Finite Group Databasebeta

← Group #11709167

Character table — Group #11709167

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42
size1111226666888816161616161616162424242424242424323232323232323232323232
order12442422448888336612121212444488886612122424242424242424
χ1111111111111111111111111111111111111111111
χ211111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ311111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ41111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ51111111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11111−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ61111111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11111−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ711-1-1-111-1-11ii−i−i1111-1-1-1-1ii−i−i11-1-1-1-111ii−i−iii−i−i
χ811-1-1-111-1-11ii−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32ii−i−i11-1-11+i321−i32−1−i32−1+i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7
χ911-1-1-111-1-11ii−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32ii−i−i11-1-11−i321+i32−1+i32−1−i32ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11
χ1011-1-1-111-1-11−i−iii1111-1-1-1-1−i−iii11-1-1-1-111−i−iii−i−iii
χ1111-1-1-111-1-11−i−iii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−i−iii11-1-11+i321−i32−1−i32−1+i32−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7
χ1211-1-1-111-1-11−i−iii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−i−iii11-1-11−i321+i32−1+i32−1−i32−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11
χ132222-2-22-22-22-22-2-1-1-1-1-1-1-1-10000000011111-11-11-11-1
χ142222-2-22-22-22-22-21+i321−i321+i321−i321+i321+i321−i321−i3200000000−1−i32−1+i32−1−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32
χ152222-2-22-22-22-22-21−i321+i321−i321+i321−i321−i321+i321+i3200000000−1+i32−1−i32−1+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32
χ162222-2-22-22-2-22-22-1-1-1-1-1-1-1-1000000001111-11-11-11-11
χ172222-2-22-22-2-22-221+i321−i321+i321−i321+i321+i321−i321−i3200000000−1−i32−1+i32−1−i32−1+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32
χ182222-2-22-22-2-22-221−i321+i321−i321+i321−i321−i321+i321+i3200000000−1+i32−1−i32−1+i32−1−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32
χ1922-2-22-222-2-22i−2i−2i2i-1-1-1-1111100000000-1-111i−i−iii−i−ii
χ2022-2-22-222-2-22i−2i−2i2i1+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32000000001+i321−i32−1−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7
χ2122-2-22-222-2-22i−2i−2i2i1−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32000000001−i321+i32−1+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11
χ2222-2-22-222-2-2−2i2i2i−2i-1-1-1-1111100000000-1-111−iii−i−iii−i
χ2322-2-22-222-2-2−2i2i2i−2i1+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32000000001+i321−i32−1−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7
χ2422-2-22-222-2-2−2i2i2i−2i1−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32000000001−i321+i32−1+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11
χ253333333333333300000000-1-1-1-1-1-1-1-1000000000000
χ263333333333-3-3-3-3000000001111-1-1-1-1000000000000
χ2733-3-3-333-3-333i3i−3i−3i00000000−i−iii-1-111000000000000
χ2833-3-3-333-3-33−3i−3i3i3i00000000ii−i−i-1-111000000000000
χ29666666-2-2-2-200000000000000002i−2i2i−2i000000000000
χ30666666-2-2-2-20000000000000000−2i2i−2i2i000000000000
χ316666-6-6-22-220000000000002-22-20000000000000000
χ326666-6-6-22-22000000000000-22-220000000000000000
χ3366-6-66-6-2-2220000000000002i−2i−2i2i0000000000000000
χ3466-6-66-6-2-222000000000000−2i2i2i−2i0000000000000000
χ3566-6-6-66-222-200000000000000002i−2i−2i2i000000000000
χ3666-6-6-66-222-20000000000000000−2i2i2i−2i000000000000
χ378-88i−8i000000000022-2-22i−2i2i−2i00000000000000000000
χ388-88i−8i0000000000−1−i3−1+i31+i31−i32ζ11−2ζ112ζ7−2ζ700000000000000000000
χ398-88i−8i0000000000−1+i3−1−i31−i31+i32ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ408-8−8i8i000000000022-2-2−2i2i−2i2i00000000000000000000
χ418-8−8i8i0000000000−1−i3−1+i31+i31−i3−2ζ112ζ11−2ζ72ζ700000000000000000000
χ428-8−8i8i0000000000−1+i3−1−i31−i31+i3−2ζ72ζ7−2ζ112ζ1100000000000000000000

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