2i00002-2−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i001−i−1+i1+i−1−i0000-11-11−ii−ii00
χ142-22-2−2i2i−2i2i00002-2−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−1+i1−i−1−i1+i0000-11-11−ii−ii00
χ15333333333333-1-1-1-1-1-111111111-1-1-1-1-1-1111100000000-1-1
χ16333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-10000000011
χ1733333333-1-1-1-13333-1-111111111-1-11111-1-1-1-100000000-1-1
χ1833333333-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111110000000011
χ1933333333-1-1-1-1-1-1-1-13311111111-1-1-1-1-1-1-1-1-1-10000000011
χ2033333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-11111111100000000-1-1
χ213333-3-3-3-311-1-133-3-3-11iiii−i−i−i−i-11ii−i−i−i−iii00000000−ii
χ223333-3-3-3-311-1-133-3-3-11−i−i−i−iiiii-11−i−iiiii−i−i00000000i−i
χ233333-3-3-3-311-1-1-1-1113-3iiii−i−i−i−i-11−i−iii−i−iii00000000i−i
χ243333-3-3-3-311-1-1-1-1113-3−i−i−i−iiiii-11ii−i−iii−i−i00000000−ii
χ253333-3-3-3-3-3-333-1-111-11iiii−i−i−i−i-11−i−iiiii−i−i00000000−ii
χ263333-3-3-3-3-3-333-1-111-11−i−i−i−iiiii-11ii−i−i−i−iii00000000i−i
χ2744-4-444-4-44-44-40000000000000000000000001-1-11-1-11100
χ2844-4-4-4-444-444-40000000000000000000000001-1-1111-1-100
χ294-44-44i−4i4i−4i00004-44i−4i000000000000000000001-11-1−ii−ii00
χ304-44-4−4i4i−4i4i00004-4−4i4i000000000000000000001-11-1i−ii−i00
χ314-4-444i−4i−4i4i00000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000011-1-1i−i−ii00
χ324-4-444i−4i−4i4i0000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000011-1-1i−i−ii00
χ334-4-44−4i4i4i−4i00000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000011-1-1−iii−i00
χ344-4-44−4i4i4i−4i0000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000011-1-1−iii−i00
χ3566666666-2-2-2-2-2-2-2-2-2-20000000022000000000000000000
χ366666-6-6-6-622-2-2-2-222-22000000002-2000000000000000000
χ3766-6-666-6-6-22-2200000022−2−222−2−2000000−22−220000000000
χ3866-6-666-6-6-22-22000000−2−222−2−2220000002−22−20000000000
χ3966-6-6-6-6662-2-22000000i2i2−i2−i2−i2−i2i2i2000000−i2i2i2−i20000000000
χ4066-6-6-6-6662-2-22000000−i2−i2i2i2i2i2−i2−i2000000i2−i2−i2i20000000000
χ416-66-66i−6i6i−6i0000-22−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−1−i1+i−1+i1−i00000000000000
χ426-66-66i−6i6i−6i0000-22−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i001+i−1−i1−i−1+i00000000000000
χ436-66-6−6i6i−6i6i0000-222i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−1+i1−i−1−i1+i00000000000000
χ446-66-6−6i6i−6i6i0000-222i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i001−i−1+i1+i−1−i00000000000000
χ458-8-888i−8i−8i8i0000000000000000000000000000-1-111−iii−i00
χ468-8-88−8i8i8i−8i0000000000000000000000000000-1-111i−i−ii00

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.