Finite Group Databasebeta

← Group #10706708

Character table — Group #10706708

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size11222222244444444448888888881212121212121616161616161616161616162424242424323248484848
order12234468868881212242424244121216161616242424448844161648484848484848488161616161212441616
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-111111111-1-111-1-1-1-111111-1-1-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-11111-1-111-1-1
χ91111111-1-11-1-1-111-1-1-1-1111ii−i−i-1-11111-1-11-1i−iii−i−iii−i−i-1ii−i−i1-11-1i−i
χ101111111-1-11-1-1-111-1-1-1-1111ii−i−i-1-11111-1-1-11−iiii−i−i−i−iii-1ii−i−i-11-11−ii
χ111111111-1-11-1-1-111-1-1-1-1111ii−i−i-1-1-1-1-1-1111-1i−iii−i−iii−i−i1−i−iii1-1-11−ii
χ121111111-1-11-1-1-111-1-1-1-1111ii−i−i-1-1-1-1-1-111-11−iiii−i−i−i−iii1−i−iii-111-1i−i
χ131111111-1-11-1-1-111-1-1-1-1111−i−iii-1-11111-1-11-1−ii−i−iii−i−iii-1−i−iii1-11-1−ii
χ141111111-1-11-1-1-111-1-1-1-1111−i−iii-1-11111-1-1-11i−i−i−iiiii−i−i-1−i−iii-11-11i−i
χ151111111-1-11-1-1-111-1-1-1-1111−i−iii-1-1-1-1-1-1111-1−ii−i−iii−i−iii1ii−i−i1-1-11i−i
χ161111111-1-11-1-1-111-1-1-1-1111−i−iii-1-1-1-1-1-111-11i−i−i−iiiii−i−i1ii−i−i-111-1−ii
χ1722222222222-2-22222-2-2-2-2-200002-222-2-222000000000000-20000000000
χ1822222222222-2-22222-2-2-2-2-200002-2-2-222-2-200000000000020000000000
χ192222222-2-22-22222-2-222-2-2-20000-2222-2-2-2-200000000000020000000000
χ202222222-2-22-22222-2-222-2-2-20000-22-2-22222000000000000-20000000000
χ21222-122-122-1222-1-1-1-1-1-12-1-12222-1-10000002222-1-1-1-1-1-1-1-100000-1-10000
χ22222-122-122-1222-1-1-1-1-1-12-1-12222-1-1000000-2-2-2-2-1-1-1-1111100000110000
χ23222-122-122-1222-1-1-1-1-1-12-1-1-2-2-2-2-1-100000022-2-21111111100000-1-10000
χ24222-122-122-1222-1-1-1-1-1-12-1-1-2-2-2-2-1-1000000-2-2221111-1-1-1-100000110000
χ25222-122-1-2-2-1-2-2-2-1-111112-1-12i2i−2i−2i110000002-22i−2i−i−iii−i−iii00000-110000
χ26222-122-1-2-2-1-2-2-2-1-111112-1-12i2i−2i−2i11000000-22−2i2i−i−iiiii−i−i000001-10000
χ27222-122-1-2-2-1-2-2-2-1-111112-1-1−2i−2i2i2i110000002-2−2i2iii−i−iii−i−i00000-110000
χ28222-122-1-2-2-1-2-2-2-1-111112-1-1−2i−2i2i2i11000000-222i−2iii−i−i−i−iii000001-10000
χ2922-222-2200-202-22-20022000−i2i2−i2i20-2002i−2i2i−2i0000−i2i2−i2i2000002−22−2000000
χ3022-222-2200-202-22-20022000−i2i2−i2i20-200−2i2i−2i2i0000−i2i2−i2i200000−22−22000000
χ3122-222-2200-202-22-20022000i2−i2i2−i20-2002i−2i2i−2i0000i2−i2i2−i200000−22−22000000
χ3222-222-2200-202-22-20022000i2−i2i2−i20-200−2i2i−2i2i0000i2−i2i2−i2000002−22−2000000
χ3322-222-2200-20-222-200-2-20002−2−2202002i−2i−2i2i00002−2−2200000i2−i2−i2i2000000
χ3422-222-2200-20-222-200-2-20002−2−220200−2i2i2i−2i00002−2−2200000−i2i2i2−i2000000
χ3522-222-2200-20-222-200-2-2000−222−202002i−2i−2i2i0000−222−200000−i2i2i2−i2000000
χ3622-222-2200-20-222-200-2-2000−222−20200−2i2i2i−2i0000−222−200000i2−i2−i2i2000000
χ374444-4-44004000-4-400000000000004-4000000000000000000000000000
χ384444-4-44004000-4-40000000000000-44000000000000000000000000000
χ39444-244-244-24-4-4-2-2-2-222-4220000-2200000000000000000000000000000
χ40444-244-2-4-4-2-444-2-222-2-2-42200002-200000000000000000000000000000
χ4144-44-44444-4-400-4444000000000-4000000000000000000000000000000
χ4244-44-444-4-4-4400-44-4-40000000004000000000000000000000000000000
χ4344-4-24-4-200204-4-2200-2-2000−2i22i2−2i22i2020000000000i2−i2i2−i2000000000000000
χ4444-4-24-4-200204-4-2200-2-20002i2−2i22i2−2i2020000000000−i2i2−i2i2000000000000000
χ4544-4-24-4-20020-44-22002200022−22−22220-20000000000−222−2000000000000000
χ4644-4-24-4-20020-44-220022000−222222−220-200000000002−2−22000000000000000
χ4744-4-2-44-2442-4002-2-2-200000000020000000000000006−66−600000000000
χ4844-4-2-44-2442-4002-2-2-20000000002000000000000000−66−6600000000000
χ4944-4-2-44-2-4-424002-222000000000-2000000000000000i6−i6−i6i600000000000
χ5044-4-2-44-2-4-424002-222000000000-2000000000000000−i6i6i6−i600000000000
χ51888-4-8-8-400-400044000000000000000000000000000000000000000000
χ528-80800-842−4200000042−420000000000000000000000000000000000000000
χ538-80800-8−4242000000−42420000000000000000000000000000000000000000
χ548-80-400442−42000000−222226−26023−2300000000000000000000000000000000000
χ558-80-400442−42000000−2222−26260−232300000000000000000000000000000000000
χ568-80-4004−424200000022−2226−260−232300000000000000000000000000000000000
χ578-80-4004−424200000022−22−2626023−2300000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).