Finite Group Databasebeta

← Group #13167045

Character table — Group #13167045

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222224444444444444444448888888888888888991212121212121212121212121818181818181824242424242424242424242436363636363672727272108108108108
order12234466633336666666666121212123666612121212121212121212122244441212121212121212244666612121212121212121212121288881212242424244444
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
χ51111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1ii−i−i11ii−i−iii−i−i
χ61111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1−i−iii11−i−iii−i−iii
χ71111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1111111ii−i−i11ii−i−i−i−iii
χ81111-1-111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1111111−i−iii11−i−iiiii−i−i
χ911-111-1-1-111111-1-1-1-1-1-111111-1-1-11-1-1-111111-1-1-111-1-1-1-11-11-111-1-111-1-111-111-1-1111-1-1-1111-1-1-1i−ii−i1-1i−ii−ii−ii−i
χ1011-111-1-1-111111-1-1-1-1-1-111111-1-1-11-1-1-111111-1-1-111-1-1-1-11-11-111-1-111-1-111-111-1-1111-1-1-1111-1-1-1−ii−ii1-1−ii−ii−ii−ii
χ1111-111-1-1-111111-1-1-1-1-1-111111-1-1-11-1-1-111111-1-1-111-1-1-1-1-11-11-1-111-1-11111-111-1-1-1-1-1111-1-1-1111i−ii−i1-1i−ii−i−ii−ii
χ1211-111-1-1-111111-1-1-1-1-1-111111-1-1-11-1-1-111111-1-1-111-1-1-1-1-11-11-1-111-1-11111-111-1-1-1-1-1111-1-1-1111−ii−ii1-1−ii−iii−ii−i
χ1311-11-11-1-111111-1-1-1-1-1-11111-11111-1-1-11-1-1-1-1111-1-111111-1-1111-1-1-1-111-11-1-1-111111-1-1-1-1-1-11111-1-111-11-1-111-1-11
χ1411-11-11-1-111111-1-1-1-1-1-11111-11111-1-1-11-1-1-1-1111-1-111111-1-1111-1-1-1-111-11-1-1-111111-1-1-1-1-1-1111-111-11-1-111-1-111-1
χ1511-11-11-1-111111-1-1-1-1-1-11111-11111-1-1-11-1-1-1-1111-1-11111-111-1-1-11111-1-1-11-1-1-111-1-1-1111111-1-1-11-1-111-11-1-11-111-1
χ1611-11-11-1-111111-1-1-1-1-1-11111-11111-1-1-11-1-1-1-1111-1-11111-111-1-1-11111-1-1-11-1-1-111-1-1-1111111-1-1-1-111-11-1-111-11-1-11
χ172222222222222222222222222222222222222222222-2-2000000000000-2-2-2-2-2-2-20000000000000000-2-200000000
χ182222-2-222222222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2220000000000002-2-222220000000000000000-2-200000000
χ19222-122-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-122-1-12-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-12-1-12-1-10000-1-100000000
χ20222-122-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-122-1-12-1-1-1-1-1-122-2-2-2-211111111222-1-1-1-1-211-211-211-2110000-1-100000000
χ21222-122-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-122-1-12-1-1-1-1-1-1-2-20000−i3i3−i3i3−i3i3−i3i3-2-2-211110−i3i30−i3i30−i3i30−i3i300001100000000
χ22222-122-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-122-1-12-1-1-1-1-1-1-2-20000i3−i3i3−i3i3−i3i3−i3-2-2-211110i3−i30i3−i30i3−i30i3−i300001100000000
χ23222-1-2-2-1-1-122-1-122-1-1-1-122-1-111-2-2-12-1-1-1-2-211-2111111220000−i3i3−i3i3i3−i3i3−i32-2-2-1-1-1-10−i3i30−i3i30i3−i30i3−i300001100000000
χ24222-1-2-2-1-1-122-1-122-1-1-1-122-1-111-2-2-12-1-1-1-2-211-2111111220000i3−i3i3−i3−i3i3−i3i32-2-2-1-1-1-10i3−i30i3−i30−i3i30−i3i300001100000000
χ25222-1-2-2-1-1-122-1-122-1-1-1-122-1-111-2-2-12-1-1-1-2-211-2111111-2-222-2-2-1-1-1-11111-22211112-1-12-1-1-211-2110000-1-100000000
χ26222-1-2-2-1-1-122-1-122-1-1-1-122-1-111-2-2-12-1-1-1-2-211-2111111-2-2-2-2221111-1-1-1-1-2221111-211-2112-1-12-1-10000-1-100000000
χ2722-222-2-2-222222-2-2-2-2-2-222222-2-2-22-2-2-222222-2-2-222-2-222000000000000-2-22-2-2220000000000000000-2200000000
χ2822-22-22-2-222222-2-2-2-2-2-22222-22222-2-2-22-2-2-2-2222-2-222-2-20000000000002-2222-2-20000000000000000-2200000000
χ2922-2-12-211-122-1-1-2-2111122-1-1-11-2-2-1-211-122-1-1-211-1-111220000−i3i3i3−i3−i3i3i3−i3-2-2211-1-10−i3i30i3−i30−i3i30i3−i300001-100000000
χ3022-2-12-211-122-1-1-2-2111122-1-1-11-2-2-1-211-122-1-1-211-1-111220000i3−i3−i3i3i3−i3−i3i3-2-2211-1-10i3−i30−i3i30i3−i30−i3i300001-100000000
χ3122-2-12-211-122-1-1-2-2111122-1-1-11-2-2-1-211-122-1-1-211-1-111-2-22-22-2-1-111-1-11122-2-1-1112-1-1-2112-1-1-2110000-1100000000
χ3222-2-12-211-122-1-1-2-2111122-1-1-11-2-2-1-211-122-1-1-211-1-111-2-2-22-2211-1-111-1-122-2-1-111-2112-1-1-2112-1-10000-1100000000
χ3322-2-1-2211-122-1-1-2-2111122-1-11-122-1-211-1-2-2112-1-111-1-1222-2-22-1-11111-1-1-22-211-1-12-1-1-211-2112-1-10000-1100000000
χ3422-2-1-2211-122-1-1-2-2111122-1-11-122-1-211-1-2-2112-1-111-1-122-222-211-1-1-1-111-22-211-1-1-2112-1-12-1-1-2110000-1100000000
χ3522-2-1-2211-122-1-1-2-2111122-1-11-122-1-211-1-2-2112-1-111-1-1-2-20000−i3i3i3−i3i3−i3−i3i32-22-1-1110−i3i30i3−i30i3−i30−i3i300001-100000000
χ3622-2-1-2211-122-1-1-2-2111122-1-11-122-1-211-1-2-2112-1-111-1-1-2-20000i3−i3−i3i3−i3i3i3−i32-22-1-1110i3−i30−i3i30−i3i30i3−i300001-100000000
χ374444444441-211111111-211144-2-2-2-2-2-2-2-2111111-2-2-2-2002222222222220000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ384444444441-211111111-211144-2-2-2-2-2-2-2-2111111-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-2000000011111111111100000000000000
χ39444444444-21-2-2-2-2-2-2-2-21-2-2-24411111111-2-2-2-2-2-21111000000000000000000000000000000000222200-1-1-1-10000
χ40444444444-21-2-2-2-2-2-2-2-21-2-2-24411111111-2-2-2-2-2-21111000000000000000000000000000000000-2-2-2-20011110000
χ414444-4-44441-211111111-2111-4-422-2-2-2-2-22-1-1-1-1-1-122220022-2-22222-2-2-2-20000000-1-1-1-1-1-111111100000000000000
χ424444-4-44441-211111111-2111-4-422-2-2-2-2-22-1-1-1-1-1-1222200-2-222-2-2-2-222220000000111111-1-1-1-1-1-100000000000000
χ434444-4-4444-21-2-2-2-2-2-2-2-21-2-2-2-4-4-1-111111-1222222-1-1-1-10000000000000000000000000000000002i2i−2i−2i00−i−iii0000
χ444444-4-4444-21-2-2-2-2-2-2-2-21-2-2-2-4-4-1-111111-1222222-1-1-1-1000000000000000000000000000000000−2i−2i2i2i00ii−i−i0000
χ45444-244-2-2-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-21-2111-21−1−3i32−1+3i321−1−3i32−1+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
χ46444-244-2-2-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-21-2111-21−1−3i32−1+3i321−1−3i32−1+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
χ47444-244-2-2-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-21-2111-21−1+3i32−1−3i321−1+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
χ48444-244-2-2-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-21-2111-21−1+3i32−1−3i321−1+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
χ49444-2-4-4-2-2-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i3222221-21112-11+3i321−3i32-11+3i321−3i32-1-1-1-10022-2-2−1−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
χ50444-2-4-4-2-2-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i3222221-21112-11+3i321−3i32-11+3i321−3i32-1-1-1-100-2-2221+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
χ51444-2-4-4-2-2-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i3222221-21112-11−3i321+3i32-11−3i321+3i32-1-1-1-10022-2-2−1+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
χ52444-2-4-4-2-2-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i3222221-21112-11−3i321+3i32-11−3i321+3i32-1-1-1-100-2-2221−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
χ5344-444-4-4-441-211-1-1-1-1-1-1-21114-422-2222-2-2111-1-1-1-2-222002-22-222-2-222-2-20000000-1-1-1111-1-1-111100000000000000
χ5444-444-4-4-441-211-1-1-1-1-1-1-21114-422-2222-2-2111-1-1-1-2-22200-22-22-2-222-2-2220000000111-1-1-1111-1-1-100000000000000
χ5544-444-4-4-44-21-2-22222221-2-2-24-4-1-11-1-1-111-2-2-222211-1-10000000000000000000000000000000002i−2i2i−2i00−ii−ii0000
χ5644-444-4-4-44-21-2-22222221-2-2-24-4-1-11-1-1-111-2-2-222211-1-1000000000000000000000000000000000−2i2i−2i2i00i−ii−i0000
χ5744-44-44-4-441-211-1-1-1-1-1-1-2111-44-2-2-2222-22-1-1-111122-2-2002-2-2222-2-2-2-2220000000-1-1-1111111-1-1-100000000000000
χ5844-44-44-4-441-211-1-1-1-1-1-1-2111-44-2-2-2222-22-1-1-111122-2-200-222-2-2-22222-2-20000000111-1-1-1-1-1-111100000000000000
χ5944-44-44-4-44-21-2-22222221-2-2-2-44111-1-1-11-1222-2-2-2-1-1110000000000000000000000000000000002-2-2200-111-10000
χ6044-44-44-4-44-21-2-22222221-2-2-2-44111-1-1-11-1222-2-2-2-1-111000000000000000000000000000000000-222-2001-1-110000
χ6144-4-24-422-21-2−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-21−1−3i32−1+3i32-222212-1-11-21−1−3i32−1+3i32-11+3i321−3i3211-1-1002-22-2−1−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
χ6244-4-24-422-21-2−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-21−1−3i32−1+3i32-222212-1-11-21−1−3i32−1+3i32-11+3i321−3i3211-1-100-22-221+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
χ6344-4-24-422-21-2−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i32-222212-1-11-21−1+3i32−1−3i32-11−3i321+3i3211-1-1002-22-2−1+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
χ6444-4-24-422-21-2−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i32-222212-1-11-21−1+3i32−1−3i32-11−3i321+3i3211-1-100-22-221−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
χ6544-4-2-4422-21-2−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-21−1−3i32−1+3i322-2-2-212-1-112-11+3i321−3i321−1−3i32−1+3i32-1-111002-2-22−1−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
χ6644-4-2-4422-21-2−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-21−1−3i32−1+3i322-2-2-212-1-112-11+3i321−3i321−1−3i32−1+3i32-1-11100-222-21+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
χ6744-4-2-4422-21-2−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i322-2-2-212-1-112-11−3i321+3i321−1+3i32−1−3i32-1-111002-2-22−1+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
χ6844-4-2-4422-21-2−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i322-2-2-212-1-112-11−3i321+3i321−1+3i32−1−3i32-1-11100-222-21−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
χ694-4040000-44444000000-4-4-4-400004000-4000000000004-4000000000000000004-400000000000000000000000000
χ704-4040000-44444000000-4-4-4-400004000-400000000000-4400000000000000000-4400000000000000000000000000
χ714-40-200−2i32i3244-2-200−2i32i3−2i32i3-4-4220000-20−2i32i32000000000004-4000000000000000−2i32i3-2200000000000000000000000000
χ724-40-200−2i32i3244-2-200−2i32i3−2i32i3-4-4220000-20−2i32i3200000000000-440000000000000002i3−2i32-200000000000000000000000000
χ734-40-2002i3−2i3244-2-2002i3−2i32i3−2i3-4-4220000-202i3−2i32000000000004-40000000000000002i3−2i3-2200000000000000000000000000
χ744-40-2002i3−2i3244-2-2002i3−2i32i3−2i3-4-4220000-202i3−2i3200000000000-44000000000000000−2i32i32-200000000000000000000000000
χ75888-488-4-4-4-4222-4-422222-422-4-422-12-1-1-12-422-422-1-1-1-100000000000000000000000000000000000000000000000
χ76888-4-8-8-4-4-4-4222-4-422222-42244-2-2-12-1-1-1-24-2-24-2-2111100000000000000000000000000000000000000000000000
χ7788-8-48-844-4-422244-2-2-2-22-422-44-2-2-1-211-12-4224-2-2-1-11100000000000000000000000000000000000000000000000
χ7888-8-4-8844-4-422244-2-2-2-22-4224-422-1-211-1-24-2-2-42211-1-100000000000000000000000000000000000000000000000
χ798-8080000-82-4226-66-6-664-2-2-20000-400040000000000000000000000000000000000000000000000000000000000
χ808-8080000-82-422-66-666-64-2-2-20000-400040000000000000000000000000000000000000000000000000000000000
χ818-8080000-8-42-4-4000000-2444006i−6i2000-20000000006i−6i00000000000000000000000000000000000000000000000
χ828-8080000-8-42-4-4000000-244400−6i6i2000-2000000000−6i6i00000000000000000000000000000000000000000000000
χ838-80-400−4i34i342-4−1−3i3−1+3i36-6−3−i33+i33−i3−3+i34-21+3i31−3i30000202i3−2i3-20000000000000000000000000000000000000000000000000000000000
χ848-80-400−4i34i342-4−1+3i3−1−3i3-663−i3−3+i3−3−i33+i34-21−3i31+3i30000202i3−2i3-20000000000000000000000000000000000000000000000000000000000
χ858-80-400−4i34i34-4222002i3−2i32i3−2i3-24-2-2006i−6i-10−i3i31000000033−33−3i3i00000000000000000000000000000000000000000000000
χ868-80-400−4i34i34-4222002i3−2i32i3−2i3-24-2-200−6i6i-10−i3i310000000−33333i−3i00000000000000000000000000000000000000000000000
χ878-80-4004i3−4i342-4−1−3i3−1+3i3-663+i3−3−i3−3+i33−i34-21+3i31−3i3000020−2i32i3-20000000000000000000000000000000000000000000000000000000000
χ888-80-4004i3−4i342-4−1+3i3−1−3i36-6−3+i33−i33+i3−3−i34-21−3i31+3i3000020−2i32i3-20000000000000000000000000000000000000000000000000000000000
χ898-80-4004i3−4i34-422200−2i32i3−2i32i3-24-2-2006i−6i-10i3−i310000000−3333−3i3i00000000000000000000000000000000000000000000000
χ908-80-4004i3−4i34-422200−2i32i3−2i32i3-24-2-200−6i6i-10i3−i31000000033−333i−3i00000000000000000000000000000000000000000000000

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