Finite Group Databasebeta

← Group #13167054

Character table — Group #13167054

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222224444444444444444448888888888888888991212121212121212121212121818181818181824242424242424242424242436363636363672727272108108108108
order12234461212333366666661212121212121236666661212121212121212124422446666121212122246612126666661212121212124444612121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111-1-11-1-111111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1111-11-111-1-111-1-1-1-11-1-111111-1-1-1111-1-1-111-1-1-1111-1-111-1-1
χ61111-1-11-1-111111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1111-11-111-1-111-1-1-1-11-1-111111-1-1-1111-1-1-1-1-111-11-1-111-1-111
χ71111-1-11-1-111111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111-11-11-1-111-1-111-1-11-1-111-1-1-1111-1-1-111111-1-1-1111-1-1-1-111
χ81111-1-11-1-111111111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111-11-11-1-111-1-111-1-11-1-111-1-1-1111-1-1-1111-1-111-11-1-11111-1-1
χ911-111-11111111-1-11111-1-11111111-1-1-1-1-111-1-1-1-111-1-1-1-11-1-1111-1-1-1-1111-11-1-1-1-1111-1-1-1-1-1-1111i−ii−i11i−ii−ii−ii−i
χ1011-111-11111111-1-11111-1-11111111-1-1-1-1-111-1-1-1-111-1-1-1-11-1-1111-1-1-1-1111-11-1-1-1-1111-1-1-1-1-1-1111−ii−ii11−ii−ii−ii−ii
χ1111-111-11111111-1-11111-1-11111111-1-1-1-1-111-1-1-1-111-1-1-1-1-111-1-1-11111-1-11-11-1-1-1-1-1-1-1111111-1-1-1i−ii−i11i−ii−i−ii−ii
χ1211-111-11111111-1-11111-1-11111111-1-1-1-1-111-1-1-1-111-1-1-1-1-111-1-1-11111-1-11-11-1-1-1-1-1-1-1111111-1-1-1−ii−ii11−ii−iii−ii−i
χ1311-11-111-1-11111-1-11111-11-1-1-1-1-1-11-1-1-1-1-11-11111-1-111-1-111-1-11111-1-1-1-1-11111-1-1111111-1-1-1-1-1-1i−i−ii-11i−i−iii−i−ii
χ1411-11-111-1-11111-1-11111-11-1-1-1-1-1-11-1-1-1-1-11-11111-1-111-1-111-1-11111-1-1-1-1-11111-1-1111111-1-1-1-1-1-1−iii−i-11−iii−i−iii−i
χ1511-11-111-1-11111-1-11111-11-1-1-1-1-1-11-1-1-1-1-11-11111-1-111-1-1-1-111-1-1-1-11111-11111-1-1-1-1-1-1-1-1111111i−i−ii-11i−i−ii−iii−i
χ1611-11-111-1-11111-1-11111-11-1-1-1-1-1-11-1-1-1-1-11-11111-1-111-1-1-1-111-1-1-1-11111-11111-1-1-1-1-1-1-1-1111111−iii−i-11−iii−ii−i−ii
χ172222222222222222222222222222222222222222222-2-2000000000000-2-2-2-2-2-2-20000000000000000-2-200000000
χ182222-2-22-2-222222222222-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-200000000000022-222-2-200000000000000002-200000000
χ19222-122-1-1-122-1-1-1222-1-12-122-1-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-12-1-12-1-10000-1-100000000
χ20222-122-1-1-122-1-1-1222-1-12-122-1-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-122-2-2-2-211111111222-1-1-1-1-211-211-211-2110000-1-100000000
χ21222-122-1-1-122-1-1-1222-1-12-122-1-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-2-20000−i3i3−i3i3−i3i3−i3i3-2-2-211110−i3i30−i3i30−i3i30−i3i300001100000000
χ22222-122-1-1-122-1-1-1222-1-12-122-1-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-2-20000i3−i3i3−i3i3−i3i3−i3-2-2-211110i3−i30i3−i30i3−i30i3−i300001100000000
χ23222-1-2-2-11122-1-1-1222-1-121-2-21111-12-1-1-1-1-1-2-2-2111111222-22-2-1-111-1-111-2-2211-1-12-1-1-2112-1-1-21100001-100000000
χ24222-1-2-2-11122-1-1-1222-1-121-2-21111-12-1-1-1-1-1-2-2-211111122-22-2211-1-111-1-1-2-2211-1-1-2112-1-1-2112-1-100001-100000000
χ25222-1-2-2-11122-1-1-1222-1-121-2-21111-12-1-1-1-1-1-2-2-2111111-2-20000−i3i3i3−i3−i3i3i3−i322-2-1-1110−i3i30i3−i30−i3i30i3−i30000-1100000000
χ26222-1-2-2-11122-1-1-1222-1-121-2-21111-12-1-1-1-1-1-2-2-2111111-2-20000i3−i3−i3i3i3−i3−i3i322-2-1-1110i3−i30−i3i30i3−i30−i3i30000-1100000000
χ2722-222-22222222-2-22222-2-22222222-2-2-2-2-222-2-2-2-222-2-222000000000000-22-222220000000000000000-2-200000000
χ2822-22-222-2-22222-2-22222-22-2-2-2-2-2-22-2-2-2-2-22-22222-2-222220000000000002-2-2-2-22200000000000000002-200000000
χ2922-2-12-2-1-1-122-1-11-222-1-1-2122-1-1-1-1-1-21111-12-2-211-1-111220000−i3i3i3−i3i3−i3−i3i3-22-2-1-1-1-10−i3i30i3−i30i3−i30−i3i300001100000000
χ3022-2-12-2-1-1-122-1-11-222-1-1-2122-1-1-1-1-1-21111-12-2-211-1-111220000i3−i3−i3i3−i3i3i3−i3-22-2-1-1-1-10i3−i30−i3i30−i3i30i3−i300001100000000
χ3122-2-12-2-1-1-122-1-11-222-1-1-2122-1-1-1-1-1-21111-12-2-211-1-111-2-22-2-22-1-11111-1-12-2211112-1-1-211-2112-1-10000-1-100000000
χ3222-2-12-2-1-1-122-1-11-222-1-1-2122-1-1-1-1-1-21111-12-2-211-1-111-2-2-222-211-1-1-1-1112-221111-2112-1-12-1-1-2110000-1-100000000
χ3322-2-1-22-11122-1-11-222-1-1-2-1-2-21111-1-21111-1-222-1-111-1-1220000−i3i3−i3i3i3−i3i3−i32-2-211-1-10−i3i30−i3i30i3−i30i3−i30000-1100000000
χ3422-2-1-22-11122-1-11-222-1-1-2-1-2-21111-1-21111-1-222-1-111-1-1220000i3−i3i3−i3−i3i3−i3i32-2-211-1-10i3−i30i3−i30−i3i30−i3i30000-1100000000
χ3522-2-1-22-11122-1-11-222-1-1-2-1-2-21111-1-21111-1-222-1-111-1-1-2-222-2-2-1-1-1-11111-222-1-1112-1-12-1-1-211-21100001-100000000
χ3622-2-1-22-11122-1-11-222-1-1-2-1-2-21111-1-21111-1-222-1-111-1-1-2-2-2-2221111-1-1-1-1-222-1-111-211-2112-1-12-1-100001-100000000
χ374444444441-2-2-2411-2-2-214-2-2-2-2-2-21-2-2-211111-2-2-21111000000000000000000000000000000000222200-1-1-1-10000
χ384444444441-2-2-2411-2-2-214-2-2-2-2-2-21-2-2-211111-2-2-21111000000000000000000000000000000000-2-2-2-20011110000
χ39444444444-21114-2-2111-24111111-2111-2-2-2-2-2111-2-2-2-2002222222222220000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ40444444444-21114-2-2111-24111111-2111-2-2-2-2-2111-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-2000000011111111111100000000000000
χ414444-4-44-4-41-2-2-2411-2-2-21-42222221-2-2-2111-1-1222-1-1-1-100000000000000000000000000000000022-2-200-1-1110000
χ424444-4-44-4-41-2-2-2411-2-2-21-42222221-2-2-2111-1-1222-1-1-1-1000000000000000000000000000000000-2-2220011-1-10000
χ434444-4-44-4-4-21114-2-2111-2-4-1-1-1-1-1-1-2111-2-2-222-1-1-12222002-22-222-2-222-2-20000000-1-1-1111-1-1-111100000000000000
χ444444-4-44-4-4-21114-2-2111-2-4-1-1-1-1-1-1-2111-2-2-222-1-1-1222200-22-22-2-222-2-2220000000111-1-1-1111-1-1-100000000000000
χ45444-244-2-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1+3i32111-2-21−1−3i32−1+3i321111002222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i30000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i3200000000000000
χ46444-244-2-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1+3i32111-2-21−1−3i32−1+3i32111100-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i300000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ47444-244-2-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1−3i32111-2-21−1+3i32−1−3i321111002222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i30000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i3200000000000000
χ48444-244-2-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1−3i32111-2-21−1+3i32−1−3i32111100-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i300000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ49444-2-4-4-222-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-22-1-11+3i321+3i321−3i321−3i3211−1−3i32−1+3i3211122-11+3i321−3i32-1-1-1-1002-22-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i30000000-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i3200000000000000
χ50444-2-4-4-222-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-22-1-11+3i321+3i321−3i321−3i3211−1−3i32−1+3i3211122-11+3i321−3i32-1-1-1-100-22-221+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i300000001−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i3200000000000000
χ51444-2-4-4-222-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-22-1-11−3i321−3i321+3i321+3i3211−1+3i32−1−3i3211122-11−3i321+3i32-1-1-1-1002-22-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i30000000-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i3200000000000000
χ52444-2-4-4-222-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-22-1-11−3i321−3i321+3i321+3i3211−1+3i32−1−3i3211122-11−3i321+3i32-1-1-1-100-22-221−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i300000001−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i3200000000000000
χ5344-444-44441-2-2-2-4-11-2-2-2-1-4-2-2-2-2-2-21222-1-111-122211-1-10000000000000000000000000000000002i−2i2i−2i00−ii−ii0000
χ5444-444-44441-2-2-2-4-11-2-2-2-1-4-2-2-2-2-2-21222-1-111-122211-1-1000000000000000000000000000000000−2i2i−2i2i00i−ii−i0000
χ5544-444-4444-2111-42-21112-4111111-2-1-1-122-2-22-1-1-1-2-222002-2-2222-2-2-2-2220000000-1-1-1111111-1-1-100000000000000
χ5644-444-4444-2111-42-21112-4111111-2-1-1-122-2-22-1-1-1-2-22200-222-2-2-22222-2-20000000111-1-1-1-1-1-111100000000000000
χ5744-44-444-4-41-2-2-2-4-11-2-2-2-142222221222-1-11-11-2-2-2-1-1110000000000000000000000000000000002i−2i−2i2i00−iii−i0000
χ5844-44-444-4-41-2-2-2-4-11-2-2-2-142222221222-1-11-11-2-2-2-1-111000000000000000000000000000000000−2i2i2i−2i00i−i−ii0000
χ5944-44-444-4-4-2111-42-211124-1-1-1-1-1-1-2-1-1-122-22-211122-2-20022-2-22222-2-2-2-20000000-1-1-1-1-1-111111100000000000000
χ6044-44-444-4-4-2111-42-211124-1-1-1-1-1-1-2-1-1-122-22-211122-2-200-2-222-2-2-2-222220000000111111-1-1-1-1-1-100000000000000
χ6144-4-24-4-2-2-2-21−1−3i32−1+3i3222-21−1−3i32−1+3i322211−1−3i32−1−3i32−1+3i32−1+3i321-11+3i321−3i32-1-11-22-11+3i321−3i3211-1-1002-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i30000000-11+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i3200000000000000
χ6244-4-24-4-2-2-2-21−1−3i32−1+3i3222-21−1−3i32−1+3i322211−1−3i32−1−3i32−1+3i32−1+3i321-11+3i321−3i32-1-11-22-11+3i321−3i3211-1-100-222-21+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i300000001−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i3200000000000000
χ6344-4-24-4-2-2-2-21−1+3i32−1−3i3222-21−1+3i32−1−3i322211−1+3i32−1+3i32−1−3i32−1−3i321-11−3i321+3i32-1-11-22-11−3i321+3i3211-1-1002-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i30000000-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i3200000000000000
χ6444-4-24-4-2-2-2-21−1+3i32−1−3i3222-21−1+3i32−1−3i322211−1+3i32−1+3i32−1−3i32−1−3i321-11−3i321+3i32-1-11-22-11−3i321+3i3211-1-100-222-21−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i300000001−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i3200000000000000
χ6544-4-2-44-222-21−1−3i32−1+3i3222-21−1−3i32−1+3i322-2-1-11+3i321+3i321−3i321−3i321-11+3i321−3i32-1-112-21−1−3i32−1+3i32-1-1110022-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ6644-4-2-44-222-21−1−3i32−1+3i3222-21−1−3i32−1+3i322-2-1-11+3i321+3i321−3i321−3i321-11+3i321−3i32-1-112-21−1−3i32−1+3i32-1-11100-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i300000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i3200000000000000
χ6744-4-2-44-222-21−1+3i32−1−3i3222-21−1+3i32−1−3i322-2-1-11−3i321−3i321+3i321+3i321-11−3i321+3i32-1-112-21−1+3i32−1−3i32-1-1110022-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i30000000-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ6844-4-2-44-222-21−1+3i32−1−3i3222-21−1+3i32−1−3i322-2-1-11−3i321−3i321+3i321+3i321-11−3i321+3i32-1-112-21−1+3i32−1−3i32-1-11100-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i300000001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i3200000000000000
χ694-40400-400444400-4-4-4-400000000400000-40000000004i−4i000000000000000004i−4i00000000000000000000000000
χ704-40400-400444400-4-4-4-400000000400000-4000000000−4i4i00000000000000000−4i4i00000000000000000000000000
χ714-40-200223−2344-2-200-4-422000023−2323−23-20000020000023−23004i−4i000000000000000−2i32i3−2i2i00000000000000000000000000
χ724-40-200223−2344-2-200-4-422000023−2323−23-20000020000023−2300−4i4i0000000000000002i3−2i32i−2i00000000000000000000000000
χ734-40-2002−232344-2-200-4-4220000−2323−2323-200000200000−2323004i−4i0000000000000002i3−2i3−2i2i00000000000000000000000000
χ744-40-2002−232344-2-200-4-4220000−2323−2323-200000200000−232300−4i4i000000000000000−2i32i32i−2i00000000000000000000000000
χ75888-488-4-4-42-422-422-4222-4-4-42222-1-422-1-1-122-422-1-1-1-100000000000000000000000000000000000000000000000
χ76888-4-8-8-4442-422-422-4222444-2-2-2-2-1-422-1-1-1-2-24-2-2111100000000000000000000000000000000000000000000000
χ7788-8-48-8-4-4-42-4224-22-422-24-4-42222-14-2-211-12-24-2-2-1-11100000000000000000000000000000000000000000000000
χ7888-8-4-88-4442-4224-22-422-2-444-2-2-2-2-14-2-211-1-22-42211-1-100000000000000000000000000000000000000000000000
χ798-80800-8002-4-4-406-2444-6000000020006-6-200000000000000000000000000000000000000000000000000000000
χ808-80800-8002-4-4-40-6-2444600000002000-66-200000000000000000000000000000000000000000000000000000000
χ818-80800-800-4222004-2-2-2006i−6i6i−6i−6i6i-400000400000000000000000000000000000000000000000000000000000000
χ828-80800-800-4222004-2-2-200−6i6i−6i6i6i−6i-400000400000000000000000000000000000000000000000000000000000000
χ838-80-400443−432-42206-24-2-2-6000−2323−2323-1000-331000003−333−3300000000000000000000000000000000000000000000000
χ848-80-400443−432-4220-6-24-2-26000−2323−2323-10003-31000003−3−333300000000000000000000000000000000000000000000000
χ858-80-400443−43-42−1−3i3−1+3i3004-21+3i31−3i3006i−6i2ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ11200000-200000−23230000000000000000000000000000000000000000000000000
χ868-80-400443−43-42−1+3i3−1−3i3004-21−3i31+3i300−6i6i−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ11200000-200000−23230000000000000000000000000000000000000000000000000
χ878-80-4004−43432-42206-24-2-2-600023−2323−23-1000-33100000−33−333300000000000000000000000000000000000000000000000
χ888-80-4004−43432-4220-6-24-2-2600023−2323−23-10003-3100000−3333−3300000000000000000000000000000000000000000000000
χ898-80-4004−4343-42−1−3i3−1+3i3004-21+3i31−3i300−6i6i−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ11200000-20000023−230000000000000000000000000000000000000000000000000
χ908-80-4004−4343-42−1+3i3−1−3i3004-21−3i31+3i3006i−6i4ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ11200000-20000023−230000000000000000000000000000000000000000000000000

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