Finite Group Databasebeta

← Group #88632

Character table — Group #88632

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size1111112229999991212121212121212181818181818181818181818181818
order1233662662266663366666624444661212121212121212
χ111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111-1-1-1-1-1-111111111-1ii−i−i-1-1iiii−i−i−i−i
χ4111111111-1-1-1-1-1-111111111-1−i−iii-1-1−i−i−i−iiiii
χ5111111-1-1-11111111111-1-1-1-1-11-11-1-1-111-1-111-1-1
χ6111111-1-1-11111111111-1-1-1-1-1-11-11-1-1-1-111-1-111
χ7111111-1-1-1-1-1-1-1-1-11111-1-1-1-11i−i−ii11ii−i−i−i−iii
χ8111111-1-1-1-1-1-1-1-1-11111-1-1-1-11−iii−i11−i−iiiii−i−i
χ92-222-2-20002-222-2-222-2-20000000000000000000
χ102-222-2-2000-22-2-22222-2-20000000000000000000
χ1133−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3211−1−i32−1+i32−1−i32−1+i32000000001ii−i−i−1−i32−1+i32ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11
χ1233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3211−1−i32−1+i32−1−i32−1+i32000000001−i−iii−1−i32−1+i32−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11
χ1333−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321−i321+i321−i3200000000-111111+i321−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ1433−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321−i321+i321−i3200000000-1-1-1-1-11+i321−i321−i321+i321−i321+i321−i321+i321−i321+i32
χ1533−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i3211−1−i32−1+i32−1−i32−1+i3200000000-1i−i−ii1+i321−i32ζ7ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11
χ1633−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i3211−1−i32−1+i32−1−i32−1+i3200000000-1−iii−i1+i321−i32−ζ7−ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11
χ1733−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32-1-11+i321−i321+i321−i320000000011-11-1−1−i32−1+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ1833−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32-1-11+i321−i321+i321−i32000000001-11-11−1−i32−1+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ1933−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3211−1+i32−1−i32−1+i32−1−i32000000001ii−i−i−1+i32−1−i32ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7
χ2033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3211−1+i32−1−i32−1+i32−1−i32000000001−i−iii−1+i32−1−i32−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7
χ2133−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321+i321−i321+i3200000000-111111−i321+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ2233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321+i321−i321+i3200000000-1-1-1-1-11−i321+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ2333−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i3211−1+i32−1−i32−1+i32−1−i3200000000-1i−i−ii1−i321+i32ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ2433−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i3211−1+i32−1−i32−1+i32−1−i3200000000-1−iii−i1−i321+i32−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
χ2533−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32-1-11−i321+i321−i321+i320000000011-11-1−1+i32−1−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ2633−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32-1-11−i321+i321−i321+i32000000001-11-11−1+i32−1−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ274444444440000001-21-211-2-2000000000000000
χ28444444444000000-21-21-2-211000000000000000
χ29444444-4-4-40000001-21-2-1-122000000000000000
χ30444444-4-4-4000000-21-2122-1-1000000000000000
χ314-444-4-40000000001-2-123-300000000000000000
χ324-444-4-40000000001-2-12-3300000000000000000
χ334-444-4-4000000000-212-1003-3000000000000000
χ344-444-4-4000000000-212-100-33000000000000000
χ356-6−3−3i3−3+3i33+3i33−3i30002-2−1−i3−1+i31+i31−i300000000000000000000000
χ366-6−3−3i3−3+3i33+3i33−3i3000-221+i31−i3−1−i3−1+i300000000000000000000000
χ376-6−3+3i3−3−3i33−3i33+3i30002-2−1+i3−1−i31−i31+i300000000000000000000000
χ386-6−3+3i3−3−3i33−3i33+3i3000-221−i31+i3−1+i3−1−i300000000000000000000000

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