Finite Group Databasebeta

← Group #10596632

Character table — Group #10596632

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size133333161613333316162666663232266666323239999948483999994848
order1222223322222266366666336666666644444412124444441212
χ1111111111111111111111111111111111111111111111111
χ2111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32
χ3111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32
χ433-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-100
χ53-13-1-1-1003-13-1-1-1003-13-1-1-1003-13-1-1-1003-13-1-1-1003-13-1-1-100
χ63-1-13-1-1003-1-13-1-1003-1-13-1-1003-1-13-1-1003-1-13-1-1003-1-13-1-100
χ73-1-1-13-1003-1-1-13-1003-1-1-13-1003-1-1-13-1003-1-1-13-1003-1-1-13-100
χ83-1-1-1-13003-1-1-1-13003-1-1-1-13003-1-1-1-13003-1-1-1-13003-1-1-1-1300
χ911111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ10111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32-1-1-1-1-1-11−i321+i32-1-1-1-1-1-11−i321+i32
χ11111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32-1-1-1-1-1-11+i321−i32-1-1-1-1-1-11+i321−i32
χ1233-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-100-3-3111100-3-3111100
χ133-13-1-1-1003-13-1-1-1003-13-1-1-1003-13-1-1-100-31-311100-31-311100
χ143-1-13-1-1003-1-13-1-1003-1-13-1-1003-1-13-1-100-311-31100-311-31100
χ153-1-1-13-1003-1-1-13-1003-1-1-13-1003-1-1-13-100-3111-3100-3111-3100
χ163-1-1-1-13003-1-1-1-13003-1-1-1-13003-1-1-1-1300-31111-300-31111-300
χ1711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ18111111−1+i32−1−i32-1-1-1-1-1-11−i321+i32111111−1+i32−1−i32-1-1-1-1-1-11−i321+i32iiiiiiζ7ζ11−i−i−i−i−i−i−ζ7−ζ11
χ19111111−1−i32−1+i32-1-1-1-1-1-11+i321−i32111111−1−i32−1+i32-1-1-1-1-1-11+i321−i32iiiiiiζ11ζ7−i−i−i−i−i−i−ζ11−ζ7
χ2033-1-1-1-100-3-311110033-1-1-1-100-3-31111003i3i−i−i−i−i00−3i−3iiiii00
χ213-13-1-1-100-31-3111003-13-1-1-100-31-3111003i−i3i−i−i−i00−3ii−3iiii00
χ223-1-13-1-100-311-311003-1-13-1-100-311-311003i−i−i3i−i−i00−3iii−3iii00
χ233-1-1-13-100-3111-31003-1-1-13-100-3111-31003i−i−i−i3i−i00−3iiii−3ii00
χ243-1-1-1-1300-31111-3003-1-1-1-1300-31111-3003i−i−i−i−i3i00−3iiiii−3i00
χ2511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ26111111−1+i32−1−i32-1-1-1-1-1-11−i321+i32111111−1+i32−1−i32-1-1-1-1-1-11−i321+i32−i−i−i−i−i−i−ζ7−ζ11iiiiiiζ7ζ11
χ27111111−1−i32−1+i32-1-1-1-1-1-11+i321−i32111111−1−i32−1+i32-1-1-1-1-1-11+i321−i32−i−i−i−i−i−i−ζ11−ζ7iiiiiiζ11ζ7
χ2833-1-1-1-100-3-311110033-1-1-1-100-3-3111100−3i−3iiiii003i3i−i−i−i−i00
χ293-13-1-1-100-31-3111003-13-1-1-100-31-311100−3ii−3iiii003i−i3i−i−i−i00
χ303-1-13-1-100-311-311003-1-13-1-100-311-31100−3iii−3iii003i−i−i3i−i−i00
χ313-1-1-13-100-3111-31003-1-1-13-100-3111-3100−3iiii−3ii003i−i−i−i3i−i00
χ323-1-1-1-1300-31111-3003-1-1-1-1300-31111-300−3iiiii−3i003i−i−i−i−i3i00
χ332222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ34222222−1+i3−1−i3222222−1+i3−1−i3-1-1-1-1-1-11−i321+i32-1-1-1-1-1-11−i321+i320000000000000000
χ35222222−1−i3−1+i3222222−1−i3−1+i3-1-1-1-1-1-11+i321−i32-1-1-1-1-1-11+i321−i320000000000000000
χ3666-2-2-2-20066-2-2-2-200-3-3111100-3-31111000000000000000000
χ376-26-2-2-2006-26-2-2-200-31-311100-31-3111000000000000000000
χ386-2-26-2-2006-2-26-2-200-311-31100-311-311000000000000000000
χ396-2-2-26-2006-2-2-26-200-3111-3100-3111-31000000000000000000
χ406-2-2-2-26006-2-2-2-2600-31111-300-31111-3000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ42222222−1+i3−1−i3-2-2-2-2-2-21−i31+i3-1-1-1-1-1-11−i321+i32111111−1+i32−1−i320000000000000000
χ43222222−1−i3−1+i3-2-2-2-2-2-21+i31−i3-1-1-1-1-1-11+i321−i32111111−1−i32−1+i320000000000000000
χ4466-2-2-2-200-6-6222200-3-311110033-1-1-1-1000000000000000000
χ456-26-2-2-200-62-622200-31-3111003-13-1-1-1000000000000000000
χ466-2-26-2-200-622-62200-311-311003-1-13-1-1000000000000000000
χ476-2-2-26-200-6222-6200-3111-31003-1-1-13-1000000000000000000
χ486-2-2-2-2600-62222-600-31111-3003-1-1-1-13000000000000000000

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