Finite Group Databasebeta

← Group #11789736

Character table — Group #11789736

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111224444444444888816161616181818181818181824242424242424242424242424242424363636363636363648484848
order124424336688121212126612122424242422444444244488881212121224242424448888886122424
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111
χ51111111111-1-111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ61111111111-1-111111111-1-1-1-111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ71111111111-1-111111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ81111111111-1-111111111-1-1-1-1111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ911-1-1-111111i−i-1-1-1-1-1-111i−ii−i1-1-1ii−i−i11-1i−ii−i1-1ii−i−i11-1-1i−ii−i11-1-11-1i−i
χ1011-1-1-111111i−i-1-1-1-1-1-111i−ii−i1-1-1ii−i−i1-11−ii−ii-11−i−iii-1-111i−ii−i11-1-1-11−ii
χ1111-1-1-111111i−i-1-1-1-1-1-111i−ii−i1-1-1−i−iii11-1i−i−ii-11ii−i−i-1-111−iii−i-1-1111-1−ii
χ1211-1-1-111111i−i-1-1-1-1-1-111i−ii−i1-1-1−i−iii1-11−iii−i1-1−i−iii11-1-1−iii−i-1-111-11i−i
χ1311-1-1-111111−ii-1-1-1-1-1-111−ii−ii1-1-1ii−i−i11-1−iii−i-11−i−iii-1-111i−i−ii-1-1111-1i−i
χ1411-1-1-111111−ii-1-1-1-1-1-111−ii−ii1-1-1ii−i−i1-11i−i−ii1-1ii−i−i11-1-1i−i−ii-1-111-11−ii
χ1511-1-1-111111−ii-1-1-1-1-1-111−ii−ii1-1-1−i−iii11-1−ii−ii1-1−i−iii11-1-1−ii−ii11-1-11-1−ii
χ1611-1-1-111111−ii-1-1-1-1-1-111−ii−ii1-1-1−i−iii1-11i−ii−i-11ii−i−i-1-111−ii−ii11-1-1-11i−i
χ17222222222222222222222222-2-2-20000-2000000000000000000-2-200000000
χ182222222222-2-222222222-2-2-2-2-2-2-20000-20000000000000000002200000000
χ192222-2-22222002222-2-2-2-200002-220000-2000000000000000000002i−2i2i−2i0000
χ202222-2-22222002222-2-2-2-200002-220000-200000000000000000000−2i2i−2i2i0000
χ212222-2-22222002222-2-2-2-20000-22-2222220000000000000000-2-20000000000
χ222222-2-22222002222-2-2-2-20000-22-2-2-2-2-220000000000000000220000000000
χ2322-2-22-2222200-2-2-2-222-2-2000022-20000-2000000000000000000002i−2i−2i2i0000
χ2422-2-22-2222200-2-2-2-222-2-2000022-20000-200000000000000000000−2i2i2i−2i0000
χ2522-2-22-2222200-2-2-2-222-2-20000-2-222i2i−2i−2i20000000000000000−2i2i0000000000
χ2622-2-22-2222200-2-2-2-222-2-20000-2-22−2i−2i2i2i200000000000000002i−2i0000000000
χ2722-2-2-2222222i−2i-2-2-2-2-2-2222i−2i2i−2i-2220000-2000000000000000000−2i2i00000000
χ2822-2-2-222222−2i2i-2-2-2-2-2-222−2i2i−2i2i-2220000-20000000000000000002i−2i00000000
χ294444441-21-244-2-2111-2-21-2-21100000000000022220000-1-1-1-10000000000-1-1
χ304444441-21-244-2-2111-2-21-2-211000000000000-2-2-2-200001111000000000011
χ314444441-21-2-4-4-2-2111-2-2122-1-100000000000022-2-2000011110000000000-1-1
χ324444441-21-2-4-4-2-2111-2-2122-1-1000000000000-2-2220000-1-1-1-1000000000011
χ33444444-21-214411-2-2-211-211-2-20000000022220000-1-1-1-1000000000000-1-100
χ34444444-21-214411-2-2-211-211-2-200000000-2-2-2-2000011110000000000001100
χ35444444-21-21-4-411-2-2-211-2-1-1220000000022-2-200001111000000000000-1-100
χ36444444-21-21-4-411-2-2-211-2-1-12200000000-2-2220000-1-1-1-10000000000001100
χ3744-4-4-441-21-24i−4i22-1-1-12-21−2i2ii−i0000000000002i−2i2-20000-1-1110000000000−ii
χ3844-4-4-441-21-24i−4i22-1-1-12-21−2i2ii−i000000000000−2i2i-22000011-1-10000000000i−i
χ3944-4-4-441-21-2−4i4i22-1-1-12-212i−2i−ii0000000000002i−2i-22000011-1-10000000000−ii
χ4044-4-4-441-21-2−4i4i22-1-1-12-212i−2i−ii000000000000−2i2i2-20000-1-1110000000000i−i
χ4144-4-4-44-21-214i−4i-1-1222-11-2i−i−2i2i000000002-22i−2i0000−i−iii000000000000-1100
χ4244-4-4-44-21-214i−4i-1-1222-11-2i−i−2i2i00000000-22−2i2i0000ii−i−i0000000000001-100
χ4344-4-4-44-21-21−4i4i-1-1222-11-2−ii2i−2i000000002-2−2i2i0000ii−i−i000000000000-1100
χ4444-4-4-44-21-21−4i4i-1-1222-11-2−ii2i−2i00000000-222i−2i0000−i−iii0000000000001-100
χ454-44i−4i0044-4-4004i−4i4i−4i000000000002+2i−2−2i2−2i−2+2i00000000000000000000000000000
χ464-44i−4i0044-4-4004i−4i4i−4i00000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000000
χ474-4−4i4i0044-4-400−4i4i−4i4i000000000002−2i−2+2i2+2i−2−2i00000000000000000000000000000
χ484-4−4i4i0044-4-400−4i4i−4i4i00000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000000
χ498888-8-82-42-400-4-422-244-20000000000000000000000000000000000000000
χ508888-8-8-42-420022-4-44-2-240000000000000000000000000000000000000000
χ5188-8-88-82-42-40044-2-22-44-20000000000000000000000000000000000000000
χ5288-8-88-8-42-4200-2-244-42-240000000000000000000000000000000000000000
χ538-88i−8i002-4-2400−4i4i2i−2i0000000000000000000000000000i6−i66−6000000000000
χ548-88i−8i002-4-2400−4i4i2i−2i0000000000000000000000000000−i6i6−66000000000000
χ558-88i−8i00-424-2002i−2i−4i4i000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000
χ568-88i−8i00-424-2002i−2i−4i4i000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000
χ578-8−8i8i002-4-24004i−4i−2i2i0000000000000000000000000000i6−i6−66000000000000
χ588-8−8i8i002-4-24004i−4i−2i2i0000000000000000000000000000−i6i66−6000000000000
χ598-8−8i8i00-424-200−2i2i4i−4i000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000
χ608-8−8i8i00-424-200−2i2i4i−4i000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000

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