Finite Group Databasebeta

← Group #13167300

Character table — Group #13167300

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222224444444444444444448888888888888888991212121212121212121212121818181818181824242424242424242424242436363636363672727272108108108108
order12222366633336666666666666636666666666666664422446666121212124441212121266666612121212121244441212121212128888
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
χ5111-1-111111111-1-11111111111-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1ii−i−i11ii−i−iii−i−i
χ6111-1-111111111-1-11111111111-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1−i−iii11−i−iii−i−iii
χ7111-1-111111111-1-11111111111-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111ii−i−i11ii−i−i−i−iii
χ8111-1-111111111-1-11111111111-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111−i−iii11−i−iiiii−i−i
χ911-11-11-1-1111111-11-1-1-1-1-1-1111-1-11-11111-1-1-11-1-111-1-1-1-11-11-111-1-111-1-11-1111-1-1111-1-1-1111-1-1-1i−ii−i1-1i−ii−ii−ii−i
χ1011-11-11-1-1111111-11-1-1-1-1-1-1111-1-11-11111-1-1-11-1-111-1-1-1-11-11-111-1-111-1-11-1111-1-1111-1-1-1111-1-1-1−ii−ii1-1−ii−ii−ii−ii
χ1111-11-11-1-1111111-11-1-1-1-1-1-1111-1-11-11111-1-1-11-1-111-1-1-1-1-11-11-1-111-1-1111-1111-1-1-1-1-1111-1-1-1111i−ii−i1-1i−ii−i−ii−ii
χ1211-11-11-1-1111111-11-1-1-1-1-1-1111-1-11-11111-1-1-11-1-111-1-1-1-1-11-11-1-111-1-1111-1111-1-1-1-1-1111-1-1-1111−ii−ii1-1−ii−iii−ii−i
χ1311-1-111-1-111111-111-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-11111-1-111-11-1-111-1-11
χ1411-1-111-1-111111-111-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1111-111-11-1-111-1-111-1
χ1511-1-111-1-111111-111-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-11-1-1-1-111-1-1-1111111-1-1-11-1-111-11-1-11-111-1
χ1611-1-111-1-111111-111-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-11-1-1-1-111-1-1-1111111-1-1-1-111-11-1-111-11-1-11
χ172222222222222222222222222222222222222222222-2-2000000000000-2-2-2-2-2-2-20000000000000000-2-200000000
χ1822222-1-1-1-122-1-1-1-1222-1-1-1-12-1-122-1222-1-12-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-12-1-12-1-10000-1-100000000
χ1922222-1-1-1-122-1-1-1-1222-1-1-1-12-1-122-1222-1-12-1-1-1-1-1-1-1-1-122-2-2-2-211111111222-1-1-1-1-211-211-211-2110000-1-100000000
χ2022222-1-1-1-122-1-1-1-1222-1-1-1-12-1-122-1222-1-12-1-1-1-1-1-1-1-1-1-2-20000−i3i3−i3i3−i3i3−i3i3-2-2-211110−i3i30−i3i30−i3i30−i3i300001100000000
χ2122222-1-1-1-122-1-1-1-1222-1-1-1-12-1-122-1222-1-12-1-1-1-1-1-1-1-1-1-2-20000i3−i3i3−i3i3−i3i3−i3-2-2-211110i3−i30i3−i30i3−i30i3−i300001100000000
χ22222-2-222222222-2-22222222222-2-222-2-2-2-2-2-2-2222-2-2-2-222000000000000-2-2222220000000000000000-2-200000000
χ23222-2-2-1-1-1-122-1-111222-1-1-1-12-1-1-2-2-12-2-211-211-1-1-11111220000−i3i3−i3i3i3−i3i3−i3-2-22-1-1-1-10−i3i30−i3i30i3−i30i3−i300001100000000
χ24222-2-2-1-1-1-122-1-111222-1-1-1-12-1-1-2-2-12-2-211-211-1-1-11111220000i3−i3i3−i3−i3i3−i3i3-2-22-1-1-1-10i3−i30i3−i30−i3i30−i3i300001100000000
χ25222-2-2-1-1-1-122-1-111222-1-1-1-12-1-1-2-2-12-2-211-211-1-1-11111-2-222-2-2-1-1-1-1111122-211112-1-12-1-1-211-2110000-1-100000000
χ26222-2-2-1-1-1-122-1-111222-1-1-1-12-1-1-2-2-12-2-211-211-1-1-11111-2-2-2-2221111-1-1-1-122-21111-211-2112-1-12-1-10000-1-100000000
χ2722-22-22-2-2222222-22-2-2-2-2-2-2222-2-22-22222-2-2-22-2-222-2-222000000000000-22-2-2-2220000000000000000-2200000000
χ2822-22-2-111-122-1-1-112-2-211112-1-1-2-2-1-222-1-1-211-111-1-111220000−i3i3i3−i3−i3i3i3−i3-22-211-1-10−i3i30i3−i30−i3i30i3−i300001-100000000
χ2922-22-2-111-122-1-1-112-2-211112-1-1-2-2-1-222-1-1-211-111-1-111220000i3−i3−i3i3i3−i3−i3i3-22-211-1-10i3−i30−i3i30i3−i30−i3i300001-100000000
χ3022-22-2-111-122-1-1-112-2-211112-1-1-2-2-1-222-1-1-211-111-1-111-2-22-22-2-1-111-1-1112-22-1-1112-1-1-2112-1-1-2110000-1100000000
χ3122-22-2-111-122-1-1-112-2-211112-1-1-2-2-1-222-1-1-211-111-1-111-2-2-22-2211-1-111-1-12-22-1-111-2112-1-1-2112-1-10000-1100000000
χ3222-2-222-2-222222-222-2-2-2-2-2-2222222-2-2-2-2-22222-2-2-2-222-2-2000000000000-22222-2-20000000000000000-2200000000
χ3322-2-22-111-122-1-11-12-2-211112-1-122-1-2-2-2112-1-1-11111-1-1222-2-22-1-11111-1-12-2-211-1-12-1-1-211-2112-1-10000-1100000000
χ3422-2-22-111-122-1-11-12-2-211112-1-122-1-2-2-2112-1-1-11111-1-122-222-211-1-1-1-1112-2-211-1-1-2112-1-12-1-1-2110000-1100000000
χ3522-2-22-111-122-1-11-12-2-211112-1-122-1-2-2-2112-1-1-11111-1-1-2-20000−i3i3i3−i3i3−i3−i3i3-222-1-1110−i3i30i3−i30i3−i30−i3i300001-100000000
χ3622-2-22-111-122-1-11-12-2-211112-1-122-1-2-2-2112-1-1-11111-1-1-2-20000i3−i3−i3i3−i3i3i3−i3-222-1-1110i3−i30−i3i30−i3i30i3−i300001-100000000
χ374444444441-2-2-2441-2-2-2-2-2-2-2-2-211111-2-2-2-2-2-21111111000000000000000000000000000000000222200-1-1-1-10000
χ384444444441-2-2-2441-2-2-2-2-2-2-2-2-211111-2-2-2-2-2-21111111000000000000000000000000000000000-2-2-2-20011110000
χ39444444444-211144-2111111111-2-2-2-2-2111111-2-2-2-2-2-2-2002222222222220000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ40444444444-211144-2111111111-2-2-2-2-2111111-2-2-2-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-2000000011111111111100000000000000
χ4144444-2-2-2-2-21−1−3i32−1+3i32-2-2-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-21-2-21−1−3i32−1+3i321−1−3i32−1+3i321111111002222−1−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
χ4244444-2-2-2-2-21−1−3i32−1+3i32-2-2-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-21-2-21−1−3i32−1+3i321−1−3i32−1+3i32111111100-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i300000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ4344444-2-2-2-2-21−1+3i32−1−3i32-2-2-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-2-21-2-21−1+3i32−1−3i321−1+3i32−1−3i321111111002222−1+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
χ4444444-2-2-2-2-21−1+3i32−1−3i32-2-2-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-2-21-2-21−1+3i32−1−3i321−1+3i32−1−3i32111111100-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i300000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ45444-4-444441-2-2-2-4-41-2-2-2-2-2-2-2-2-2-1-111-1222222111-1-1-1-10000000000000000000000000000000002i2i−2i−2i00−i−iii0000
χ46444-4-444441-2-2-2-4-41-2-2-2-2-2-2-2-2-2-1-111-1222222111-1-1-1-1000000000000000000000000000000000−2i−2i2i2i00ii−i−i0000
χ47444-4-44444-2111-4-4-211111111122-2-22-1-1-1-1-1-1-2-2-222220022-2-22222-2-2-2-20000000-1-1-1-1-1-111111100000000000000
χ48444-4-44444-2111-4-4-211111111122-2-22-1-1-1-1-1-1-2-2-2222200-2-222-2-2-2-222220000000111111-1-1-1-1-1-100000000000000
χ49444-4-4-2-2-2-2-21−1−3i32−1+3i3222-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32221-22-11+3i321−3i32-11+3i321−3i32111-1-1-1-10022-2-2−1−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
χ50444-4-4-2-2-2-2-21−1−3i32−1+3i3222-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32221-22-11+3i321−3i32-11+3i321−3i32111-1-1-1-100-2-2221+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
χ51444-4-4-2-2-2-2-21−1+3i32−1−3i3222-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32221-22-11−3i321+3i32-11−3i321+3i32111-1-1-1-10022-2-2−1+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
χ52444-4-4-2-2-2-2-21−1+3i32−1−3i3222-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32221-22-11−3i321+3i32-11−3i321+3i32111-1-1-1-100-2-2221−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
χ5344-44-44-4-441-2-2-24-41222222-2-2-2-1-11-11-2-2-22221-1-111-1-10000000000000000000000000000000002i−2i2i−2i00−ii−ii0000
χ5444-44-44-4-441-2-2-24-41222222-2-2-2-1-11-11-2-2-22221-1-111-1-1000000000000000000000000000000000−2i2i−2i2i00i−ii−i0000
χ5544-44-44-4-44-21114-4-2-1-1-1-1-1-111122-22-2111-1-1-1-222-2-222002-22-222-2-222-2-20000000-1-1-1111-1-1-111100000000000000
χ5644-44-44-4-44-21114-4-2-1-1-1-1-1-111122-22-2111-1-1-1-222-2-22200-22-22-2-222-2-2220000000111-1-1-1111-1-1-100000000000000
χ5744-44-4-222-2-21−1−3i32−1+3i32-22-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i322212-21−1−3i32−1+3i32-11+3i321−3i321-1-111-1-1002-22-2−1−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
χ5844-44-4-222-2-21−1−3i32−1+3i32-22-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i322212-21−1−3i32−1+3i32-11+3i321−3i321-1-111-1-100-22-221+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
χ5944-44-4-222-2-21−1+3i32−1−3i32-22-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i322212-21−1+3i32−1−3i32-11−3i321+3i321-1-111-1-1002-22-2−1+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
χ6044-44-4-222-2-21−1+3i32−1−3i32-22-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i322212-21−1+3i32−1−3i32-11−3i321+3i321-1-111-1-100-22-221−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
χ6144-4-444-4-441-2-2-2-441222222-2-2-2111-1-1222-2-2-21-1-1-1-1110000000000000000000000000000000002-2-2200-111-10000
χ6244-4-444-4-441-2-2-2-441222222-2-2-2111-1-1222-2-2-21-1-1-1-111000000000000000000000000000000000-222-2001-1-110000
χ6344-4-444-4-44-2111-44-2-1-1-1-1-1-1111-2-2-222-1-1-1111-22222-2-2002-2-2222-2-2-2-2220000000-1-1-1111111-1-1-100000000000000
χ6444-4-444-4-44-2111-44-2-1-1-1-1-1-1111-2-2-222-1-1-1111-22222-2-200-222-2-2-22222-2-20000000111-1-1-1-1-1-111100000000000000
χ6544-4-44-222-2-21−1−3i32−1+3i322-2-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-2-2122-11+3i321−3i321−1−3i32−1+3i321-1-1-1-111002-2-22−1−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
χ6644-4-44-222-2-21−1−3i32−1+3i322-2-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-2-2122-11+3i321−3i321−1−3i32−1+3i321-1-1-1-11100-222-21+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
χ6744-4-44-222-2-21−1+3i32−1−3i322-2-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-2-2122-11−3i321+3i321−1+3i32−1−3i321-1-1-1-111002-2-22−1+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
χ6844-4-44-222-2-21−1+3i32−1−3i322-2-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-2-2122-11−3i321+3i321−1+3i32−1−3i321-1-1-1-11100-222-21−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
χ694-4000400-4444400-4000000-4-4-400400000000-40000004i−4i000000000000000004i−4i00000000000000000000000000
χ704-4000400-4444400-4000000-4-4-400400000000-4000000−4i4i00000000000000000−4i4i00000000000000000000000000
χ714-4000-2−2i32i3244-2-200-400−2i32i3−2i32i3-42200-2000000002−2i32i300004i−4i00000000000000023−23−2i2i00000000000000000000000000
χ724-4000-2−2i32i3244-2-200-400−2i32i3−2i32i3-42200-2000000002−2i32i30000−4i4i000000000000000−23232i−2i00000000000000000000000000
χ734-4000-22i3−2i3244-2-200-4002i3−2i32i3−2i3-42200-20000000022i3−2i300004i−4i000000000000000−2323−2i2i00000000000000000000000000
χ744-4000-22i3−2i3244-2-200-4002i3−2i32i3−2i3-42200-20000000022i3−2i30000−4i4i00000000000000023−232i−2i00000000000000000000000000
χ7588888-4-4-4-42-422-4-42-4-42222-42222-122-422-422-1-1-1-1-1-1-100000000000000000000000000000000000000000000000
χ76888-8-8-4-4-4-42-422442-4-42222-422-2-2-12-24-2-24-2-2-1-1-1111100000000000000000000000000000000000000000000000
χ7788-88-8-444-42-422-44244-2-2-2-2-422-2-2-1-22-4224-2-2-111-1-11100000000000000000000000000000000000000000000000
χ7888-8-88-444-42-4224-4244-2-2-2-2-42222-1-2-24-2-2-422-11111-1-100000000000000000000000000000000000000000000000
χ798-8000800-82-4-4-400-20000004446-6200000000-200006-600000000000000000000000000000000000000000000000
χ808-8000800-82-4-4-400-2000000444-66200000000-20000-6600000000000000000000000000000000000000000000000
χ818-8000800-8-42220046-66-6-66-2-2-200-400000000400000000000000000000000000000000000000000000000000000
χ828-8000800-8-4222004-66-666-6-2-2-200-400000000400000000000000000000000000000000000000000000000000000
χ838-8000-4−4i34i342-42200-2002i3−2i32i3−2i34-2-26-6-1000000001−i3i3−3i33i3-3300000000000000000000000000000000000000000000000
χ848-8000-4−4i34i342-42200-2002i3−2i32i3−2i34-2-2-66-1000000001−i3i33i3−3i33-300000000000000000000000000000000000000000000000
χ858-8000-4−4i34i34-42−1−3i3−1+3i30046-6−3−i33+i33−i3−3+i3-21+3i31−3i300200000000-22i3−2i3000000000000000000000000000000000000000000000000000
χ868-8000-4−4i34i34-42−1+3i3−1−3i3004-663−i3−3+i3−3−i33+i3-21−3i31+3i300200000000-22i3−2i3000000000000000000000000000000000000000000000000000
χ878-8000-44i3−4i342-42200-200−2i32i3−2i32i34-2-26-6-1000000001i3−i33i3−3i3-3300000000000000000000000000000000000000000000000
χ888-8000-44i3−4i342-42200-200−2i32i3−2i32i34-2-2-66-1000000001i3−i3−3i33i33-300000000000000000000000000000000000000000000000
χ898-8000-44i3−4i34-42−1−3i3−1+3i3004-663+i3−3−i3−3+i33−i3-21+3i31−3i300200000000-2−2i32i3000000000000000000000000000000000000000000000000000
χ908-8000-44i3−4i34-42−1+3i3−1−3i30046-6−3+i33−i33+i3−3−i3-21−3i31+3i300200000000-2−2i32i3000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).