Finite Group Databasebeta

← Group #5435

Character table — Group #5435

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size1111222222333366666644448888884444888888
order122222444422222244443666661212121236666612121212
χ11111111111111111111111111111111111111111
χ2111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ31111-1-111-1-11111-1-111-1-11111-1-111-1-11111-1-111-1-1
χ41111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111
χ511-1-11-1i−ii−i11-1-11-1i−ii−i11-1-11-1i−ii−i11-1-11-1i−ii−i
χ611-1-11-1−ii−ii11-1-11-1−ii−ii11-1-11-1−ii−ii11-1-11-1−ii−ii
χ711-1-1-11i−i−ii11-1-1-11i−i−ii11-1-1-11i−i−ii11-1-1-11i−i−ii
χ811-1-1-11−iii−i11-1-1-11−iii−i11-1-1-11−iii−i11-1-1-11−iii−i
χ92-22-20000002-22-20000002-22-20000002-22-2000000
χ102-2-220000002-2-220000002-2-220000002-2-22000000
χ1111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ12111111-1-1-1-1111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ131111-1-111-1-11111-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ141111-1-1-1-1111111-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ1511-1-11-1i−ii−i11-1-11-1i−ii−i−1+i32−1+i321−i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i32−1−i321+i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11
χ1611-1-11-1−ii−ii11-1-11-1−ii−ii−1+i32−1+i321−i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i32−1−i321+i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11
χ1711-1-1-11i−i−ii11-1-1-11i−i−ii−1+i32−1+i321−i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−1−i32−1−i321+i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11
χ1811-1-1-11−iii−i11-1-1-11−iii−i−1+i32−1+i321−i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−1−i32−1−i321+i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11
χ192-22-20000002-22-2000000−1+i31−i3−1+i31−i3000000−1−i31+i3−1−i31+i3000000
χ202-2-220000002-2-22000000−1+i31−i31−i3−1+i3000000−1−i31+i31+i3−1−i3000000
χ2111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ22111111-1-1-1-1111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ231111-1-111-1-11111-1-111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ241111-1-1-1-1111111-1-1-1-111−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ2511-1-11-1i−ii−i11-1-11-1i−ii−i−1−i32−1−i321+i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1+i32−1+i321−i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7
χ2611-1-11-1−ii−ii11-1-11-1−ii−ii−1−i32−1−i321+i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1+i32−1+i321−i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7
χ2711-1-1-11i−i−ii11-1-1-11i−i−ii−1−i32−1−i321+i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−1+i32−1+i321−i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7
χ2811-1-1-11−iii−i11-1-1-11−iii−i−1−i32−1−i321+i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11−1+i32−1+i321−i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7
χ292-22-20000002-22-2000000−1−i31+i3−1−i31+i3000000−1+i31−i3−1+i31−i3000000
χ302-2-220000002-2-22000000−1−i31+i31+i3−1−i3000000−1+i31−i31−i3−1+i3000000
χ313333333333-1-1-1-1-1-1-1-1-1-100000000000000000000
χ32333333-3-3-3-3-1-1-1-1-1-1111100000000000000000000
χ333333-3-333-3-3-1-1-1-111-1-11100000000000000000000
χ343333-3-3-3-333-1-1-1-11111-1-100000000000000000000
χ3533-3-33-33i−3i3i−3i-1-111-11−ii−ii00000000000000000000
χ3633-3-33-3−3i3i−3i3i-1-111-11i−ii−i00000000000000000000
χ3733-3-3-333i−3i−3i3i-1-1111-1−iii−i00000000000000000000
χ3833-3-3-33−3i3i3i−3i-1-1111-1i−i−ii00000000000000000000
χ396-66-6000000-22-2200000000000000000000000000
χ406-6-66000000-222-200000000000000000000000000

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