Finite Group Databasebeta

← Group #13181070

Character table — Group #13181070

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222224444444444444444444444444444888888888812121212121212121212121212121212121212121212121212121212121212121212121218181818363636363636363672727272108108108108
order1244234666121212123333666666666612121212121212121212121212123666612121212122244666666666666666612121212121212121212121212121212224422446612126612128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ51111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-11-11-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-1-111-11-11-11-11-11-111-1-1
χ61111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-11-11-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-1-11-11-111-11-1-11-11-1-111
χ71111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-1-11-11-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111111-1-111-11-11-11-11-11-1-1-111
χ81111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-1-11-11-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111111-1-11-11-111-11-1-11-1111-1-1
χ911-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1111-1-111-11-1
χ1011-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-111-111-1-11-11
χ1111-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111-1-11-1-1111-1-11-11-11
χ1211-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-111-1-1-111-111-11-11-1
χ1311-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-1111-1-1111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-11-1111-1-1-111-111-1-11-1-11
χ1411-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-1111-1-1111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-11-11-1-111-111-1-1-111-111-1
χ1511-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-111-111-1-1-111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-11-1111-1-1-111-111-1-1-111-1
χ1611-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-111-111-1-1-111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-11-11-1-111-111-1-1-1111-1-11
χ172222222222222222222222222222222222222222222222222222000000000000000000000000000000000000-2-2-2-20000-2-2-2-200000000
χ1822222-12-1-1-1-1-1-1-12-1-1222-1-1-1-12-1-1222-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-10000−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-2-2-2-20000111100000000
χ1922222-12-1-1-1-1-1-1-12-1-1222-1-1-1-12-1-1222-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-10000i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-2-2-2-20000111100000000
χ2022222-12-1-1-1-1-1-1-12-1-1222-1-1-1-12-1-1222-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122220000-1-1-1-100000000
χ2122222-12-1-1-1-1-1-1-12-1-1222-1-1-1-12-1-1222-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-1-2-2-2-21111-2-21111-2-211111111-2-21111-2-2111122220000-1-1-1-100000000
χ222222-22-2-2-2222-2-22222-2-2-2-2-2-22222222222-2-2-2-2-2-2222-2-2-22-222-2-2000000000000000000000000000000000000-222-20000-22-2200000000
χ232222-2-1-211-1-1-1112-1-12-2-211112-1-1222-1-1-1-1-2-2111122-1-211-1-2-1-1110000−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3-222-200001-11-100000000
χ242222-2-1-211-1-1-1112-1-12-2-211112-1-1222-1-1-1-1-2-2111122-1-211-1-2-1-1110000i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3-222-200001-11-100000000
χ252222-2-1-211-1-1-1112-1-12-2-211112-1-1222-1-1-1-1-2-2111122-1-211-1-2-1-1112-22-2-1-11122-1-1-1-1-2-21111-1-11122-1-1-1-1-2-211112-2-220000-11-1100000000
χ262222-2-1-211-1-1-1112-1-12-2-211112-1-1222-1-1-1-1-2-2111122-1-211-1-2-1-111-22-2211-1-1-2-2111122-1-1-1-111-1-1-2-2111122-1-1-1-12-2-220000-11-1100000000
χ2722-2-222-2222-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-200000000000000000000000000000000000022-2-2000022-2-200000000
χ2822-2-22-1-2-1-1-111112-1-1222-1-1-1-12-1-12-2-21111-2-21111-2-2-12-1-1-1-211110000−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3i3−i3i3−i300i3i3−i3−i300i3i3−i3−i322-2-20000-1-11100000000
χ2922-2-22-1-2-1-1-111112-1-1222-1-1-1-12-1-12-2-21111-2-21111-2-2-12-1-1-1-211110000i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3−i3i3−i3i300−i3−i3i3i300−i3−i3i3i322-2-20000-1-11100000000
χ3022-2-22-1-2-1-1-111112-1-1222-1-1-1-12-1-12-2-21111-2-21111-2-2-12-1-1-1-2111122-2-2-1-1-1-122-1-1-1-122-1-1-1-11111-2-21111-2-21111-2-222000011-1-100000000
χ3122-2-22-1-2-1-1-111112-1-1222-1-1-1-12-1-12-2-21111-2-21111-2-2-12-1-1-1-21111-2-2221111-2-21111-2-21111-1-1-1-122-1-1-1-122-1-1-1-1-2-222000011-1-100000000
χ3222-2-2-222-2-22-2-2222222-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-22-2-2-222-2-2220000000000000000000000000000000000002-22-200002-2-2200000000
χ3322-2-2-2-1211-111-1-12-1-12-2-211112-1-12-2-2111122-1-1-1-1-2-2-1-211-1211-1-10000−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3i3−i3−i3i300i3i3−i3−i300−i3−i3i3i32-22-20000-111-100000000
χ3422-2-2-2-1211-111-1-12-1-12-2-211112-1-12-2-2111122-1-1-1-1-2-2-1-211-1211-1-10000i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3−i3i3i3−i300−i3−i3i3i300i3i3−i3−i32-22-20000-111-100000000
χ3522-2-2-2-1211-111-1-12-1-12-2-211112-1-12-2-2111122-1-1-1-1-2-2-1-211-1211-1-12-2-22-1-11122-1-1-1-1-2-2111111-1-1-2-2111122-1-1-1-1-22-2200001-1-1100000000
χ3622-2-2-2-1211-111-1-12-1-12-2-211112-1-12-2-2111122-1-1-1-1-2-2-1-211-1211-1-1-222-211-1-1-2-2111122-1-1-1-1-1-11122-1-1-1-1-2-21111-22-2200001-1-1100000000
χ3744444444444444111-2111111111-2111111111111-2-2-2-2-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ3844444444444444111-2111111111-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111-2-2-2-211111111111100000000000000000000
χ3944444444444444-2-2-21-2-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000000022220000-1-1-1-10000
χ4044444444444444-2-2-21-2-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000000000000000000-2-2-2-2000011110000
χ4144444-24-2-2-2-2-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-2-21-2111-211112222−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000000000
χ4244444-24-2-2-2-2-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-2-21-2111-21111-2-2-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ4344444-24-2-2-2-2-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-2-21-2111-211112222−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000000000000
χ4444444-24-2-2-2-2-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-2-21-2111-21111-2-2-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ454444-44-4-4-4444-4-4111-2-1-1-1-1-1-1111-2111111-1-1-1-1-1-1-2-2-2222-22-2-2222-22-222-2-2-1-1-1-1-1-111111122-2-2-1-1-1-1-1-111111100000000000000000000
χ464444-44-4-4-4444-4-4111-2-1-1-1-1-1-1111-2111111-1-1-1-1-1-1-2-2-2222-22-2-222-22-22-2-222111111-1-1-1-1-1-1-2-222111111-1-1-1-1-1-100000000000000000000
χ474444-44-4-4-4444-4-4-2-2-21222222-2-2-21-2-2-2-2-2-2222222111-1-1-11-111-1-100000000000000000000000000000000000000002-22-20000-11-110000
χ484444-44-4-4-4444-4-4-2-2-21222222-2-2-21-2-2-2-2-2-2222222111-1-1-11-111-1-10000000000000000000000000000000000000000-22-2200001-11-10000
χ494444-4-2-422-2-2-2221−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-2-212-1-11211-1-12-22-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ504444-4-2-422-2-2-2221−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-2-212-1-11211-1-1-22-221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3200000000000000000000
χ514444-4-2-422-2-2-2221−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-2-212-1-11211-1-12-22-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ524444-4-2-422-2-2-2221−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-2-212-1-11211-1-1-22-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3200000000000000000000
χ5344-4-444-4444-4-4-4-4111-2111111111-2-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-22222222-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000000000
χ5444-4-444-4444-4-4-4-4111-2111111111-2-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-222222-2-222-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ5544-4-444-4444-4-4-4-4-2-2-21-2-2-2-2-2-2-2-2-21222222222222-1-111111-1-1-1-1-100000000000000000000000000000000000000002-2-220000-111-10000
χ5644-4-444-4444-4-4-4-4-2-2-21-2-2-2-2-2-2-2-2-21222222222222-1-111111-1-1-1-1-10000000000000000000000000000000000000000-222-200001-1-110000
χ5744-4-44-2-4-2-2-222221−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i32221-21112-1-1-1-122-2-2−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i321+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ5844-4-44-2-4-2-2-222221−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i32221-21112-1-1-1-1-2-2221+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.