Finite Group Databasebeta

← Group #13161122

Character table — Group #13161122

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size11222222222222222222222444444444444444444444444444888888888888888888888888888888888881212121212121212121212121212121212121212242424242424242436367272727272108108216
order122333334466666666666663333666666666666612121212121212121212266666666666666666666666666121212121212121244441212121212121212121212121212121212121212121212122468122424248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-111-1
χ611111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-111-1-11
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111111111-1-1-1-1-1-1-1-1111-11-1-1-1-11
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-11-11111-1
χ922222222-2-2222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000-2-2-2-2-2-2-2-22-20000000000000000002222-2-2-2-20000000000
χ1022222222-2-2222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000-2-2-2-2-2-2-2-2-22000000000000000000-2-2-2-222220000000000
χ112222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000022-12-1-1-1000
χ122222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000-2-21-2111000
χ132222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-2-2-2-2-2-2-2-2-2111111111111111111-1-1-1-1-1-1-1-1000000000000000000000000000022-1-2-111000
χ142222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-2-2-2-2-2-2-2-2-2111111111111111111-1-1-1-1-1-1-1-10000000000000000000000000000-2-2121-1-1000
χ152222-1-1-122222-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12-1-1-12-1-1-10000000000
χ162222-1-1-122222-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111-2111-21110000000000
χ172222-1-1-122222-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-2-2-2111111-2-2-2-2-2-211111111111122-1-1-1-1-1-122-2-2-2-2-2-21111111111112-1-1-12-1-1-10000000000
χ182222-1-1-122222-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-2-2-2111111-2-2-2-2-2-211111111111122-1-1-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-2111-21110000000000
χ192222-1-1-12-2-222-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-12-1-1-1-2-2111111-2-2000−i3−i3−i3i3i3i3000000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-2-21111112-2000000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i32-1-1-1-21110000000000
χ202222-1-1-12-2-222-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-12-1-1-1-2-2111111-2-2000−i3−i3−i3i3i3i3000000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-2-2111111-22000000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-21112-1-1-10000000000
χ212222-1-1-12-2-222-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-12-1-1-1-2-2111111-2-2000i3i3i3−i3−i3−i3000000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-2-21111112-2000000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i32-1-1-1-21110000000000
χ222222-1-1-12-2-222-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-12-1-1-1-2-2111111-2-2000i3i3i3−i3−i3−i3000000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-2-2111111-22000000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-21112-1-1-10000000000
χ23222-12-1-1222-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1222-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-12-1-1-12-1-10000000000
χ24222-12-1-1222-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1222-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-2-2-21111-2-21111-2-211111-2111-2110000000000
χ25222-12-1-1222-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-12-1-1-1-122-1-1-1-122-211-211-211-2-21111-2-21111-2-21111-1-122-1-1-1-122-2-21111-2-21111-2-21111-12-1-1-12-1-10000000000
χ26222-12-1-1222-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-12-1-1-1-122-1-1-1-122-211-211-211-2-21111-2-21111-2-21111-1-122-1-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-11-2111-2110000000000
χ27222-12-1-12-2-2-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-12-1-111-2-21111-2-20−i3i30−i3i30−i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i311-2-211112-200−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-12-1-11-2110000000000
χ28222-12-1-12-2-2-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-12-1-111-2-21111-2-20−i3i30−i3i30−i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i311-2-21111-2200i3i3−i3−i300i3i3−i3−i300i3i3−i3−i31-211-12-1-10000000000
χ29222-12-1-12-2-2-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-12-1-111-2-21111-2-20i3−i30i3−i30i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i311-2-211112-200i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-12-1-11-2110000000000
χ30222-12-1-12-2-2-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-12-1-111-2-21111-2-20i3−i30i3−i30i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i311-2-21111-2200−i3−i3i3i300−i3−i3i3i300−i3−i3i3i31-211-12-1-10000000000
χ31222-1-12-1222-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1222-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-12-1-1-12-10000000000
χ32222-1-12-1222-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1222-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-2-2-2-2111111-2-2111111-2-211-2111-210000000000
χ33222-1-12-1222-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-12-1-1-1-1-122-1-122-2111-2111-2-2-2111111-2-2111111-2-2-1-1-1-122-1-122-2-2111111-2-2111111-2-2-1-12-1-1-12-10000000000
χ34222-1-12-1222-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-12-1-1-1-1-122-1-122-2111-2111-2-2-2111111-2-2111111-2-2-1-1-1-122-1-1-2-222-1-1-1-1-1-122-1-1-1-1-1-12211-2111-210000000000
χ35222-1-12-12-2-2-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-12-11111-2-211-2-20−i3i3i30−i3−i3i3000−i3−i3i3i3i3i300−i3−i3−i3−i3i3i3001111-2-2112-200−i3−i3i3i3i3i300−i3−i3−i3−i3i3i300-1-12-111-210000000000
χ36222-1-12-12-2-2-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-12-11111-2-211-2-20−i3i3i30−i3−i3i3000−i3−i3i3i3i3i300−i3−i3−i3−i3i3i3001111-2-211-2200i3i3−i3−i3−i3−i300i3i3i3i3−i3−i30011-21-1-12-10000000000
χ37222-1-12-12-2-2-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-12-11111-2-211-2-20i3−i3−i30i3i3−i3000i3i3−i3−i3−i3−i300i3i3i3i3−i3−i3001111-2-2112-200i3i3−i3−i3−i3−i300i3i3i3i3−i3−i300-1-12-111-210000000000
χ38222-1-12-12-2-2-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-12-11111-2-211-2-20i3−i3−i30i3i3−i3000i3i3−i3−i3−i3−i300i3i3i3i3−i3−i3001111-2-211-2200−i3−i3i3i3i3i300−i3−i3−i3−i3i3i30011-21-1-12-10000000000
χ39222-1-1-12222-1-1-1-1-1-122-1-1-122-1-1-122-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122222-1-1-1-12-12-122-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-12-1-1-120000000000
χ40222-1-1-12222-1-1-1-1-1-122-1-1-122-1-1-122-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122222-1-1-1-12-12-122-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-2-2-2-211111111-2-211-2-211111-2111-20000000000
χ41222-1-1-12222-1-1-1-1-1-122-1-1-122-1-1-122-1-1-1-1-1-122-1-1-12-1-1-1-1-1-12222-21111-21-21-2-211111111-2-211-2-211-1-1-1-1-1-12222-2-211111111-2-211-2-211-1-1-12-1-1-120000000000
χ42222-1-1-12222-1-1-1-1-1-122-1-1-122-1-1-122-1-1-1-1-1-122-1-1-12-1-1-1-1-1-12222-21111-21-21-2-211111111-2-211-2-211-1-1-1-1-1-122-2-222-1-1-1-1-1-1-1-122-1-122-1-1111-2111-20000000000
χ43222-1-1-122-2-2-1-1-1-1-1-122-1-1-122-1-1-122-1-1-1-1-1-122-1-1-12111111-2-2-2-20−i3i3−i3i30i30−i300−i3−i3i3i3−i3−i3i3i300i3i300−i3−i3111111-2-22-200−i3−i3i3i3−i3−i3i3i300i3i300−i3−i3-1-1-12111-20000000000
χ44222-1-1-122-2-2-1-1-1-1-1-122-1-1-122-1-1-122-1-1-1-1-1-122-1-1-12111111-2-2-2-20−i3i3−i3i30i30−i300−i3−i3i3i3−i3−i3i3i300i3i300−i3−i3111111-2-2-2200i3i3−i3−i3i3i3−i3−i300−i3−i300i3i3111-2-1-1-120000000000
χ45222-1-1-122-2-2-1-1-1-1-1-122-1-1-122-1-1-122-1-1-1-1-1-122-1-1-12111111-2-2-2-20i3−i3i3−i30−i30i300i3i3−i3−i3i3i3−i3−i300−i3−i300i3i3111111-2-22-200i3i3−i3−i3i3i3−i3−i300−i3−i300i3i3-1-1-12111-20000000000
χ46222-1-1-122-2-2-1-1-1-1-1-122-1-1-122-1-1-122-1-1-1-1-1-122-1-1-12111111-2-2-2-20i3−i3i3−i30−i30i300i3i3−i3−i3i3i3−i3−i300−i3−i300i3i3111111-2-2-2200−i3−i3i3i3−i3−i3i3i300i3i300−i3−i3111-2-1-1-120000000000
χ4722-2222222-2-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-222222-22-22-22-2-220000000000000000000000000002-22-22-22-200000000000000000000000000002-220-200000
χ4822-2222222-2-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-222222-22-22-22-2-220000000000000000000000000002-22-22-22-20000000000000000000000000000-22-20200000
χ4922-222222-22-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22222-22-22-22-222-2000000000000000000000000000-22-22-22-22000000000000000000000000000000000002-20
χ5022-222222-22-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22222-22-22-22-222-2000000000000000000000000000-22-22-22-2200000000000000000000000000000000000-220
χ5122-22222-12-2-2-2-2-2-2-2-2-22222-1-1-1-1-1111111111-1-1-1-12-22-22-22-21-1000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3-11-11-11-1100000000000000000000000000002-2-101−i3i3000
χ5222-22222-12-2-2-2-2-2-2-2-2-22222-1-1-1-1-1111111111-1-1-1-12-22-22-22-21-1000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3-11-11-11-110000000000000000000000000000-2210-1i3−i3000
χ5322-22222-12-2-2-2-2-2-2-2-2-22222-1-1-1-1-1111111111-1-1-1-12-22-22-22-21-1000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3-11-11-11-1100000000000000000000000000002-2-101i3−i3000
χ5422-22222-12-2-2-2-2-2-2-2-2-22222-1-1-1-1-1111111111-1-1-1-12-22-22-22-21-1000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3-11-11-11-110000000000000000000000000000-2210-1−i3i3000
χ554444444-2-4-4444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-4-4-4-4-4-4-4220000000000000000000000000002222222200000000000000000000000000000000000000
χ564444-2-2-2-24444-2-2-2-2-2-24-2-2-2-2-2111-2-2-2111111-211144-2-2-2-2-2-2-2-2444-2-2-2-2-2-2-2-2-2-2-2-2111111111111-2-211111100000000000000000000000000000000000000
χ574444-2-2-2-24444-2-2-2-2-2-24-2-2-2-2-2111-2-2-2111111-211144-2-2-2-2-2-2-2-2-4-4-4222222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-211111100000000000000000000000000000000000000
χ584444-2-2-2-2-4-444-2-2-2-2-2-24-2-2-2-2-2111-2-2-2111111-2111-4-422222222000−2i3−2i3−2i32i32i32i3000000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i322-1-1-1-1-1-100000000000000000000000000000000000000
χ594444-2-2-2-2-4-444-2-2-2-2-2-24-2-2-2-2-2111-2-2-2111111-2111-4-4222222220002i32i32i3−2i3−2i3−2i3000000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i322-1-1-1-1-1-100000000000000000000000000000000000000
χ60444-24-2-2-244-2-244-2-2-2-2-24-2-2-21-211-211-2-211111-211-2-244-2-2-2-2-2-24-2-24-2-24-2-2-2-21111-2-21111-2-2111111-2-2111100000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.