Finite Group Databasebeta

← Group #72242417

Character table — Group #72242417

Order 3456.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size11222224444666688888888888888888888881212121218182424242432323232323232323232323232323232323232323232323236363636363648484848484848484848108108108108144144144144144144144144
order122366633664444333336666666666666666612121212221212121233333366666666666666666624668812121212121212121212248866121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111111111111−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ41111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-111-1-1111111−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32
χ51111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32111111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111111111111−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ61111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32111111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-111-1-1111111−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32
χ711-11-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1-1-11-11-11-1111-1-1-11-11-1-111-111-1-11-11-1
χ811-11-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-11111-1-1-11-11-11-1-11-1-111-11-11
χ911-11-1-11−1+i32−1−i32−1+i32−1−i321-1-11111−1+i32−1−i321−i321+i32-1-1-1-1-1-11−i321−i321+i321+i32111−1+i32−1−i3211-1-11-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321-11-11-1111-1-1-1−1+i321−i32−1−i321+i32-111-1−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i32
χ1011-11-1-11−1+i32−1−i32−1+i32−1−i321-1-11111−1+i32−1−i321−i321+i32-1-1-1-1-1-11−i321−i321+i321+i32111−1+i32−1−i3211-1-11-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32-111-1-11111-1-1-1−1+i321−i32−1−i321+i321-1-111−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i32
χ1111-11-1-11−1−i32−1+i32−1−i32−1+i321-1-11111−1−i32−1+i321+i321−i32-1-1-1-1-1-11+i321+i321−i321−i32111−1−i32−1+i3211-1-11-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321-11-11-1111-1-1-1−1−i321+i32−1+i321−i32-111-1−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i32
χ1211-11-1-11−1−i32−1+i32−1−i32−1+i321-1-11111−1−i32−1+i321+i321−i32-1-1-1-1-1-11+i321+i321−i321−i32111−1−i32−1+i3211-1-11-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32-111-1-11111-1-1-1−1−i321+i32−1+i321−i321-1-111+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i32
χ13222222222222222-1-1-12222-1-1-1-1-1-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002200-1-1-1-1-1-12222000000000000
χ142222222−1+i3−1−i3−1+i3−1−i32222-1-1-1−1+i3−1−i3−1+i3−1−i3-1-1-1-1-1-1−1+i3−1+i3−1−i3−1−i3-1-1-1−1+i3−1−i3222222−1+i3−1−i3−1+i3−1−i31−i321−i321−i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32002200-1-1-1-1-1-1−1+i3−1+i3−1−i3−1−i3000000000000
χ152222222−1−i3−1+i3−1−i3−1+i32222-1-1-1−1−i3−1+i3−1−i3−1+i3-1-1-1-1-1-1−1−i3−1−i3−1+i3−1+i3-1-1-1−1−i3−1+i3222222−1−i3−1+i3−1−i3−1+i31+i321+i321+i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32002200-1-1-1-1-1-1−1−i3−1−i3−1+i3−1+i3000000000000
χ16222-1-1-1-1222222222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-12222222-1-12-1-12-1-122-1-1-1-12-1-122-1-1-1-100-1-1002-1-12-1-1-1-1-1-1000000000000
χ17222-1-1-1-122222222-12-1-1-122-1-122-1-1-1-1-1-1-12-1-1-1-1-1-1-1222222-12-1-12-1-12-1-1-122-1-1-12-1-1-122-1-100-1-100-12-1-12-1-1-1-1-1000000000000
χ18222-1-1-1-122222222-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-1-1-1-1222222-1-12-1-12-1-12-1-1-1-122-1-12-1-1-1-12200-1-100-1-12-1-12-1-1-1-1000000000000
χ19222-1-1-1-1−1+i3−1−i3−1+i3−1−i322222-1-11−i321+i32−1+i3−1−i322-1-1-1-11−i321−i321+i321+i322-1-11−i321+i32-1-1-1-122−1+i3−1−i3−1+i3−1−i3−1+i31−i321−i32−1−i31+i321+i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i3200-1-1002-1-12-1-11−i321−i321+i321+i32000000000000
χ20222-1-1-1-1−1+i3−1−i3−1+i3−1−i32222-12-11−i321+i32−1+i3−1−i3-1-122-1-11−i321−i321+i321+i32-12-11−i321+i32-1-1-1-122−1+i3−1−i3−1+i3−1−i31−i32−1+i31−i321+i32−1−i31+i321−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i3200-1-100-12-1-12-11−i321−i321+i321+i32000000000000
χ21222-1-1-1-1−1+i3−1−i3−1+i3−1−i32222-1-121−i321+i32−1+i3−1−i3-1-1-1-1221−i321−i321+i321+i32-1-121−i321+i32-1-1-1-122−1+i3−1−i3−1+i3−1−i31−i321−i32−1+i31+i321+i32−1−i31−i321−i32−1+i31−i321−i321−i321−i32−1+i3−1+i31+i321+i32−1−i31+i321+i321+i321+i32−1−i3−1−i300-1-100-1-12-1-121−i321−i321+i321+i32000000000000
χ22222-1-1-1-1−1−i3−1+i3−1−i3−1+i322222-1-11+i321−i32−1−i3−1+i322-1-1-1-11+i321+i321−i321−i322-1-11+i321−i32-1-1-1-122−1−i3−1+i3−1−i3−1+i3−1−i31+i321+i32−1+i31−i321−i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i3200-1-1002-1-12-1-11+i321+i321−i321−i32000000000000
χ23222-1-1-1-1−1−i3−1+i3−1−i3−1+i32222-12-11+i321−i32−1−i3−1+i3-1-122-1-11+i321+i321−i321−i32-12-11+i321−i32-1-1-1-122−1−i3−1+i3−1−i3−1+i31+i32−1−i31+i321−i32−1+i31−i321+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i3200-1-100-12-1-12-11+i321+i321−i321−i32000000000000
χ24222-1-1-1-1−1−i3−1+i3−1−i3−1+i32222-1-121+i321−i32−1−i3−1+i3-1-1-1-1221+i321+i321−i321−i32-1-121+i321−i32-1-1-1-122−1−i3−1+i3−1−i3−1+i31+i321+i32−1−i31−i321−i32−1+i31+i321+i32−1−i31+i321+i321+i321+i32−1−i3−1−i31−i321−i32−1+i31−i321−i321−i321−i32−1+i3−1+i300-1-100-1-12-1-121+i321+i321−i321−i32000000000000
χ2522-22-2-2222222-2-22-1-1-122-2-2111111-2-2-2-2-1-1-12222-2-22-2-2-222-1-1-1-1-1-1-1-1-1111111-1-1-1111111002-200-1-1-11112-22-2000000000000
χ2622-22-2-22−1+i3−1−i3−1+i3−1−i32-2-22-1-1-1−1+i3−1−i31−i31+i31111111−i31−i31+i31+i3-1-1-1−1+i3−1−i322-2-22-21−i31+i3−1+i3−1−i31−i321−i321−i321+i321+i321+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32002-200-1-1-1111−1+i31−i3−1−i31+i3000000000000
χ2722-22-2-22−1−i3−1+i3−1−i3−1+i32-2-22-1-1-1−1−i3−1+i31+i31−i31111111+i31+i31−i31−i3-1-1-1−1−i3−1+i322-2-22-21+i31−i3−1−i3−1+i31+i321+i321+i321−i321−i321−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32002-200-1-1-1111−1−i31+i3−1+i31−i3000000000000
χ2822-2-111-122222-2-222-1-1-1-1-2-2-2-2111111112-1-1-1-1-1-1112-2-2-2222-1-12-1-12-1-1-2-211112-1-1-2-2111100-11002-1-1-211-11-11000000000000
χ2922-2-111-122222-2-22-12-1-1-1-2-211-2-2111111-12-1-1-1-1-1112-2-2-222-12-1-12-1-12-111-2-211-12-111-2-21100-1100-12-11-21-11-11000000000000
χ3022-2-111-122222-2-22-1-12-1-1-2-21111-2-21111-1-12-1-1-1-1112-2-2-222-1-12-1-12-1-121111-2-2-1-121111-2-200-1100-1-1211-2-11-11000000000000
χ3122-2-111-1−1+i3−1−i3−1+i3−1−i32-2-222-1-11−i321+i321−i31+i3-2-21111−1+i32−1+i32−1−i32−1−i322-1-11−i321+i32-1-1112-21−i31+i3−1+i3−1−i3−1+i31−i321−i32−1−i31+i321+i32−1+i31−i321−i321−i31−i3−1+i32−1+i32−1+i32−1+i32−1−i31+i321+i321+i31+i3−1−i32−1−i32−1−i32−1−i3200-11002-1-1-2111−i32−1+i321+i32−1−i32000000000000
χ3222-2-111-1−1+i3−1−i3−1+i3−1−i32-2-22-12-11−i321+i321−i31+i311-2-211−1+i32−1+i32−1−i32−1−i32-12-11−i321+i32-1-1112-21−i31+i3−1+i3−1−i31−i32−1+i31−i321+i32−1−i31+i321−i32−1+i31−i32−1+i32−1+i321−i31−i3−1+i32−1+i321+i32−1−i31+i32−1−i32−1−i321+i31+i3−1−i32−1−i3200-1100-12-11-211−i32−1+i321+i32−1−i32000000000000
χ3322-2-111-1−1+i3−1−i3−1+i3−1−i32-2-22-1-121−i321+i321−i31+i31111-2-2−1+i32−1+i32−1−i32−1−i32-1-121−i321+i32-1-1112-21−i31+i3−1+i3−1−i31−i321−i32−1+i31+i321+i32−1−i31−i321−i32−1+i3−1+i32−1+i32−1+i32−1+i321−i31−i31+i321+i32−1−i3−1−i32−1−i32−1−i32−1−i321+i31+i300-1100-1-1211-21−i32−1+i321+i32−1−i32000000000000
χ3422-2-111-1−1−i3−1+i3−1−i3−1+i32-2-222-1-11+i321−i321+i31−i3-2-21111−1−i32−1−i32−1+i32−1+i322-1-11+i321−i32-1-1112-21+i31−i3−1−i3−1+i3−1−i31+i321+i32−1+i31−i321−i32−1−i31+i321+i321+i31+i3−1−i32−1−i32−1−i32−1−i32−1+i31−i321−i321−i31−i3−1+i32−1+i32−1+i32−1+i3200-11002-1-1-2111+i32−1−i321−i32−1+i32000000000000
χ3522-2-111-1−1−i3−1+i3−1−i3−1+i32-2-22-12-11+i321−i321+i31−i311-2-211−1−i32−1−i32−1+i32−1+i32-12-11+i321−i32-1-1112-21+i31−i3−1−i3−1+i31+i32−1−i31+i321−i32−1+i31−i321+i32−1−i31+i32−1−i32−1−i321+i31+i3−1−i32−1−i321−i32−1+i31−i32−1+i32−1+i321−i31−i3−1+i32−1+i3200-1100-12-11-211+i32−1−i321−i32−1+i32000000000000
χ3622-2-111-1−1−i3−1+i3−1−i3−1+i32-2-22-1-121+i321−i321+i31−i31111-2-2−1−i32−1−i32−1+i32−1+i32-1-121+i321−i32-1-1112-21+i31−i3−1−i3−1+i31+i321+i32−1−i31−i321−i32−1+i31+i321+i32−1−i3−1−i32−1−i32−1−i32−1−i321+i31+i31−i321−i32−1+i3−1+i32−1+i32−1+i32−1+i321−i31−i300-1100-1-1211-21+i32−1−i321−i32−1+i32000000000000
χ3733333330000-13-1333300003333330000333003-13-1-1-1000000000000000000000000000033-1-133-1-1-1-1-1-10000-1-1-1-100000000
χ3833333330000-13-1333300003333330000333003-13-1-1-10000000000000000000000000000-3-3-1-1-3-3-1-1-1-1-1-10000111100000000
χ39333333333333-13-10003333000000333300033-13-13-1-1-1-1-1-100000000000000000000000011-1-1-1-1000000-1-1-1-111-1-11111-1-1-1-1
χ40333333333333-13-10003333000000333300033-13-13-1-1-1-1-1-1000000000000000000000000-1-1-1-111000000-1-1-1-1-1-111-1-1-1-11111
χ413333333−3+3i32−3−3i32−3+3i32−3−3i323-13-1000−3+3i32−3−3i32−3+3i32−3−3i32000000−3+3i32−3+3i32−3−3i32−3−3i32000−3+3i32−3−3i32-13-13-1-11−i321+i321−i321+i3200000000000000000000000011-1-1-1-10000001−i321−i321+i321+i3211-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ423333333−3+3i32−3−3i32−3+3i32−3−3i323-13-1000−3+3i32−3−3i32−3+3i32−3−3i32000000−3+3i32−3+3i32−3−3i32−3−3i32000−3+3i32−3−3i32-13-13-1-11−i321+i321−i321+i32000000000000000000000000-1-1-1-1110000001−i321−i321+i321+i32-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32
χ433333333−3−3i32−3+3i32−3−3i32−3+3i323-13-1000−3−3i32−3+3i32−3−3i32−3+3i32000000−3−3i32−3−3i32−3+3i32−3+3i32000−3−3i32−3+3i32-13-13-1-11+i321−i321+i321−i3200000000000000000000000011-1-1-1-10000001+i321+i321−i321−i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
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Here i is the imaginary unit (i² = −1).